1. Introduction to modeling and simulation of heat transfer
In recent times, numerical modeling and simulation techniques have been increasingly applied to the problems of heat transfer. Various studies have been carried out utilizing the basic techniques and their modifications and/or customized variants to customize, operate, test, evaluate, optimize and judge the performance of experimental systems and actual engineering problems. Problems particularly related to engineering issues in the fields of energy [2], oil and gas, metallurgy [3], chemical, process and reaction engineering, fuel cell technologies, manufacturing technologies [2], nanotechnology [4, 5], and aerospace have been extensively studied.
This chapter enlists, describes, explains and elaborates with examples these techniques as applied to problems and practical scenarios of heat transfer.
2. Basic techniques of modeling and simulation
Modeling and simulation, like any other field of science and technology has some certain basic techniques using which all practices are carried out. These are the foundation stones on which the building of modeling and simulation practices and procedures is built.
2.1. Introduction
Various techniques have evolved in modeling and simulation since its inception [6] for the solution of technical and engineering problems, ranging from ancient Roman military techniques to classical analog methods to modern Runge – Kutta method and Monte Carlo techniques. [7]. The history of modeling and simulation dates back to ancient times. It was first used by ancient Romans to simulate the actual war conditions in areas of peace to train its soldiers to fight in areas where they have never been. These war games were based upon very well and adequately designed models. Later, techniques of modeling and simulation were used by artists and scientists to test their designs of statuary or edifices during the age of the Renaissance (1200 – 1600 C.E). The renowned Leonardo da Vinci, extensively made use of techniques of modeling and simulation to test and validate his models in art, military, and civil works. [7]. Chess, also known as the world’s first war game and its evolution in to a computer game is a result of rigorous use of techniques of modeling and simulation [8]. Similarly, war games (a technique of modeling and simulation) were used in Europe (Prussia, modern-day northeastern Germany) and same was used by Army Corps of Engineers in the United States [9]. In technical fields, the first successful use is reported in the production and use of “Link Flight Simulator”, which was patented in 1929 by the American Edward Link. [10]. SAGE – semi, automated ground environment (1949);, MEW – Microwave early warning (1950) [11];, “Whirlwind”, MIT,
2.2. Energy minimization
Energy minimization (also called energy optimization or geometry optimization) methods are numerical procedures for finding a minimum on the potential energy surface/state starting from a higher energy initial structure/state [1, 14]. These are extensively used in chemistry, mathematics, computer science, image processing, biology, metallurgical engineering, materials science, mechanical engineering, chemical engineering, electrical engineering etc. to find the stable/equilibrium states of molecules, solids, and items. Extensive studies have been carried out in various fields making use of energy minimization techniques to formulate models highlighting the importance, significance, and use of this method in modeling and simulation and solution of engineering problems.
Levitt [12] used energy minimization to formulate solutions of protein folding. The potential energy functions used are detailed and include terms that allow bond stretching, bond angle bending, bond twisting, van der Waals’ forces, and hydrogen bonds. A unique feature of the methods used includes easy approach for restrained energy minimization work (including all terms) to anneal the conformations and reduce their energies further. The methods used were very versatile and were proposed to be applicable for building models of protein conformations that have low energy values and obey a wide variety of restraints. Recently, Micheletti and Maritan, [13] also used energy minimization methods to formulate solutions of protein design. They went a step further in their approach, and defined actual real-world scenarios and formulated alternative design strategies based upon correct treatment of free energy. Sutton [14] presented the use of energy minimization methods to determine the solution of atomic structures and solute concentration profiles at defects in elemental solids and substitutional alloys as a function of temperature. He used mean field approximation, rewrote free energy, used Einstein models and auto-correlation approximation and showed that the better statistical averaging of the auto-correlation approximation leads to better temperature – and concentration – dependent pair interactions. His formula was fairly simple and effective. Lwin [15] used spreadsheets to solve chemical equilibrium problems by Gibbs energy minimization.
