Solution of inverse heat conduction problem.
\r\n\tSolar radiation is the radiant energy that originated from the sun in the form of electromagnetic radiation at various wavelengths. Solar radiation is the source of renewable energy and can be captured and converted into various forms of energy (e.g. electricity and heat) using different technologies.
\r\n\tA very vast amount of solar energy reaches the atmosphere and surface of the earth and solar energy has been used for heating purposes for a very long-time and after solar cells’ invention in 1954, solar cells have also been used widely for electricity generation. Solar cells convert the sunlight into electricity by the creation of voltage and electric current through the so-called photovoltaic effect.
\r\n\tPhotovoltaic (PV) solar energy has attracted significant attention in the recent decade as a reliable source for power generation due to various merits such as the free source of energy, abundant materials resources, environmentally friendly and noise-free, longtime service life, requiring low maintenance, technological advancements, market potential, and very importantly, low cost. The growth of using photovoltaic (PV) solar energy as a promising renewable energy technology, is being increased more and more worldwide. Therefore, much further research is needed for possible future developments in the field of solar photovoltaic energy.
\r\n\tThe aim of this book is to provide detailed information about solar radiation as the source of photovoltaic (PV) solar energy for a broad range of readership including undergraduate and postgraduate students, young or experienced researchers and engineers.
\r\n\tThis should be accomplished by addressing the various technical and practical aspects of solar radiation fundamentals, modeling and the measurement for photovoltaic (PV) solar energy applications.
\r\n\tThe majority of this book should describe the basic, modern, and contemporary knowledge and technology of extraterrestrial and terrestrial solar irradiance for photovoltaic (PV) solar energy.
\r\n\tThe book covers the most recent developments, innovation and applications concerning the following topics:
\r\n\t• Fundamental of solar radiation and photovoltaic solar energy
\r\n\t• Solar radiation and photovoltaic solar energy potential
\r\n\t• Solar irradiance measurement: techniques, instrumentation and uncertainty analysis
\r\n\t• Solar radiation modeling for photovoltaic solar energy applications
\r\n\t• Solar monitoring and data quality assessment
\r\n\t• Solar resource assessment and photovoltaic system performance
\r\n\t• Solar energy and photovoltaic power forecasting
\r\n\tThese are accompanied with other useful research topics and material.
",isbn:"978-1-83968-859-1",printIsbn:"978-1-83968-858-4",pdfIsbn:"978-1-83968-860-7",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"4c3d1319d7286e81bfb15c1f4b20460a",bookSignature:"Dr. Mohammadreza Aghaei",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/9862.jpg",keywords:"Solar Radiation Modeling, Solar Data Assessment, Solar Monitoring, Solar Radiation Forecasting, Solar Irradiance Measurements, Solar Instruments, Solar Spectral Distributions, Uncertainty Analysis, Solar Cell Technologies, Photovoltaics (PV), Solar Resource Assessment, Photovoltaics Power Forecasting",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 17th 2020",dateEndSecondStepPublish:"October 15th 2020",dateEndThirdStepPublish:"December 14th 2020",dateEndFourthStepPublish:"March 4th 2021",dateEndFifthStepPublish:"May 3rd 2021",remainingDaysToSecondStep:"5 months",secondStepPassed:!0,currentStepOfPublishingProcess:4,editedByType:null,kuFlag:!1,biosketch:"A senior researcher in the field of photovoltaic solar energy, a postdoctoral scientist at Eindhoven University of Technology (TU/e), Chair of the WG2: reliability and durability of PV in EU COST PEARL PV.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"317230",title:"Dr.",name:"Mohammadreza",middleName:null,surname:"Aghaei",slug:"mohammadreza-aghaei",fullName:"Mohammadreza Aghaei",profilePictureURL:"https://mts.intechopen.com/storage/users/317230/images/system/317230.jpg",biography:"Mohammadreza Aghaei is a senior researcher in the field of photovoltaic solar energy, Eindhoven University of Technology (TU/e), The Netherlands. He is chair of the Working Group 2: reliability and durability of PV in European Cooperation in Science and Technology, COST Action PEARL PV.\nHe received the M.S. degree in electrical engineering from the Universiti Tenaga Nasional (UNITEN), Selangor, Malaysia, in 2013, and the Ph.D. degree in electrical engineering from the Politecnico di Milano, Milan, Italy, in 2016.\nHe was a Postdoctoral Scientist with Fraunhofer ISE and Helmholtz-Zentrum Berlin (HZB)-PVcomB, Germany, in 2017 and 2018, respectively. He is a Guest Scientist with the Department of Microsystems Engineering (IMTEK), Solar Energy Engineering, University of Freiburg since 2017. He is currently a Postdoctoral Scientist with the Design of Sustainable Energy Systems Group, Eindhoven University of Technology (TU/e), The Netherlands. He has authored numerous publications in international refereed journals, book chapters, and conference proceedings. The main his research interests include Solar Energy, Photovoltaic systems, PV monitoring, LSC PV, solar cells, machine learning, and UAVs.\nDr. Aghaei is a member of the International Energy Agency, PVPS program-Task 13 and International Solar Energy Society, and also an MC member in EU COST Action PEARL PV.",institutionString:"Eindhoven University of Technology",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Eindhoven University of Technology",institutionURL:null,country:{name:"Netherlands"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"10",title:"Earth and Planetary Sciences",slug:"earth-and-planetary-sciences"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"247865",firstName:"Jasna",lastName:"Bozic",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/247865/images/7225_n.jpg",email:"jasna.b@intechopen.com",biography:"As an Author Service Manager, my responsibilities include monitoring and facilitating all publishing activities for authors and editors. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"70787",title:"Influence of Input Parameters on the Solution of Inverse Heat Conduction Problem",doi:"10.5772/intechopen.91000",slug:"influence-of-input-parameters-on-the-solution-of-inverse-heat-conduction-problem",body:'\nThe basic theory of heat and structure of solid body is associated with the internal energy of matter which in the first law of thermodynamics is referred to as the internal energy concerned with the physical state of the material. The first law of thermodynamics defines that the flowing heat energy is conserved in the absence of heat sources and sinks. It is, therefore, important to study the influence of thermocouple lead wires and distortion due to the thermocouple cavity in solution of the inverse heat conduction problem. According to the second law of thermodynamics, the heat will be transferred from one body to another body only when the bodies are at two different temperatures level and the heat will flow from the point of higher to the point of lower temperature.
\nA direct solution of transient heat conduction equation with prescribed initial and boundary conditions yields temperature distribution inside a slab of finite thickness. The direct solution is mathematically considered as well-posed because the solution exists, unique and continuously depends on input data. The estimation of unknown parameters from the measured temperature history is called as inverse problem of heat conduction. It is mathematically known as an ill-posed problem since the solution now does not continuously depend on the input data. Measurement data error in temperature, thermal lagging, thermocouple’s cavity, signal noise, etc. makes stability problem in the estimation of unknown parameters.
\nNumerical inversion of the integral solution [1], exact solution [2], numerical techniques [3], least-squares method [4], transform methods [5], different series approach [6], variable time-step size [7] have been applied to solve inverse heat conduction problems. Solutions of the ill-posed inverse heat conduction problem have been presented in detail by Beck et al. [8] and Özisik et al. [9]. Tikhonov regularization method [10] has been described for cross-validation criterion for selecting the regularization parameter to obtain a stable approximation to the solution. Kurpisz et al. [11] have presented series with derivatives with temperature to solve inverse thermal problem. Hensel [12] has described space marching numerical methods to solve inverse heat transfer problem. Various mathematical methods and numerical algorithms for solving inverse heat conduction problems are described and compared by Alifanov [13]. Taler and Duda [14] have presented solutions of direct and inverse heat conduction problems.
\nInverse heat conduction analysis provides an efficient tool for estimating the thermophysical properties of materials, the boundary conditions, or the initial conditions. Estimation of surface heat flux has been carried out without [15] and with [16] heat conduction and comparison between them shows discrepancies as high as about 27% [17]. Moving window optimization method [18] has been applied to predict the aerodynamic heating in a free-flight of sounding rocket by comparing numerically calculated and measured temperature history. Howard [19] developed a numerical procedure for estimating the heat flux with variable thermal properties using a single embedded thermocouple. Simultaneous identification of the temperature-dependent thermal conductivity and the asymmetry parameter of the Henyey-Greenstein scattering phase function have been shown by Zmywaczyk and Koniorczyk [20].
\nThe conjugate gradient method with adjoint problem for function estimation iterative technique is used to solve IHCP to estimate heat flux and internal wall temperature of the throat section of the rocket nozzle [21]. Heisler [22] have reported supplementary “short-time” temperature-time charts for the center, mid-location and surface of large plates, long cylinders and spheres for the dimensionless time sub-domain. Convective heat transfer coefficient and combustion temperature in a rocket nozzle is determined using transient-temperature response chart [23].