Similarly, Olga Veksler during her PhD thesis at Cornell University [16] presented the use of energy minimization techniques in computer vision problems. She developed algorithms for several important classes of energy functions incorporating everywhere smooth, piecewise constant and piecewise smooth priors. These algorithms primarily rely on graph cuts as an optimization technique. For a certain everywhere smooth prior, an algorithm based on finding the exact minimum by computing a single graph cut was developed. For piecewise smooth priors, two approximate iterative algorithms, computing several graph cuts at each iteration, were developed and for certain piecewise constant prior, same algorithms were used along with a new one which finds a local minimum in yet another move space. The approach was quite effective on image restoration, stereo, and motion. [16]. Similar studies were carried out later as well to further test and evaluate energy minimization in computer vision [17, 19]. Nikolova [20] explained the use of energy minimization methods in the field of image analysis and processing. Onofrio and Tubaro applied the same to the problem of three-dimensional (3D) face recognition [21]. Standard [22] explained the use of energy minimization to determine the states for a molecule in chemistry; he explained that the geometry of molecule is changed in a stepwise fashion so that the energy is reduced to lowest minimum.
Figure 1 shows energy minimization process for a molecule in steps. “
There are other methods for actually varying the geometry to find the minimum [22]. Many of these, which are used to find a minimum on the potential energy surface of a molecule, use an iterative formula to work in a step wise fashion. These are all based on formulas of the following type:
where,
2.2.1. Newton Raphson method
The correction term depends on both the first derivative (also called the slope or gradient) of the potential energy surface at the current geometry and also on the second derivative (also called the curvature). The Newton Raphson method involves fewest steps to reach the minimum.
2.2.2. Steepest descent method
This is a method which relies on an approximation. In this method, the second derivative is assumed to be a constant.
where γ is a constant. In this method, the gradient at each point is again calculated. Because of the approximation, it is not efficient, so more steps are required to find the minimum. [22]
2.2.3. Conjugate gradient method
2.2.4. Simplex method
In the Simplex Method, the energies at the initial geometry and two neighboring geometries on the potential energy surface are calculated (points A, B, and C in Fig. 2).
2.3. Molecular Dynamics (MD) simulations
Molecular dynamics (MD) is a technique in which physical movements of atoms and molecules is simulated using computers. In this the atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms. MD simulation circumvents the problem of finding the properties of complex molecular systems by using numerical methods. In the most common version, the trajectories of molecules and atoms are determined by numerically solving Newton’s equations of motion for a system of interacting particles [1, 23]. This is one of the two main families of simulation techniques [23]. The results of molecular dynamics simulation can be used in various fields such as thermodynamics, biology, chemistry, materials science and engineering, statistical mechanics and nanotechnology [1, 24, 25].
van Gunsteren, [26] explained in detail about methodology, applications and prospective of molecular dynamics in chemistry. He effectively explained molecular dynamics in terms of choosing unavoidable assumptions, approximations and simplifications of the molecular model and computational procedure such that their contributions to the overall inaccuracy are of comparable size, without affecting – significantly the property of interest.
Kupka [30] applied molecular dynamics in computer-based graphic accelerators. He proposed an algorithm consisting of CPU and GPU parts, The CPU part is responsible for streams preparations and running kernel functions from the GPU part, while the GPU part consists of two kernels and one reduce function.
A very nice study about molecular dynamics simulation for heat transfer problems is given by Maruyama [31]. He also applied MD simulations to the problem of heat conduction of finite length single walled-carbon nanotubes [32]. The measured thermal conductivity did not converge to a finite value with increase in tube length up to 404 nm, but an interesting power law relation was observed.
Wang and Xu applied MD techniques to problems of heat transfer and phase change during laser matter interaction [33]. They irradiated argon crystal by a picoseconds pulsed laser and investigated the phenomena using molecular dynamics simulations. Result reveals transition region, superheating, and rapid movement of solid-liquid interface and vapors during phase change. Lin and Hu [34] applied the same techniques to the problems of ablation and bio heat transfer in bimolecular systems and biotissues and developed a new model.