\nThe solution of transient IHCP can be obtained using analytical or numerical schemes in conjunction with measured temperature-time history. The estimation of the unknown parameters can be carried out by employing gradient or non-gradient methods to predict the unknown parameters in a prescribed tolerance limit. The focus of the present work is to investigate the influence of various parameters on the solution of inverse heat conduction problem.
\nExperimental difficulties [24] are noticed in implanting thermocouples at the surface for temperature measurements. Temperature response delays have been studied to solve IHCP applied to cooled rocket thrust chamber [25]. The temperature measured inside the slab may delay and damp depending on xm\n as illustrated in Figure 1. A thermocouple indicates temperature lag behind the actual temperature. The effect of the thermocouple sensor dynamics on prediction of a triangular heat flux history has been analyzed with simulated data in a one-dimensional domain by Woodbury [26].
\nGeometry of the specimen.
Chen and Danh [27] have carried out experimental studies to obtain transient temperature distortion and thermal delay in a slab due to presence of thermocouple cavity. The distortion of temperature profiles inside the slab may be influenced by the dissimilar thermophysical properties of thermocouple and surrounding materials and by the diameter and depth of the cavity. The temperature distortion [28] inside a slab is a function of the thermocouple cavity diameter d and location xm\n.
\nStandard statistical analysis consists of error in the measurement as an additive of true plus random, in zero mean, in constant variance, uncorrelated, normal, bell shaped probability density function, constant variance known, errors in the dependent variables and no-prior information about the parameters. The error in measurement can be obtain using exact analytical solution [29] as
\nwhere ε and δτ refer to error in measurement of thermocouple location and in time recording, respectively. One of the important points that must be mentioned, here, is the use of a starting solution. In the case of a solid rocket motor where boundary conditions are suddenly imposed by a wall, there will be high intensity of heat flux on cold wall, and the heat flux during the first few steps in time may not be very accurate. The numerical solution is initiated using an exact analytical solution instead of starting from the initial constant condition. Such solutions can be obtained from to exact analytical solution [30] of transient heat conduction equation. Heat transfer rates to the calorimetric probe are estimated from measurements of temperature and rate of temperature change using energy conservation considerations [31].
\nAn optimization method based on a direct and systematic search region reduction optimization method [32] can be employed to estimate the unknown convective heat transfer coefficient in a typical rocket nozzle. The most attractive feature of the direct search scheme is the simplicity of computer programming. The pseudo-random algorithm, an effective tool for optimization, does not require computation of derivatives but depends only on function evaluation. It works even when the differentiability requirements cannot be ensured in the feasible domain. For initiating the search only an estimate of the feasible domain is needed. Therefore, another advantage of the method is that the starting condition is not crucial; any reasonable value will do.
\nThe computation of the turbulent convective heat transfer coefficient from combustion gases to the rocket nozzle wall is based on the Bartz’s equation [33] incorporating the effects of compressibility, throat curvature and variation of transport properties in the boundary layer. The transient heat conduction in a one-dimensional Cartesian coordinate system having two parallel plane surfaces Sn\n (n = 1, 2) of a slab may be written in dimensional form [34] as.
\nwith following initial and boundary conditions:
\nwhere fi\n is initial temperature distribution in the region R of the slab. Eq. (4) represents both convective heat transfer or heat flux condition as applied to the inner surface.
\nWe now consider the constant thermal property solution and can be written in terms of eigen function \n
In the above Eq. (5), Bi or qw\n is the unknown parameter to be determined using measured temperature time history at location xm\n as depicted in Figure 1. In estimating the unknown condition, one has to minimize the absolute difference between the calculated and measured temperature at specified location and time (xm\n, τ) in a prescribed tolerance value using an iteration procedure. The iteration scheme is described in the following sections.
\nThe IHCP is solved by comparing calculated and measured temperature using an iterative technique [30]. In estimating qw\n, one minimizes
\nwhere θc\n and θm\n are the calculated and measured temperatures at (Xm\n, τ), respectively. The computed temperature is a nonlinear function of unknown parameters such as wall heat flux or convective heat transfer coefficient. Temperature is calculated using Eq. (6) and compared with the measured temperature as expressed in Eq. (7). The inverse problem starts with initial guess value of the unknown parameter. The second step is to correct the previous guessed unknown parameter using the Newton-Raphson method. The sensitivity coefficient can be obtained by differentiating temperature with respect to wall heat flux qw\n. The iteration procedure will continue until │F(qw\n)│ ≤ 10−4. This iterative scheme estimates the component of the qw\n at a time and thus may be considered on-line method.
\nThe inverse method for solving a value of qw\n(0, τ) is as follows. Initiate with an initial guess value of qw\n, satisfy the convergence criterion, and implement the Newton-Raphson to obtain the estimate value.
\nNow, it is possible to estimate convective heat transfer coefficient and combustion gas temperature in conjunction with measured temperature history [35]. The equation for converting the calculated heat flux to the heat transfer coefficient is
\nIn the foregoing equation, T\ng is an unknown quantity and can be estimated using again the above-mentioned minimization and iteration methods. The convergence criterion for the iterative scheme remains same as mentioned above.
\nIt is not always feasible to obtain analytical solution of temperature-dependent thermal conductivity and radiation boundary condition. The Crank-Nicolson finite difference method with two-time level implicit numerical scheme [36] has been employed to solve the nonlinear conduction problem with the Newton-Raphson method to consider the radiation boundary condition.
\nDeforming or moving finite elements method [37] is used to solve linear heat conduction equation. The moving finite element [38] is used to consider the time delay in the measurement of back wall temperature.
\nFor only two nodes the system of [39] equations reduce to the following pair of equations:
\nwhere 0 and 1 represent node in a slab of finite thickness. These are the exact solutions to the system of two ordinary differential equations which resulted from a two-node finite-difference approximation to the original problem.
\nwhere \n
Solution of the above simultaneous equation calculates the temperature with a given value of Bi. The solution is now solving simultaneously Eqs. (11) and (12) to determine the unknown parameter.
\nThe influence of constant (average) thermal conductivity, temperature-dependent thermal conductivity, computational grid in numerical solver, nonlinear boundary condition, cylindrical coordinate and the estimation of the wall heat flux and convective heat transfer is carried out by employing measured temperature history of a rocket nozzle of a solid motor. Solution of linear heat conduction equation is used to estimate the convective heat transfer coefficient with the measured temperature data of outer wall of a rocket nozzle. The running time of rocket motor is 16 s. The nozzle wall thickness L = 0.0211 m. The thermo-physical properties of the material are: ρ = 7900 kg m−3, Cp\n = 545 J kg−1 K−1, K (average) = 35 Wm−1 K−1. Initial temperature Ti\n = 300 K and combustion gas temperature Tg\n = 2946.2 K are used in the solution of the heat conduction equation.
\nPrediction of convective heat transfer coefficient is carried out in conjunction with the calculated and measured temperature history at outer surface of nozzle divergent in a solid rocket motor static test. The constant thermal conductivity solution of the linear transient heat conduction problem [30] is
\nFor estimating unknown boundary condition, the heat conduction equation is and solved with the following boundary and initial conditions.
\nand
\nExact analytical solution of transient heat conduction as written in Eq. (13) is used to estimate convective heat transfer on the inner surface of the rocket nozzle. An iterative scheme is used to solve inverse problem [30]. The iteration is carried out till the absolute difference between calculated and measured temperature is less than or equal to 10−4. Table 1 exhibits the comparison between the estimated values of the convective heat transfer coefficient based on the exact solution of heat conduction equation with the calculated values of Bartz [33]. Bartz’s equation calculates conservative estimates for the convective heat transfer to the wall [40].
\n\nt, s | \n\nθ\n0 at inner surface | \n\nθc\n at outer surface | \n\nθm\n at outer surface | \n\nh, W/m2K | \n\nhB\n, W/m2K | \n
---|---|---|---|---|---|
6 | \n0.2950 | \n0.0098 | \n0.0096 | \n1821.9 | \n2254.2 | \n
7 | \n0.3109 | \n0.0159 | \n0.0158 | \n1810.0 | \n2254.2 | \n
8 | \n0.2996 | \n0.0212 | \n0.0211 | \n1610.3 | \n2254.2 | \n
9 | \n0.3244 | \n0.0301 | \n0.0302 | \n1690.9 | \n2254.2 | \n
10 | \n0.3340 | \n0.0386 | \n0.0385 | \n1669.7 | \n2254.2 | \n
11 | \n0.3416 | \n0.0473 | \n0.0472 | \n1641.9 | \n2254.2 | \n
12 | \n0.3302 | \n0.0529 | \n0.0529 | \n1497.6 | \n2254.2 | \n
13 | \n0.3312 | \n0.0602 | \n0.0604 | \n1443.1 | \n2254.2 | \n
14 | \n0.3409 | \n0.0677 | \n0.0676 | \n1387.0 | \n2254.2 | \n
15 | \n0.3442 | \n0.0781 | \n0.0782 | \n1413.0 | \n2254.2 | \n
16 | \n0.3475 | \n0.0862 | \n0.0861 | \n1383.7 | \n2254.2 | \n
Solution of inverse heat conduction problem.
An iteration procedure [41] is employed in conjunction with exact solution to predict convective heat transfer coefficient from the measured temperature-time data at the outer wall of the nozzle as shown in Table 2. The expression for temperature-dependent conductivity is K(T) = k0\n − βT. The value of k0\n and β are 57 Wm−1 K−1 and 2.718 Wm−1 K−2, respectively. The advantage of using the exact solution is found directly at specified location and time as compared to the numerical method which needs the computation from the initial state.
\n\nt, s | \n\nθ(0, τ) | \n\n | \nh, W/m2K | \n|||
---|---|---|---|---|---|---|
Iterative method | \nBeck method | \n\nθc\n(1, τ) | \nθ\nm\n(1, τ) | \nIterative method | \nBeck method | \n|
6 | \n0.0883 | \n0.0838 | \n0.0099 | \n0.0098 | \n536.6 | \n581.7 | \n
7 | \n0.1067 | \n0.1075 | \n0.0158 | \n0.0159 | \n600.6 | \n587.0 | \n
8 | \n0.1144 | \n0.1116 | \n0.0220 | \n0.0212 | \n592.6 | \n598.4 | \n
9 | \n0.1367 | \n0.1367 | \n0.0302 | \n0.0302 | \n674.2 | \n685.3 | \n
10 | \n0.1522 | \n0.1545 | \n0.0386 | \n0.0385 | \n712.9 | \n693.2 | \n
11 | \n0.1654 | \n0.1690 | \n0.0472 | \n0.0472 | \n737.4 | \n730.0 | \n
12 | \n0.1686 | \n0.1639 | \n0.0529 | \n0.0529 | \n718.2 | \n721.9 | \n
13 | \n0.1773 | \n0.1777 | \n0.0605 | \n0.0605 | \n723.6 | \n725.8 | \n
14 | \n0.1844 | \n0.1813 | \n0.0677 | \n0.0676 | \n723.0 | \n725.1 | \n
15 | \n0.1944 | \n0.2040 | \n0.0781 | \n0.0782 | \n753.6 | \n765.0 | \n
16 | \n0.2083 | \n0.2174 | \n0.0862 | \n0.0862 | \n758.3 | \n770.0 | \n
Comparison between iterative and Beck methods.
Deforming or moving finite element is used to consider the time delay in temperature at the outer wall of the slab [37]. Estimated values of wall heat flux and heat transfer coefficient are tabulated in Table 3. It can be observed from the table that the estimated wall quantities are having significant influence on the predicted unknown boundary conditions. This example is extended to consider spatial grid changed and temporal dependence on the numerical solution using moving finite element method [38].
\n\nt, s | \n\nTm\n K at X = 1 | \nUniform grid | \nNon-uniform grid | \nMoving grid | \n|||
---|---|---|---|---|---|---|---|
\nqw\n × 106, W/m2\n | \n\nh\nc, W/m2K | \n\nqw\n × 106, W/m2\n | \n\nh\nc, W/m2K | \n\nqw\n × 106, W/m2\n | \n\nh\nc, W/m2K | \n||
6 | \n326 | \n3.715 | \n1964.5 | \n3.846 | \n2044.9 | \n4.517 | \n2412.1 | \n
7 | \n342 | \n2.700 | \n1408.8 | \n2.848 | \n1449.6 | \n2.818 | \n1485.9 | \n
8 | \n356 | \n2.698 | \n1436.9 | \n2.840 | \n1531.6 | \n2.820 | \n1512.8 | \n
9 | \n380 | \n2.704 | \n1463.0 | \n2.589 | \n1569.8 | \n2.842 | \n1552.8 | \n
10 | \n402 | \n2.705 | \n1491.4 | \n2.858 | \n1603.3 | \n2.846 | \n1586.7 | \n
11 | \n425 | \n2.704 | \n1518.9 | \n2.852 | \n1632.6 | \n2.845 | \n1618.5 | \n
12 | \n440 | \n2.691 | \n1539.7 | \n2.805 | \n1636.2 | \n2.812 | \n1630.8 | \n
13 | \n460 | \n2.683 | \n1564.6 | \n2.776 | \n1649.7 | \n2.791 | \n1650.6 | \n
14 | \n479 | \n2.673 | \n1588.1 | \n2.738 | \n1657.1 | \n2.764 | \n1665.9 | \n
15 | \n507 | \n2.094 | \n1226.4 | \n2.015 | \n1190.6 | \n2.091 | \n1235.4 | \n
16 | \n528 | \n2.086 | \n1231.8 | \n1.981 | \n1178.5 | \n2.067 | \n1231.6 | \n
Wall heat flux at various grid arrangements.
Numerical analysis of nonlinear heat conduction with a radiation boundary condition [36] is carried out to estimate wall heat flux using temperature history on the back wall of the rocket nozzle. The high temperature variation alters thermophysical properties of the material of mild steel. Table 4 shows comparison between the estimated convective heat transfer coefficients with the Bartz solution [33]. Effects of nonlinear IHCP with radiation boundary condition are investigated and results are presented in Table 4.
\n\nt, s | \n\nTo\n, K at X = 0 | \n\nTm\n K at X = 1 | \n\nqc\n × 106 W/m2\n | \n\nh W/m2K | \n\nhB\n W/m2K | \n\nTgc\n K | \n\nTg\n K | \n
---|---|---|---|---|---|---|---|
6 | \n659.8 | \n326 | \n2.3547 | \n950.0 | \n2254.2 | \n3137 | \n2946.2 | \n
7 | \n801.0 | \n342 | \n2.3899 | \n1019.6 | \n2254.2 | \n3122 | \n2946.2 | \n
8 | \n900.7 | \n356 | \n2.2211 | \n992.4 | \n2254.2 | \n3115 | \n2946.2 | \n
9 | \n996.3 | \n380 | \n2.6489 | \n1237.1 | \n2254.2 | \n3113 | \n2946.2 | \n
10 | \n1050.5 | \n402 | \n2.3670 | \n1135.5 | \n2254.2 | \n3108 | \n2946.2 | \n
11 | \n1066.4 | \n425 | \n1.7100 | \n827.3 | \n2254.2 | \n3104 | \n2946.2 | \n
12 | \n1201.8 | \n440 | \n2.8144 | \n1459.2 | \n2254.2 | \n3099 | \n2946.2 | \n
13 | \n1320.0 | \n460 | \n2.6559 | \n1467.0 | \n2254.2 | \n3098 | \n2946.2 | \n
14 | \n1354.8 | \n479 | \n1.7595 | \n991.7 | \n2254.2 | \n3095 | \n2946.2 | \n
15 | \n1383.4 | \n507 | \n1.3810 | \n791.4 | \n2254.2 | \n3094 | \n2946.2 | \n
16 | \n1414.9 | \n528 | \n1.1684 | \n681.8 | \n2254.2 | \n3094 | \n2946.2 | \n
Solution with nonlinear boundary condition.
A grid point shift strategy [42] is adapted to solve inverse conduction problem in a radial coordinate of rocket nozzle with inner and outer radius of rocket nozzle. The inner and outer radius of the nozzle is 0.0839 m and 0.0105 m, respectively. The purpose of the present example to investigate the influence of radial coordinate on the estimated values of heat transfer coefficient. Table 5 shows the effect of geometrical parameters on the predicted heat transfer coefficient.
\n\nt, s | \n\nTo\n K at X = 0 | \n\nTm\n K at X = 1 | \n\nqc\n × 106 W/m2\n | \n\nh, W/m2K | \n\nhB\n, W/m2K | \nθg, K | \nθgc, K | \n
---|---|---|---|---|---|---|---|
6 | \n1260.2 | \n326 | \n3.6805 | \n1789.6 | \n2254.2 | \n3316 | \n2946 | \n
7 | \n1175.9 | \n342 | \n3.3995 | \n1628.0 | \n2254.2 | \n3264 | \n2946 | \n
8 | \n1160.7 | \n356 | \n2.4745 | \n1181.4 | \n2254.2 | \n3255 | \n2946 | \n
9 | \n1165.8 | \n380 | \n2.5385 | \n1194.7 | \n2254.2 | \n3290 | \n2946 | \n
10 | \n1196.0 | \n402 | \n2.5348 | \n1261.1 | \n2254.2 | \n3206 | \n2946 | \n
11 | \n1192.3 | \n425 | \n2.3385 | \n1166.4 | \n2254.2 | \n3197 | \n2946 | \n
12 | \n1205.8 | \n440 | \n2.2094 | \n1114.8 | \n2254.2 | \n3187 | \n2946 | \n
13 | \n1211.0 | \n460 | \n2.1333 | \n1229.5 | \n2254.2 | \n2946 | \n2946 | \n
14 | \n1222.1 | \n479 | \n2.0441 | \n1187.5 | \n2254.2 | \n3943 | \n2946 | \n
15 | \n1237.1 | \n507 | \n2.0626 | \n1206.7 | \n2254.2 | \n2946 | \n2946 | \n
16 | \n1249.1 | \n528 | \n2.0027 | \n1180.9 | \n2254.2 | \n2945 | \n2946 | \n
Inverse problem in a hollow cylinder.