Krivtsov, [35] discussed the problems of heat conductivity in monocrystalline materials with defects via molecular dynamics simulation. “
He also applied the same technique for determining and simulating the mechanical properties of polycrystals as well earlier. [36]. Recently, Steinhauser applied molecular dynamics simulation technique to various condensed matter forms [37]. He showed how semi flexibility or stiffness of polymers can be included in the potentials describing the interactions of particles in proteins and biomolecules. For ceramics he modeled the brittle failure behavior of a typical ceramic and simulated explicitly the set-up of corresponding high-speed impact experiments. It was shown that this multiscale particle model reproduces the macroscopic physics of shock wave propagation in brittle materials very well while at the same time allowing for a resolution of the material on the microscale.
2.4. Monte Carlo (MC) simulations
Monte Carlo (MC) methods/simulations are a set of simulation techniques that rely on repeated random sampling to compute their results. They are often used in computer simulations of physical and mathematical systems. These are also used to complement theoretical derivations. Monte Carlo methods are especially useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures. They are widely used in business (calculation of risk), mathematics, (evaluate multidimensional definite integrals), Space exploration, and oil exploration (predictions of failures, cost overruns and schedule overruns) [1, 38].
Howell [39] explained in detail the use of Monte Carlo method in radiative heat transfer problems. He used the method for computations of complex geometries, configurations, and exchange factors, inverse design, packed beds, and fiber layers, etc., and also explained the use of related algorithms (READ, REM, Markov Chains, etc.). A similar study was also conducted by Zeeb [40] and Kersch (1993) [41]. Modest [42] used various implementations of the backward Monte Carlo method for problems with arbitrary radiation sources. His focus area was backward Monte Carlo simulation. He included small collimated beams, point sources, etc., in media of arbitrary optical thickness and solved radiative heat transfer equation with specified internal source and boundary intensity.
Frijns et al. [43] used Monte Carlo simulation to discuss and solve problems of heat transfer in micro and nanochannels. They proposed and utilized a combination algorithm of Monte Carlo and molecular dynamics simulation to argue about its effectiveness.
Steps of performing simulation are: I) define an initial condition. II) Assign particles to MD or MC part. III) Distribute over MD and MC codes. IV) Compute new positions and velocities. V) Update the particles in the buffer layer. VI) Start over with step III.
An extensive use of Monte Carlo in gas flow problems is explained by Wang and co-workers [44, 45, 46]. They used direct simulation MC for simulation of gas flows in MEMS devices. They examined orifice and corner flow using modified DSMC codes and showed that the channel geometry significantly affects the micro gas flow [44]. For orifice flow, the flow separation occurred at very small Reynolds numbers while in corner flow, no flow separation occurred even with a high driving pressure. The results were found to have good agreement with continuum theory and existing experimental data. In a later study, they used the same methods to discuss and solve the problem of gas mixing in micro channels [45]. Very high Knudsen numbers were used. The simulation results show that the wall characteristics have little effect on the mixing length. The mixing length is nearly inversely proportional to the gas temperature. The dimensionless mixing coefficient is proportional to the Mach number and inversely proportional to the Knudsen number. They also extended the use of their codes to heat transfer and gas flow problems in vacuum-packaged MEMS devices [46] and found to have good results in explaining the heat transfer and gas flow behavior on chip surfaces.
2.5. Langevin dynamics
Langevin dynamics is an approach to the mathematical modeling of the dynamics of molecular systems. The approach is characterized by the use of simplified models while accounting for omitted degrees of freedom by the use of stochastic differential equations. [1]. In philosophy, the Langevin equation is a stochastic differential equation in which two force terms have been added to Newton’s second law to approximate the effects of neglected degrees of freedom. One term represents a frictional force, the other a
Quigley [50] discussed the advantages of using LD in constant pressure extended systems and showed it to be effective technique for simulating the equilibrium isobaric–isothermal ensemble. They analyzed canonical ensemble, Hoover ensemble, and Parrinello–Rahman ensemble and showed that despite the presence of intrinsic probability gradients in this system, a Langevin dynamics approach samples the extended phase space in the correct fashion. Wu, Li and Nies [51] applied Langevin dynamics method to the problem of cross-linking into polymer networks. Commercially available software package GROMACS 4.0 was used for simulation. Their study revealed that cross-linking is associated with effects such as changes in thermodynamic stability of reacting mixture or the presence of nanoparticles. This also facilitated the study of macromolecules.