The calculated convective heat transfer coefficients and inner wall temperature are used to determine the wall heat flux and the combustion temperature using Eq. (8). The iterative scheme is based on relation between wall heat flux and convective heat transfer coefficient [35]. Table 6 shows the predicted values of wall heat flux and convective heat transfer coefficient. The IHCP is extended to determine wall heat flux in conjunction with convective heat transfer coefficient. A similar IHCP but referring to the 122 mm medium-range missile during correction engine operation has been considered by Zmywaczyk et al. [43].
\n\nt, s | \n\nT0\n K at X = 0 | \n\nTm\n K at X = 1 | \n\nqc\n × 106, W/m2\n | \n\nh, W/m2K | \n\nhB\n, W/m2K | \n\nTg\n, K | \n\nTgc\n, K | \n
---|---|---|---|---|---|---|---|
6 | \n1355.6 | \n326 | \n3.2502 | \n2631.2 | \n2254.2 | \n3351 | \n2946 | \n
7 | \n1287.8 | \n342 | \n3.2950 | \n1805.3 | \n2254.2 | \n3113 | \n2946 | \n
8 | \n1315.6 | \n356 | \n3.2974 | \n1861.5 | \n2254.2 | \n3087 | \n2946 | \n
9 | \n1368.9 | \n380 | \n3.2967 | \n1885.9 | \n2254.2 | \n3117 | \n2946 | \n
10 | \n1414.4 | \n402 | \n3.2837 | \n1962.1 | \n2254.2 | \n3088 | \n2946 | \n
11 | \n1463.6 | \n425 | \n3.2718 | \n2049.5 | \n2254.2 | \n3060 | \n2946 | \n
12 | \n1370.8 | \n440 | \n2.3825 | \n1476.0 | \n2254.2 | \n2985 | \n2946 | \n
13 | \n1360.9 | \n460 | \n2.4140 | \n1502.1 | \n2254.2 | \n2968 | \n2946 | \n
14 | \n1370.3 | \n479 | \n2.3625 | \n1520.6 | \n2254.2 | \n2924 | \n2946 | \n
15 | \n1382.5 | \n507 | \n2.3675 | \n1517.2 | \n2254.2 | \n2943 | \n2946 | \n
16 | \n1399.3 | \n528 | \n2.3645 | \n1540.7 | \n2254.2 | \n2934 | \n2946 | \n
Wall heat flux and convective heat transfer coefficient.
A two-node exact solution is used to calculate the back-wall temperature as described in Section 3.4. The iterative method described above has been used for estimating aerodynamic heating for a sounding rocket in free flight test. Here, the wall heat flux is estimated using the measured temperature history in conjunction with the iterative technique [30]. The aerodynamic heating rate is estimated for a typical sounding rocket as depicted in Figure 2. The location of thermocouple is marked in the diagram. The thermophysical properties of Inconel and wall thickness are k = 18 Wm−1 K−1, α = 4.47 × 10−6 m2/s, L = 0.7874 × 10−3 m. Figure 3 depicts the measured temperature time history at different locations measured from the tip of the cone in the free flight of a sounding rocket as delineated in Figure 2. It can be observed from temperature history that the initial time delay in thermal response is 6 s. The unknown qw\n are estimated using an iterative technique which starts with an initial value of wall heat flux and is repeated until |F(qw\n)| ≤ 10−4.
\nSchematic sketch of sounding rocket showing location of thermocouple.
Measured temperature history in free flight of the sounding rocket.
A two-node exact solution is used to calculate the wall temperature distribution. The unknown qw\n are estimated using an iterative technique which starts with an initial value of wall heat flux and is repeated until |F(qw\n)| ≤ 10−4. Figure 4 displays the estimated variation of the wall heat flux as a function of flight time of the sounding rocket.
\nVariations of wall heat flux vs. flight time.
The wall heat flux variation depends on the sounding rocket speed. The increase and decrease of the aerodynamic heating are a function of flight Mach number.
\nThe estimated wall heat flux is compared with Van Driest’s results [44]. Table 7 depicts the estimated values of wall heat flux as a function of flight time at thermocouple location 29 as shown in Figure 2. It can be observed from the table that highest aerodynamic heating occurs during 7–8 s, another significant peak wall heat flux was found at 22 s.
\n\nt, s | \n\nTm\n, K | \n\nTc\n, K | \n\n\n | \n\n\n | \n
---|---|---|---|---|
6 | \n313.0 | \n320.0 | \n2.756 | \n8.246 | \n
7 | \n341.3 | \n349.4 | \n16.695 | \n14.82 | \n
8 | \n408.0 | \n412.3 | \n19.387 | \n22.647 | \n
9 | \n469.7 | \n469.3 | \n8.657 | \n18.876 | \n
10 | \n495.2 | \n495.8 | \n8.145 | \n10.117 | \n
11 | \n504.1 | \n513.3 | \n9.302 | \n4.569 | \n
12 | \n502.4 | \n521.2 | \n2.757 | \n1.176 | \n
13 | \n495.2 | \n506.8 | \n−7.695 | \n−0.977 | \n
14 | \n487.4 | \n487.6 | \n−0.040 | \n−2.320 | \n
15 | \n477.4 | \n477.0 | \n−0.037 | \n−3.134 | \n
16 | \n467.4 | \n467.0 | \n−0.028 | \n−3.578 | \n
17 | \n457.4 | \n457.5 | \n−0,034 | \n−3.769 | \n
18 | \n445.8 | \n447.2 | \n−0.905 | \n−3.789 | \n
19 | \n438.6 | \n437.5 | \n−0,005 | \n−1.628 | \n
20 | \n444.1 | \n445.9 | \n5.173 | \n4.135 | \n
21 | \n469.1 | \n467.5 | \n13.518 | \n11.524 | \n
22 | \n533.0 | \n521.2 | \n20.618 | \n19.732 | \n
23 | \n556.3 | \n558.4 | \n9.180 | \n13.122 | \n
24 | \n567.1 | \n573.5 | \n6.514 | \n8.581 | \n
25 | \n584.1 | \n587.2 | \n8.592 | \n5.467 | \n
26 | \n596.9 | \n602.2 | \n7.018 | \n3.314 | \n
Comparison between calculated and Van Driest’s heat flux at location 29.
Analytical, transient numerical and two-node methods are used to compute temperature distribution in a finite slab. Numerical solution is carried out with temperature-dependent thermal conductivity. Implicit finite difference scheme with two-time level technique is implemented to solve nonlinear problem of heat conduction. Time delay is studied using finite element method with deforming grid strategy. A boundary shifting numerical scheme is used to solve transient heat conduction in radial coordinate. Evidence of temporal accuracy and dependence on time-step is demonstrated in the numerical solving of IHCP. Influence of thermocouple cavity and measurement errors in location and time are discussed. The IHCP is applied to predict the wall heat flux in a rocket nozzle of a solid motor. Wall heat flux is estimated in a free flight of a sounding rocket using the two-node method.
\nBiot number, hL/k\n
\nspecific heat
\nheat transfer coefficient
\nthermal conductivity, k(θ)/k0\n\n
\nreference thermal conductivity at Ti\n\n
\nslab thickness
\nnondimensional parameter, αΔT/(Δx)2\n
\nwall heat flux
\ntemperature
\ntime
\ndistance from the inner surface
\ndimensionless coordinate
\nthermal diffusivity
\ndensity
\nnondimensional temperature, = (T − Tg\n)/(Tg\n − Ti\n)
\nnondimensional time, αt/L2\n\n
\nBartz
\ncomputed
\ncombustion gas temperature
\ninitial value
\nmeasured
\nouter wall
\nwall
\nconstant thermal conductivity coefficient
\nChildren’s experiences with digital technologies actually involve an increasing quote of young users (also defined as “digital natives”) who are born and are developing in environments in which new digital technologies are widely available [1]. This currently occurs from early infancy, due to the rapid diffusion of touchscreen devices among younger children (or “touch generation”; [2, 3]). Children aged 2–4 years actually are able to use touchscreen devices, such as tablets or smartphones, to play or watch movies, and often parents themselves introduce kids to use them in boring social situations (i.e., in the pediatrician’s waiting rooms or in the restaurant; [4]). On the basis of the most recent report on worldwide diffusion of the Internet among young people [1], one in three users is estimated to be a child or teenager (under 18). Generally children use digital technologies in their home, particularly younger children, with intense and prolonged activities especially on weekends. Children often use their digital technologies at school at least a day a week (almost 30% among 9–11 years), although it is prohibited in many countries by school regulations. The access to digital technologies is expanding among young generations, even if many inequalities of resources remain between developed or developing countries [1]: for example, it has been estimated that in Africa (Ghana) children mainly use 0.9 mobile devices to connect to the Internet, against 2.9 in South America (Chile) or 2.6 in Europe (Italy). Similarly, only 12% of children in Africa (Ghana), 21% in the Philippines, and 26% in Albania can connect to the Internet at school, against 63–54% of children in other South America or European countries, such as Argentina, Uruguay, or Bulgaria. This reality raises several questions on how to guarantee the young generations the opportunities offered by new technologies (for studying, enhancing skills, socializing, etc.), protecting them from potential dangers of digitalized world (i.e., contacts with unknown people, exposure to violent/pornographic contents, etc.). In fact, although children grow in a reality permeated by new media, they are not automatically “digitally literate,” that is, able to juggle the digital world and to reflect on it. Studies show that not only young users, but also teenager users “have difficulties in finding, managing and evaluating information, managing their privacy online and ensuring their online personal safety […]and may thus vary in their digital skills” ([5], p. 186).
Together with their children, parents themselves are largely exposed to media experiences in many fields of their life. Digital technologies have quickly changed the way in which family members communicate, enjoy themselves, acquire information, and solve daily problems. Parents are also the first mediators of children’s experiences with digital tools: they have the task of integrating their use into ordinary routines (play, entertainment, learning, mealtime, etc.), promoting constructive and safety uses. Digital parenting describes parental efforts and practices for comprehending, supporting, and regulating children’s activities in digital environments. A growing research on digital parenting identified the main approaches that can allow parents to “mediate” children’s activities with digital technologies [6, 7, 8]. According to Vygotsky’s theory of child development and his concept of proximal development zone [9], parental mediation can be considered a key aspect in facilitating the interactions between children and new media. The proximal development zone is an intermediate area between what the child is able to do alone and what he/she can learn thanks to the guidance of others. In the course of a shared activity, the support and the help are adapted so that the child can improve his/her skills and gradually assume responsibility for acting alone. However, the activities that take place in the virtual environments of the web, unlike the experiences in the real environments, can reverse the relationship between the competent person (the adult) and the learner (the child). Today’s children have an early, almost “intuitive” approach to digital technologies, so in some cases they can become active agents towards their parents. When children’s knowledge and digital competence (e.g., functions/benefits of a new app) overcome that of parents, many shared experiences can be child-initiated, and children can also perform some forms of support and digital teaching to parents. This reverse socialization [10] seems to be a peculiar feature of digital experiences, and it poses new challenges to parental role. Reverse socialization describes all situations where children possess a better understanding or more advanced skills than adults. This gap between generations is more marked in low-income families or low-educated parents who possess limited resources and access to digital technologies [11]. However, over the past years, many parents have developed adequate knowledge and technical skills to share digital experiences with their children [3, 12]; they appreciate benefits of the web and strive to comprehend its complexity.
A common difficulty that parents actually encounter derives from the diffusion of “portable” devices (smartphone and tablet) that children start to use in early infancy (under the age of 2; [13]). Later, due to unlimited Wi-Fi access and enhanced connectivity, children insert activities with mobile devices into many daily routines, for example, during mealtime, school homework, conversations with parents, or before sleeping [14]. Particularly, parents worry about the “pervasiveness” (or ubiquitous) of mobile technologies in daily activities [15], and they fear that an effective guidance and control over them may decrease. Studies with large samples of young digital users (9–16 years old) in many European countries have compared parents’ opinions before (2010 Eu Kids Online Survey; [12]) and after (Net Children Go Mobile; [3]) the diffusion of mobile devices. After 4 years, many parents declare that they know less about their children’s online activities and have more difficulties to closely monitor children’s usage (e.g., time spent connected). Interestingly, parents now are more aware of the risks of using the web [16], and they prefer to talk to children about Internet security (e.g., do not leave personal data online or block unknown people) rather than limiting or prohibiting Internet use [17]. Parents can encourage or limit the use of digital technologies to children according to the opportunities or danger they attribute to them. Since parents themselves are regular, sometimes enthusiastic, users of digital media, their digital skills and confidence and daily frequency of usage (or overuse; [18]), together with beliefs about digital world [3], are all crucial factors that researchers have begun to explore systematically.
Each parent has beliefs, that is, convictions and personal opinions, regarding the usage of media by children, such as their usefulness or damage, or the age at which children should use them. Beliefs are the cognitive dimension of attitudes, guiding individual’s behavior and choices. When parents raise their children, they act and make choices for them following their own perceptions of what is desirable or what they positively value for their child’s development [19]. Although parents are not always aware of their beliefs, these influence parent-child interaction and the child’s opportunity to learn, do experiences [20], and develop digital skills [5]. Parental beliefs are important aspects of parenting and family microsystem, together with factors such as parent’s history and education, socioeconomic status, and culture.
Parents possess personal ideas about modern technologies: they can be considered a source of entertainment/relaxation or a learning tool [21, 22]; conversely, for other people, PC, tablet, and smartphone can be harmful to children’s health (such as sleep problems, obesity, etc.; [23]), for social risks (such as contacts with unfamiliar or social isolation; [24]), or because they interfere with parent-child activities and time spent together [25].
A qualitative study [26] shows that parents have more pessimistic (70.55%) than optimistic opinions (29.45%) on the Internet use by primary school children: for example, parents worry about the excessive time spent online, the interference in face-to-face conversation, or that children lack of skills and maturity in dealing with some contents suitable for older children (such as violence, sex, or drug-related contents). Other worries concern negative consequences on learning and academic performance (i.e., reduced attention span), physical development (i.e., prolonged sedentary activities), social skills and peer interactions (i.e., fewer opportunities to “learn to play together”), and child’s well-being (i.e., using smartphone to overcome boredom). Interestingly, many parents fear losing control over their children’s online behaviors. Conversely, the positive beliefs concern positive effects of digital technologies on child’s entertainment, communication and learning, access to information, and enhancing of child’s skills (such as brain functioning, self-regulation, autonomy, critical attitude, etc.).
Other researchers [27] explored parent’s perceptions about positive (i.e., they are shared by generations) or negative impact (i.e., they expose family privacy to risks) of social media—such as Facebook or WhatsApp—on family open communication. Teenagers are intensely involved in social media use, but adults also are regular users. On the one hand, parents use social networks to communicate; on the other hand, they fear that they negatively impact family relationships, for example, through the phubbing phenomenon (i.e., ignoring someone or interrupting a conversation or mealtime to check the smartphone). Authors found that parents’ perceptions are a meditational variable between the collective family efficacy (i.e., the perceived efficacy to manage family relationships, to support each other, etc.) and the openness of communication: “it is not only the actual impact of social media on family systems that matters but also parents’ perceptions about it and how much they feel able to manage their children’s social media use without damaging their family relationships” (p. 1).
Parental beliefs may influence the degree to which parents give opportunities or restrict their children’s media use, but beliefs should not be considered the “cause” of behavior towards children. Researches show that parents’ positive beliefs (e.g., “the tablet improves reading skills”) are associated with favorable attitudes, co-using approach, communication, or suggestions to enhance their child’s appropriate use of the Internet [28]. For example, when parents think that smartphones are useful tools (i.e., they promote child’s intelligence and knowledge), they more often allow their preschool children to use them (i.e., at the restaurant), and children become regular users, spending more time (at least 2 h a day) with smartphone activities [29]. Conversely, parents who attribute negative effects to digital media tend to limit activities to children (i.e., put time limits or react for smartphone overuse); in turn, these restrictive behaviors can influence how much the children use these devices [28]. Therefore, the influences of parental beliefs on child’s behaviors are not directed, but they are mediated by parental practices and other factors such as parental education or involvement with mobile device (“attachment”; see, e.g., [30]) that can intervene.
Parental beliefs include also self-efficacy [31, 32], that is, parent’s sense of competence in their own digital skills and in managing their children’s technology usage. An example of parental self-referent estimation of competence is “I won’t bother setting parental controls or passwords because my kids will “hack” around them” (cfr. [33]). In many studies, parental self-efficacy is positively associated with active parental practices: when parents feel confident about their Internet skills, they more often are involved in or monitor their children’s media activities [6]. Recently Shin [34] distinguishes general self-efficacy (the confidence to be a good parent; [35]) from two self-efficacy domains assessing parental beliefs more strictly related to digital tasks: parental “media competency” in using media technology (such as sending/receiving email with a smartphone) and “perceived control over mediation strategies” (the degree to which the parent feels to be able to guide or modify their children’s behaviors on smartphone). All these domains of parenting self-efficacy are associated with each other [34], suggesting that perceived competence on their own digital skills can positively influence parents’ involvement with children (e.g., discussing about smartphone use).
Sanders et al. [33] found that when parents are confident to have adequate digital skills, they more often intervene (i.e., with rules and reinforcement strategies) with their children. Parental self-efficacy also influences parental opinions about technologies and how they talk about them with children [33]. Moreover, parental perception of influence in managing technologies decreased with preadolescents that generally are seen as more self-regulated and reluctant to the parental control than younger children. These findings suggest the importance to recognize the influence of child characteristics (such as age, technology usage, perceived competence, etc.) on digital parenting.