2.6. Normal mode (harmonic) analysis
Normal mode (harmonic) analysis is a method of simulation in which the characteristic vibrations of an energy-minimized system and the corresponding frequencies are determined assuming its energy function is harmonic in all degrees of freedom. Normal mode analysis is less expensive than MD simulation, but requires much more memory [52]. These are extensively used in science and engineering to model, simulate and solve engineering problems. Magyari [53] used this method to examine the convection model of the fully developed flow in a differentially heated vertical slot with open to capped ends. He found that the method is quite transparent and has algebraic and computational efficiency. It is shown that dimensionless temperature field and the velocity field scaled by the Grashof number are characterized by only two physical parameters; also, capped slot is an ideal heat transfer device. Schuyler et al., [54] used the same method to Cα – based elastic network model (Cα – NMA) of protein analysis and “
2.7. Stimulated annealing
3. Modeling and simulation of heat transfer — Applications
Modeling and simulation of heat transfer phenomena is the subject matter of various recent studies in many technical and/or engineering applications. It has helped a great deal in operation, achieving enhanced results, increasing efficiency, and optimizing processes. It is one of the basic engineering techniques used in analysis of engineering problems/processes during initial steps/stages of design. This section highlights this significance of heat transfer in various engineering applications via modeling and simulation approach.
3.1. Introduction
Heat transfer analysis has made its distinct position among engineering analyses carried out for any technical/engineering problem/application at first hand. Providing initial data, it paves the way for in-depth analysis and incursion into the problem solving technical intimacies. Its use has gained more importance and popularity especially after the introduction of computer/simulation techniques [2, 3]. Ironically, its use started in complex engineering problems such as determining the heat transfer profile of single crystal turbine blades, determining heat transfer coefficients for material(s) in tube and shells heat exchangers for measuring and enhancing process efficiency [3] and then extended to simpler situation and scenarios.
3.2. Modelling & simulation of heat transfer in process industry
Process industry is one of the major industries that utilise heat transfer and thermodynamic studies to operate and optimize its processes. Equipment such as Heat Exchangers, Boilers, Evaporators, Dryers, Condensers, Ovens, Reboilers, etc., rely and heavily make use of heat transfer studies for their optimum and efficient operation. Several tools such as FLUENT, Modelica, FEMLAB, APROS (Powerful dynamic simulation), BALAS (Conceptual process design), ChemSheet (Process Chemistry), KilnSimu (Rotary Kiln Simulator), etc., are being frequently used to model and simulate the process engineering parameters of different units/unit operations [58].
3.2.1. Boilers
Heat transfer of boilers is extensively studied as it helps immensely in finding the parameters and determining the process efficiency of equipment as well as suggesting its design improvement. Bordbar and Hyppänen [59] explained the use of modeling for problem of radiation heat transfer in a boiler furnace. Temperature and heat flux within the furnace and on the heat surfaces was investigated. They used CFD method for solving velocity field of combusted fuel from the burner using some empirical equations and found that use of CFD on the model developed conforms to measured data and greatly helps in achieving the results.
Earlier, Zeeb [60] used the Monte Carlo method to study the same problem in axisymmetric furnace and got good results. Gómez, Fueyo and Díez, used the same CFD method to solve a model for the calculation of “
In this study, the object function to be optimized takes the weight of the boiler and its dynamic capability into account. “
3.2.2. Heat exchanger
Heat transfer and its modeling and simulation for heat exchangers have been nicely reported in various excellent studies. Dafe., [64] presented the use of FLUENT for CFD codes used to solve problems of heat transfer in plate heat exchangers. The work was carried out to determine the effect of channel geometry and flow conditions on the heat transfer. Two PHE’s, one with wave geometry and the other with chevron design were studied. Temperature of the wall was kept constant, water was used as the working fluid, and the mass flow rate varied to study the effect of Reynolds number. Simulated Reynolds number range is 100 – 25, 600.