Initially studies on parental engagement in children’s activities with media assumed as theoretical basis the traditional parenting styles [36, 37]. According to Darling and Steinberg [38], parenting styles are defined as the context (or emotive climate) in which parents raise and socialize their children, and they are distinct from practices, that is, the distinct actions contingent to the child’s behavior (e.g., scolding when the child uses the smartphone during mealtime). As it is well known, two main dimensions of the parent’s behaviors, and their natural variations along a continuum, describe the styles: responsiveness/warmth (involvement, acceptance, and affect that the parent expresses towards the child’s needs) and demandingness/control (rules, control, and maturity expectations for the child’s socialization). Parenting styles derive from the combination of these variable dimensions: authoritative parenting (high warmth and high control, e.g., parents listen to the child’s wishes, but they put clear limits to the child’s behaviors); laissez-faire parenting (low warmth and low control; the parents are detached from the needs expressed by the child; they did not give rules or limits to child’s behavior); authoritarian parenting (low warmth and high control; parents expect the child to obey; they neither discuss nor listen to the child’s opinions and can react with harsh discipline); and permissive parenting (high warmth and low control; parents are very affectionate, but they lack in guidance through rules and give few limits to the child’s behavior).
Studies that applied these “classic” parenting styles to children’s behaviors with new communication media did not provide convincing results [39]. As an alternative to the “broad” parenting styles, a description of specific media-related practices is more useful in empirical studies for exploring the link between parental behaviors and child outcomes (e.g., time spent online). Therefore, researchers strove to identify the key dimensions of parental warmth/control more strictly referred to children’s behaviors on the Internet or new media (Table 1). These Internet parenting styles are more strictly linked to children’s actual use of digital technologies, for example, low parental control predicted more time of Internet usage by school-aged children [8].
Style dimensions | Item (examples) |
---|---|
Parental control | Supervision: “I’m around when my child surfs on the Internet” |
Stopping internet usage: “I stop my child when he/she visits a less suitable website” | |
Internet usage rules: “I limit the time my child is allowed in the Internet (e.g., only 1 h a day)” | |
Parental warmth | Communication: “I talk with my child about the dangers related to the Internet (costs, addiction to games, computer viruses, privacy violation, etc.)” |
Support: “I show my child “child friendly” websites (library, songs, crafts, school website, etc.)” |
Dimensions of the internet parenting style (adapted from [8], p. 89).
Parenting style dimensions seem influenced by parents’ individual characteristics such as gender, instruction, beliefs, or prior experiences with digital technologies. For example, in Valcke et al. [8] study, mothers are more controlling but also warmer than fathers, both dimensions associated with an authoritative style. In other studies, younger fathers and those who use the Internet more frequently with their teenagers are higher in control [40]. Parental instruction and experiences with digital technologies are other important variables: higher educated parents are more involved and high in control, probably because higher instructional levels also correspond to greater parents’ competence with the Internet [8].
The first studies explored parenting styles related to Internet usage at home, but more recently other authors explored the influence of digital parenting styles on children’s usage of mobile devices (tablet and smartphone). Konok et al. [30] found that children (3–7 years old) who use the devices for more time every day have parents who are more permissive (e.g., they talk with children about applications on devices, but have low levels of demandingness), more authoritative (e.g., they give time limits, but they do not block the use because they expect the child to regulate himself), and less authoritarian (i.e., the parent restricts and prohibits mobile use). Interestingly, these parenting styles are also associated with parental beliefs about positive/negative consequences of early media usage: parents who have higher permissive or authoritative digital style declared more beneficial (i.e., skill improvement, entertainment, and early learning of digital skills) than negative effects (i.e., reduced time for other activities, developmental problems, and danger/addiction) for children’s mobile usage.
Digital parenting styles change also according to children’s characteristics, such as age [41], self-esteem [42], emotion regulation [43], or behavioral problems [44] that can intervene, mediating the link between parenting and children’s actual behavior with digital technologies. Particularly, styles vary and accommodate with children’s age: authoritative parents during infancy become more permissive with older children [41]. Overall, these findings reappraise the idea that there is a linear, cause-effect relationship between parenting and child outcomes on digital behaviors, but bidirectional and transactional parent-child influences [45] should be considered.
Alternatively to digital parenting styles, many researchers adopted parental mediation as perspective for exploring parental influences on children’s digital behaviors. Parental mediation refers to “the diverse practices through which parents try to manage and regulate their children’s experiences with the media” ([7], p. 7). Parental mediation strategies were initially introduced in empirical studies as a potential factor influencing children’s use of television [46] and videogames [47]. These studies, exploring how parents can effectively reduce excessive exposure or enhance children’s self-regulated behaviors, inspired the following researches on digital technologies. Actually in literature two broad mediation approaches are distinct: enabling (or instructive) mediation and restrictive mediation [16]. These strategies are only partially similar to those parents who adopt “traditional” media: for example, co-viewing is a mediation strategy generally applied to television use [48], but it is difficult to apply it to portable media (particularly, smartphone and tablet) that children often use alone or outside the home environment. As a consequence, parents can feel worried because they cannot effectively control their children’s media use and involvement in digital life [11, 49].
The (a) enabling mediation is also defined as “active” or “instructive mediation” in that parents engage different activities with the aim to enhance their child’s appropriate use of the digital technologies: for example, they explain to him/her how to use a media device, talk about the contents of new app/websites, or play a videogame together (co-use mediation). Nevertheless, in many empirical studies, (b) co-use (or co-viewing mediation) does not imply parent-child conversations, but the parent is present when the child displays the activity with the media without discussing the content [13]. The (c) restrictive mediation is characterized by a strict attention to rules and control to the child’s digital activities: for example, parents decide when the child can have his/her tablet, pose time restrictions, or react when the child uses the smartphone too long. The (d) technical restriction is a particular kind of restrictive approach adopting software applications or other technical tools to control the child’s activities (e.g., installing filters on PC for children’s safety). Nevertheless, parents rarely use them and declare they prefer child-directed strategies, such as giving explanations or sharing the device [6].
Active mediation is the most frequent approach adopted in European families with 9–16 years old children, whereas restrictive mediation strategies are more common with younger children [16]. Interestingly, when children are interviewed about the mediation approach adopted in the family, they agree with their parents’ responses [12].
All mediation strategies are linked with changes in children’s digital behaviors, for example, less time exposure with online activities [12], or reduction of negative outcomes (i.e., aggressive behaviors, overuse, etc.; see [50]), but their efficacy is relative and it changes as a function of the child’s development (i.e., age and digital skills) and his/her actual activity with media. Active mediation is linked with positive outcomes (such as social and cognitive skills), particularly with younger children (0–3 ages): for example, during video/movie watching, parents stimulate attention, comment, or pose questions to children, giving them occasions for language exposure and cognitive and digital learning [51]. Nevertheless, we cannot link children’s outcomes uniquely to a distinct mediation strategy, since parent-child interactions are complex and many contextual or individual factors can intervene. Parents often use a combination of mediation strategies, and they change the mediation approach according to the activity the child is doing (e.g., using the tablet for school homework or for visiting Facebook; [11]).
Other authors explored the influence of family sociocultural factors. For mediation to be effective to guide children’s experiences in the web, parents need to have themselves knowledge and skills of the new digital media (see Section 4 in this chapter). Particularly in conditions of sociocultural disadvantage, parents may lack basic digital skills [52], or they may not be able to explain to children how digital reality works and rapidly changes [53]. Unlike the traditional media (such as television or video game console), parents can give a difficult task to assure a help or guide children with the ever-changing technologies. Recently, Nikken and Opree [11] found that mostly low-educated, low-income, and single parents are likely to experience low competence and greater insecurity with new devices (such as electronic screen), declaring that it is difficult to apply co-use or active mediation strategies with their young children (1–9 ages). In addition, Warren and Aloia [49] found that when parents perceive high stress levels, the restrictive mediation and the discussions with children about contents and the use of media increase.
Parental mediation strategies may change according to their child’s age and his/her digital skills, but longitudinal studies are scarce in literature. Developmental changes have been observed from childhood to adolescence: active mediation strategies more often are adopted with younger children, whereas restrictive mediation fades with older and adolescents [17]. Parents generally expect greater autonomy and self-regulation skills from adolescents, and the influence of some parental strategies decrease over time: for example, the efficacy of restrictive strategies (i.e., rules for time or negative consequences for overuse) in reducing screen time decreases with older children [33]. From a developmental perspective, particularly the effects of restrictive approach are unclear. Some studies evidence that restrictive strategies (such as limiting access to media) are effective with younger children [6], but not with older kids. Adolescents can perceive parental control/limitations as a violation of their needs (i.e., self-determination, privacy, peer relationships, etc.) and react with increased online activities [54].
After all, parents wish their children can develop self-regulation, critical view, and awareness of opportunities or risks of digital technologies. In many studies, parental active mediation—for example, discussing with children issues such as cyberbullying, sexting, and online frauds—is more effective than restrictive mediation in reducing risks [16, 55]. Conversely, the efficacy of restrictive mediation must be considered relatively, since in literature both positive and negative associations with online risks emerge [56]. Mascheroni et al. [57] comment, “While restrictive mediation can be effective in reducing children’s exposure to online risks, it has numerous side-effects, because it limits children’s opportunities to develop digital literacy and build resilience and discourages children’s agency within the child-parent relationship. Enabling mediation, instead, encompasses a set of mediation practices (including co-use, active mediation of internet safety, monitoring and technical restrictions such as parental controls) that are aimed at empowering children and supporting their active engagement with online media. The question is, then, how to ensure children’s access to online opportunities while protecting them from potential harmful effects.”
Interestingly, parents adopt their approach according to their child’s competence in digital technology use (digital literacy). In line with a bidirectional model of parent-child influences [45], not only parenting influences child’s behaviors, but also the child’s actual behavior or perceived digital competence influences parental behaviors. Generally, restrictive mediation strategies are more often adopted with less digitally skilled children, but this approach could be counterproductive: limiting online activities for protecting the child from risks, in turn, can deprive him/her to opportunities for developing adequate digital skills [5]. Conversely, parents more often use active mediation strategies (e.g., they share experiences or talk about media) with skilled children than with children who have scarce competencies [58].
The predominance of online activities in the life of many children often worries parents, who observe that spending much time online removes children from face-to-face relationships and social activities. Empirical studies confirm the negative effects of Internet unsuitable use on social participation, since high levels of online activities are associated with few friends, reduced offline relationships [59], and increased loneliness [60]. Particularly loneliness, that is, social isolation and lack of intimacy with close friends, was found to be strongly associated with Internet excessive use [61]. However, causal relationship between Internet excessive use and loneliness is still under investigation [62], in an attempt to understand if loneliness can be the antecedent or the consequence of the individual’s excessive involvement with Internet activities. Two alternative hypotheses have been proposed to explain the link between poor social involvement, feeling lonely, and the development of problematic Internet use in children. According to the first hypothesis, loneliness is one of the main antecedents of excessive online activities, together with low self-esteem, poor social skills, social anxiety, and frequent conflict with parents. Some authors (e.g., [63]) hypothesized that adolescents who feel lonely or experience high anxiety in face-to-face social situations may use social networks and online exchanges more frequently than non-lonely adolescents. According to this “compensation hypothesis,” they are increasingly involved in Internet activities that provide alternative experiences for social life. The second hypothesis assumes that time spent online causes loneliness and social withdrawal, isolating and depriving people of real social experiences. Therefore, loneliness can be considered as a possible outcome of Internet overuse [64], like when prolonged activities online reduce time spent with family and friends. Finally, there are studies that did not confirm the link between loneliness and Internet problematic use [65] or that evidence some positive consequences on individual socioemotional well-being. For example, contradicting the assumption that using the web impoverishes social life and increases isolation, in some studies higher levels of Internet activities are positively associated with social connection and perceived support. Unfortunately studies with children and adolescents are still lacking, but the attention among researchers is growing [60, 66].
Given the paucity of research with adolescents, we conducted an unpublished study1 to explore the relationships among excessive Internet use, preferred online activities, and adolescent’s perceived loneliness. In addition, we hypothesized that among adolescents better parent-child communication and higher parental emotional availability were positively related with less time spent online and less frequent online activities. In fact, studies indicate that parent-child communication and parental involvement play a protective role to excessive online activities [67]. A community sample of 177 high school students (66% females), aged 16–22 years old (M = 18, DS = 1.01), completed a questionnaire measuring the sense of loneliness (UCLA Loneliness Scale; [68]) and the Compulsive Internet Use2 Scale (CIUS, [69]) for assessing problematic involvement in Internet activities. Daily frequency of favorite online activities (chatting, e-mailing, visiting social networking sites, listening to music, watching videos, playing online games, etc.) was also measured. Regarding parenting factors, adolescents filled out (a) the Lum Emotional Availability of Parents questionnaire (LEAP; [71]) assessing adolescent’s perception of parental responsiveness, sensitivity, and emotional involvement and (b) two scales (derived from [70]) measuring the frequency of communication (how often the adolescent communicates with parents about his/her online activities) and the quality of parent-child communication (the adolescent feels understood, or comforted, or taking seriously from parents when he/she talks about Internet activities). In our study loneliness was not associated with Internet compulsive use (CIUS scores), but with specific online activities. Adolescents with higher loneliness levels reported higher frequency of music listening, but they declared less access to social networks (such as Facebook). This result contradicts the hypothesis of social compensation assuming that the teenagers use online exchanges to replace the sense of loneliness in real life [61]. An alternative explanation, proposed by others [72] is that a process downward with a “spiral pattern” is activated: loneliness leads to a decrease in social involvement which in turn increases the sense of isolation. Interestingly, those who spent more time online and were problematic users (higher CIUS scores) were more frequently involved in solitary activities, such as watching videos, listening to music, playing games offline, and visiting social networking sites. Perceived emotional availability from the father (but not from the mother) was negatively related with time that adolescents spent online. Teenagers who perceived greater emotional availability from both parents used the Internet more often for working on school projects and homework or doing search. A better quality of communication with parents is associated with less use of the Internet for gambling and online games. Overall these results confirm a virtuous relationship between quality of family communication, emotional availability of parents, and productive use of the web.
An interesting evidence emerging from empirical literature is the protective role of parent-child communication for preventing Internet unsuitable use in children [73]. Conversely, Internet excessive use is associated with low quality of communication in the family [74]. Particularly with teenagers, the open and effective parent-child communication is a key dimension of family relationships and climate. Assuming a bidirectional perspective of adolescent-child influences, some authors focus on the role of youths’ self-disclosure and spontaneous communication on parenting. Stattin and Kerr [75] claim that parental efforts to monitor adolescent’s activities or to discuss about them are ineffective if teenagers do not trust their parents and if they are not willing to open up spontaneously. Parental monitoring on children’s activities can be less effective when it is parent-driven (e.g., the parent tries to follow the child’s activities on Facebook) than when it is child-driven, that is, activated by children’s self-disclosure and open communication. Conversely, when parents try to control teenagers’ online communication (e.g., the friends on Facebook, the photos posted on Instagram, etc.), parent-child conflicts increase, and adolescents can perceive parental behaviors as an obstacle to their autonomy or an intrusion to privacy [76].
Van den Eijnden et al. [70] identify two key dimensions of parent-child communication about children’s digital behaviors. The first parenting practice refers to the frequency of communication about Internet usage (e.g., “How often do you and your parents talk about who you have Internet contact with?”), whereas the quality of communication about Internet use measures adolescent’s perception of mutual respect and acceptance during conversation (“When my parents and I talk about my Internet use, I feel taken seriously”). Authors explore how these parental behaviors, together with other Internet-specific parental practices (rules about time online, rules about contents, reactions to excessive use), link to compulsive Internet use (CIU) in adolescents. Findings from their longitudinal study are particularly interesting, showing a protective effect of the quality of communication, but not of frequency of communication, on the risk of developing CIU. In other words, a good quality of parent-child communication about the use of Internet decreased the risk of CIU (6 months later), whereas this relationship was not observed for the frequency of parent-child exchanges about adolescent’s online activities. Authors discuss these findings by highlighting the bidirectional nature of parent-child influences. When adolescents show compulsive Internet behaviors, the frequency of parent-child communication decreases. Probably gradually parents get discouraged and give up the idea of achieving a positive change in their child’s problematic behaviors through frequent conversations.
Regarding the parental rules about online activities, studies evidence some mixed results. When parents give their children rules about the content of the Internet, the compulsive use of web decreases; conversely, strict rules about time allowed for online activities seem to be counterproductive, linking to compulsive Internet behaviors in children [70]. Moreover, considering the child’s influences on parent’s behaviors, it is possible that when the child remains connected online without time limits, her/his behavior in turn stimulates stricter rules by parents. Other studies evidence that parental rules about Internet use are less influential on their children’s behaviors than their parents’ behaviors. Liu et al. [77] found that when parental behaviors are consistent with parental rules regarding digital technologies and the Internet (e.g., the smartphone must not be used during mealtime, personal data cannot be given online, etc.), the rules negatively predict Internet problematic use in adolescents. This result reminds us the importance of educational consistency (i.e., rule-behavior agreement) from parents. Conversely, when parental rules and parental behaviors do not agree, only the parents’ behaviors are positively predictive of children’s excessive Internet use. According to social learning theory [78], a parental modeling process intervenes, that is, an observational learning in which the parent’s behavior acts as antecedent for similar behavior in the child. Therefore, parents act as a role model for their children’s digital behaviors, and young children learn how and under what circumstances to use a mobile, for example, the smartphone, observing parents’ activities with that device. Interestingly, studies show that the time parents spend with computers positively relates with time spent by their children [79]. Similarly, parental involvement in favorite Internet activities (visiting social networking sites, video streaming, etc.) is positively associated with the same activities engaged by children. In addition, as some researchers remind us “it is not only overt parental behavior (i.e., digital device use) but also attitudes and emotions that can be modelled for children to imitate” ([30], p. 4). Taken together, these findings suggest that parents’ agreement and modeling of adequate behaviors are crucial factors for promoting self-regulation and safety use of digital technologies in young children.