It was efficiently shown that choice of PHE geometry is a strong function of application. Convective design is shown to give better convective properties for low Reynolds number applications while at higher Reynolds numbers chevron design gives better convective properties. Tomas et al., [65] described the use of object-oriented heat exchanger models for simulation of fluid property transitions. The models were written in Modelica. Three models were developed and employed, namely, Model 1: instantaneous property change; Model 2: Ideally mixed volume; Model 3: Transition port delay. Simulations showed that Model 3 is the best for determining computational performance as well as affording flexibility in fluid dispersion modeling. Othman, et al. [66] used CFD as a tool in solving and analyzing problems of heat transfer in shell and tube heat exchanger. Gambit 2.4 was used as tool for simulation. Same experimental parameters at constant mass flow rate of cold water varying with mass flow rate at 0.0151 kg/s, 0.0161 kg/s and 0.0168 kg/s of hot water were used. The CFD model is validated by comparison to the experimental results within 15% error.
3.2.3. Condensers
Heat transfer in condensers is vastly discussed and has been in practice since long for solving efficiency problems and determining process parameters. Various research and industrial studies have explained the use and application of heat transfer via modeling for condensers. Corberan and Melon [67] developed a model to predict the behavior of the finned tube condenser and evaporators that work with R-134a. For simulation of evaporator and condenser, many of the phase change heat transfer coefficient correlations are considered and the most recommended correlations are used. The experimental study to validate the model has been carried out in a small air-conditioning unit with cross-flow air refrigerant type heat exchangers. The model is capable of predicting the heat transfer of an evaporator or condenser with accuracy of ±5% in the studied range. Qureshi et al. [68] developed a mathematical model of evaporative fluid coolers and evaporative condensers to perform a comprehensive design and rating analysis. A fouling model was used to investigate the risk based thermal performance of evaporative heat exchangers. It is solved by Engineering Equation Solver (EES). It showed “
3.2.4. Ovens
Therdthai, et al. [71] used 3D CFD modeling and simulation for the determination of temperature profiles and airflow patterns in continuous oven used for baking process. It was used to predict dynamic responses during continuous baking process.
Further aim of the work is to use numerical simulation for the choice of operating conditions and equipment design which was achieved nicely. Similarly, Sargolzaei et al. [73] applied 1D finite difference and 3D computational fluid dynamic models on the hamburger cooking process. Three different oven temperatures (114, 152, 204°C) and three different pressures (20, 332, 570 pa) were selected and nine experiments were performed. An optimum oven temperature in the range of 114°C to 204°C was proposed. Effect of oven temperature on weight loss is more than pressure. Decreasing oven temperature and increasing cooking time can increase uniformity of temperature distribution in the hamburger, and therefore, microbial safety will increase as well as product quality. The CFD-predicted results were in good agreement with the experimental results than the finite difference (FD) ones. But finite difference model was more economical due to longer time needed for CFD model to simulate (about 1 h). Several other authors used CFD codes for modeling and simulation of heat transfer problems in ovens and found them to be very effective in predicting the results and optimizing process. [74, 75]
3.3. Modeling and simulation of heat transfer in manufacturing industry
Heat transfer studies have also been extensively carried out in manufacturing engineering processes. The models developed, their simulations, and data generated from them have helped immensely in defining process parameters and increasing process efficiencies. Processes such as Casting, Welding, Machining, Powder Metallurgy, Forging, Rolling, Extrusion, Plastics forming have been extensively studied by heat transfer models to improve and optimize their performances. Various commercially available general – purpose and custom built software have been used to perform simulations.
3.3.1. Castings
Heat transfer and its modeling and simulation approach have been extensively applied to foundry technology and processes. Determination of time of solidification, prediction of solidification pattern and structure, improvement of gating system, furnace and mold design are the most important areas in which heat transfer has been applied. Sabau et al. [76] presented heat transfer analysis of direct chill (DC) cast process of ingot using boundary conditions.
The computed results were found in good agreement with experimental data paving the way for process operation, optimization and improvement. Ramírez-López et al. [78] discussed the problem of heat transfer and modeled it using C++ in continuous casting process. “
3.3.2. Welding
The application of heat transfer phenomena on welding and joining processes have been studied to check, determine and ascertain its effect on welding process, weld design, determination of weld structure and effect of process control parameters on weld formation. Hu et al. [80] described heat and mass transfer during gas metal arc welding using a unified comprehensive model. Based on this, a thorough investigation of the plasma arc characteristics during the gas metal arc welding process was conducted incorporating all parameters such as interactive coupling between arc plasma; melting of the electrode; droplet formation, detachment, transfer, and impingement onto the work piece; and weld pool dynamics. The assumed Gaussian distributions of the arc pressure, current and heat flux at the weld pool surface in the traditional models were shown not to be representative of the real distributions in the welding process. In the second part of this study [81], the transient melt-flow velocity and temperature distributions in the droplet and in the weld pool were calculated. They simulated the crater formation in weld pool as well as the solidification process in the electrode and in the weld pool after the current were turned off. The predicted droplet flight trajectory is in good agreement with published data. Takemori et. al. [82] studied the numerical simulation of the heat transfer on the compressor during the welding process. It is used to determinate housing and internal components temperatures of the compressor during the sealing welding. A lumped parameter model was used to study various welding variables initially. After that, the best welding process was analyzed in detail using a numerical solution of a 3D transient model. All the monitored temperatures during the simulation were found very close to the temperatures measured experimentally, thus validating the model. Daha, et al. [83] discussed the problem of heat transfer in keyhole plasma arc welding of dissimilar steel joints (2205 – A36) using 3D heat transfer and fluid flow model. An adaptive heat source is proposed as a heat source model for performing a non-linear transient thermal analysis. Temperature profiles and solidified weld pool geometry are presented for three different welding heat input. The reversed bugle shape parameters are proposed to successfully explain the observations. The model was also applied to keyhole plasma welding of 6.8 mm thick similar 2205 duplex stainless steel joint for validation. The simulation results were found in good agreement with independently obtained experimental data.
3.3.3. Machining
Machining processes have been studied by heat transfer methods and their use has increased lately with the introduction of modeling and simulation techniques. Their use has made easier the defining process, determining its parameters, driving its efficiency and optimization. Processes such as facing, turning, milling, shaping, grouching, honing have been modeled to investigate effect of process itself, material, lubricant, etc. as a function of heat transfer process. Åkerström [84] discussed the problem of heat transfer associated with thermo-mechanical forming of thin boron steel sheets into ultra-high strength components via modeling and simulation. The objective is to predict the shape accuracy, thickness distribution, and hardness distribution of the final component with high accuracy. Method based on multiple overlapping continuous cooling and compression experiments (MOCCCT) in combination with inverse modeling (mechanical response) and a model based on combined nucleation and growth rate equations (austenite decomposition) was developed and used. FE – code LS – DYNA was used for simulating these models. The results were compared for forming force, thickness distribution, hardness distribution, and shape accuracy/springback with experimental values and found to be in good agreement. Iqbal et al [85] discussed the problem of interface heat transfer coefficient for finite element modeling of high-speed machining. They used an improved heat transfer coefficient for heat generation and frictional contact, derived from an experimental setup, consisting of an uncoated cemented carbide pin rubbing against a steel workpiece while the latter was rotated at speeds similar to the cutting tests. This “pin-on disc” set-up had temperature and force monitoring equipment attached to it for measurements. Results show that the estimated interface heat transfer coefficient decreases at low rubbing speeds and then becomes approximately constant for high rubbing speeds. At these low rubbing speeds, the estimated values show a dependence on temperature. Interface heat transfer coefficient for a range of rubbing speeds of the dry sliding process is produced from modeling and simulation results and found to be in good agreement with experimental values. In a similar study [86], they used and developed a Lagrangian finite element code DEFORM 2D for studying same phenomena and found it to be useful. Ma et al. [87] discussed and applied FE analysis on thermal characteristics of Lathe Motorized Spindle. The structure feature of the spindle was introduced defining two major internal heat sources of motorized spindle with the aim to calculate the heat transfer coefficients of the major components of the lathe spindle.