Today’s reality is widely digitized, and it offers people of all ages opportunities for socialization, amusement, learning, job, and knowledge that were unthinkable until a few decades ago. Precisely in the weeks in which the authors were engaged in the revision of this chapter, COVID-19 pandemic was involving more than 130 countries in the world. The lockdown and restrictions at home quickly changed daily activities of children and parents, transferring to the screen of the devices many activities previously carried outdoor (school lessons, play with peers, etc.). It is still too early to know what impact the epidemic will have on children’s physical and mental health, but the attention of professionals and researchers is not lacking [80]. Surely during COVID-19 screen time has increased exponentially in the families: in some ways for the parents it was a relief, because through the Internet children continued their school courses and contact with peers. In addition, children avoided boredom through videogames or website dedicated to music, creativity, etc. On the other hand, the intensive online activities have renewed parents’ concerns about the well-known risks [23, 81], such as increased sedentary and physical inactivity, prolonged use at night, sleep disorders, isolation, and escape in digital world by teenagers.
Following social distancing and the temporary closure of schools for limiting COVID-19 infection, the Ministries of Education in many developed countries quickly activated online courses and other websites for distance learning. These online solutions have the aim to guarantee children’s right of instruction but also to mitigate the negative effects of home confinement [82]. However, online courses shift the teaching from school to home and make the parents a resource for support and effective learning. The question is: what can be the role of parental mediation and digital competence? As the authors know, there are no empirical studies on this topic, but previous studies with primary school children showed negative associations between parental control, interference in homework, and children’s learning [83]. Currently, in many cases teachers expect parents to ensure that their children connect on time and follow the video lessons, so parental support could be useful, but tensions and parent-child conflicts can also occur. There is also the risk that parents may help children, interfering with digital learning or impeding them from carrying out the assigned activities independently. Close attention and research effort are needed for comprehending how this aspect of digital parenting works, supporting parents in their efforts and ensuring a good home learning to children.
In line with the available studies before COVID-19 [4], we believe that during lockdown the digital activities satisfy children’s basic psychological needs, such as socialization and emotional support by the family (grandparents and cousins) and other significant people (teachers and peers). Social media facilitate the expression of emotions (such as fear and sadness), self-disclosure, and the keeping of romantic relationships by adolescents particularly [84]. Video calling and regular contacts through smartphone have been recommended as an important source of reassurance in the cases of isolation of the caregiver or family due to prevention of COVID-19 infection or recovery [85].
What probably becomes necessary in the time of COVID-19 is a renegotiation of family routines, that is, a balance between screen time and other moments of family life. In this regard, the WHO [85] recommends that parents maintain regular routines for children (school/learning, free time/relaxing, bedtime, etc.) and also to create new opportunities for joint activities (such as co-use for creative, amusing, or physical activity in front of the screen). With young children, many shared activities offer also a context to express and communicate their feelings (both fears and wishes) in a supportive parental relationship. Even in actual COVID-19 circumstances, we believe that parental behaviors (such as self-limiting screen time for smart working, chatting, or gaming) are more influential than restrictive mediation or limitations imposed to children.
Having the digital knowledge and the skills to move in the digital world, without suffering the dangers, is not a matter of age, but of education and learning, that is, digital literacy. It is a serious responsibility towards the new generations and a complex challenge for which the adults (parents, teachers, psychologists, or educators) do not feel prepared. As Martin ([86], p. 135) reminds us: “Digital literacy is the awareness, attitude and ability of individuals to appropriately use digital tools and facilities to identify, access, manage, integrate, evaluate, analyze and synthesize digital resources, construct new knowledge, create media expressions, and communicate with others, in the context of specific life situations, in order to enable constructive social action; and to reflect upon this process.” Currently, parents’ difficulties stem from the fact that they—as digital users—have different levels of involvement, technical skills, and beliefs that influence mediation practices towards their children. If parents feel less skilled or worry about unknown dangers of the web, they could activate more restrictive practices, but rarely they will be able to critically discuss with their children in a constructive manner. In addition, parents believe not to be up to their children in juggling in the digital world, in pursuing technological innovations, or in protecting children from danger or media abuse. Sometimes parents consult the websites for suggestions on how to effectively manage kids in their digital activities, but information disseminated through the websites is not always scientifically founded (fake news). The researcher Danah Boyd [87], in describing the complexity (“It’s complicated”) of teenagers’ life on the web, claims that the media magnify the virtues (the “superpowers”) of digital natives, but at the same time they trigger parental fears talking about serious dangers such as Internet addiction, sexual enticement, or incitement to suicide. Conversely, rarely parents turn to professionals for advice. A study [28] conducted with families of very young children (under 7 years) shows that parents choose the type of help (professionals such as pediatricians, or friends and family) based on the child’s problems and his/her digital activities. The professionals are consulted if the child is an only son or he/she uses the media too long. Parental sense of competence in managing the child’s activities increases if parents are confident of the usefulness of the media (e.g., educational games for learning) and if there are more kids in the family. Parents turn to friends and family for advice when they have a negative view of the effects of the media. This result makes us reflect, but unfortunately there are not many similar studies.
A correct parental mediation of children’s digital activity must build on the information and recommendations that come from the scientific community. The American Academy of Pediatrics [2] has taken a clear stance for prudent and moderate use of the web in infancy (0–5 years) and has prohibited touchscreen device use under the age of 2. The careful use of these devices at such an early age is crucial for the infants’ brain and social development. However, in contrast to these professional recommendations, often parents themselves introduce babies to media use during infancy (e.g., to “take calm” the kid, or to stop whims and cry; [30]). Young children spent daily an amount of time with screen media (iPod, smartphone, video game player, etc.) that grows during infancy (42 min under 2 years and 2 h/39 min at 2–4 years, respectively; [88]). The risks for excessive screen exposure are extensively confirmed in literature and particularly the negative consequences for early users who may present physical problems (such as obesity), developmental difficulties (i.e., language or learning), and unhealthy routines (low sleep quality) (Figure 1).
Developmental risks associated with excessive media exposure (from [88]).
The recommendations for effective parental mediation on children’s digital activities are unequivocal [2]: (a) avoid the use of digital devices before 18–24 months with the exception of video chatting in the presence of the parent; (b) do not allow the child (18–24 months older) to use the devices alone and for more than 1 h a day; (c) do not press for an early use, the child will spontaneously approach the media when ready; (d) help the child apply what he/she learns from using the device to the real world; (e) know that in infancy, direct experiences, manipulation, and unstructured play are crucial for the child’s brain and for social, cognitive, and linguistic development; (f) void the vision of fast programs, with too many distracting elements, or violent contents that the child is unable to understand; (g) avoid using devices to calm the baby, an hour before bedtime; and (h) constantly monitor the media contents to which the child is exposed. Finally, the experts (pediatricians and psychologists) turn also to the industry that produces media devices, so that it adopts a scientifically founded and more ethical approach, for example, installing apps (such as connection stop or automatic shutdown during night hours) that can protect very young children from the risks of overuse.
Therefore, parent education interventions are necessary both to disseminate scientific knowledge on the influence of new technologies on children’s health and development and to help parents to cope with the challenges of digital reality. Parent education cannot be reduced to merely correcting ineffective parenting practices or to a list of instructions on what the parent should do. In fact, all studies indicate that the effectiveness of mediation strategies (restrictive or active approach) is relative, because parental practices interact with the characteristics of both adults (digital skills, beliefs, and activities on the media) and children (age, development, digital literacy skills, etc.). Instead, professionals should help parents to improve and adjust their guidance according to children’s age and developing skills. This is possible to be realized if parents also increase their knowledge and digital skills (media literacy programs), given the importance of these factors in parenting. Less skilled parents, or those who fear the unknown pitfalls of the web, are more likely to intervene only on restricting or prohibiting children’s activities. Conversely, “it is likely that more skilled children and parents are more free to explore and benefit from online opportunities, while also building up resilience against harm by meeting a degree of online risk” ([16], p. 19).
Digital parenting is a very complex and “complicated” task not only because the digital technologies rapidly change, but also because they offer children multiple experiences (learning, communication, socialization, entertainment, etc.) that influence their development, but which are not entirely overlapping to the experiences that take place in the real environment [89]. Particularly, digital natives have the opportunity to know the reality and themselves, developing their own identity [76], with a multiplicity of means and without the supervision of the traditional agents of socialization, primarily the parents (or the teachers). With the awareness of how difficult it is to give definitive answers about the advantages or dangers of digital technologies, more effort is needed from researchers. More evidence-based studies are needed, to understand how technological progress is changing the psychological (neurocognitive, emotional, and social) development of young digital users. However, despite the growing diffusion of digital tools in infancy, studies with very young children are still lacking. Particularly, future research could benefit from longitudinal studies to which to explore the relationships between parenting and children’s experiences in digital environments, their opportunities, or risks.
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