3.3.4. Forming processes
Forming processes, in general, such as rolling, forging, extrusion have been vastly studied by heat transfer methods and their modeling and simulation. This comprises the main area of heat transfer application in metal forming industry and processes related to it. These studies have revealed in great detail the discrepancies (defect formation and its causes, energy inefficiency, etc.) in processes and helped increase their efficiency and optimization. Behrens [88] discussed the modeling and simulation of friction and heat transfer models in hot forging processes. Two representative forging tests were carried out; the forming load and surface temperature distribution were recorded incorporating effects such as prevailing normal stress and shear yield stress of the workpiece material, the temperature and surface roughness of the tool and workpiece as well as the relative sliding velocity. By means of these data, the models were appropriately extended and adjusted using the software FORGE ®.
The application of the extended models allows for a more accurate description of the interaction at the contact interface and delivers more realistic results. Rabbah et al. [89] explained the use of modeling and simulation of heat transfer along a cold rolling system.
3.4. Modeling and simulation of heat transfer in defense applications
Application of heat transfer phenomena in defense applications such as determination of efficiency of engines, their design and material design, performance, and selection; determination of heat transfer profiles of guns, barrels and shells; design and selection of suitable high-performance materials (composite structures and their design), etc., has been a major field of study. Many excellent studies explain in detail the application of heat transfer principles and their simulation approaches as applied to defense applications. Wu et al. [91] explained the phenomena of heat transfer in a 155 mm compound gun barrel cooled by midwall cooling channels.
3.5. Modeling and simulation of heat transfer in energy applications
Heat transfer via modeling and simulation has been rigorously applied in energy applications (energy generation and production methods) for process identification, operation, improvement and optimization. It has been applied in all areas of energy methods (source tapping, method determination and generation of power from source, conversion of power to energy and its distribution, etc.) and all field of energy generation and production (thermal, hydral, wind, geothermal, solar, fuel cell, nuclear, etc.) and has generated excellent results coupled with capital saving. Schimon et al. [97] modeled and simulated different components of power plant and associated heat transfer phenomena using Modelica. The heat transfer for the heat exchanger component was modeled by calculating the heat transfer coefficient in dependency on the flow velocity of the medium in the pipes. Dymola (a Modelica based tool) was used to perform simulations. The models were realized with time domain differential equations and algebraic equations. Bandyopadhyay [98] presented modeling and simulation of heat transfer phenomena in solar thermal power plants. Models developed were based on the fundamental conservation algebraic equations along with phenomenological laws and simple representative equipment characteristics whose simulations were carried out. Different detailed equipment characteristics including thermal stresses, time variations of components etc. were incorporated in the developed models and then were simulated for control and optimization. Ramousse et al. [99] presented a fuel cell model that takes into account heat transfer in MEA and bipolar plates along with gas diffusion in the porous electrodes, water diffusion, and electro-osmotic transport through the polymeric membrane. Heat and mass transfer phenomena in the cell are combined with
3.6. Modeling and simulation of heat transfer in miscellaneous applications
Apart from the above branches, heat transfer and its modeling and simulation is also applied in various other fields of engineering and technology such as electronics, environmental engineering, biomaterials and biomedical engineering, etc., to take advantage of process modeling, operation, and optimization. Guérin et al. [101] used finite volume approach to model and simulate the heat transfers between the different environmental elements to synthesize realistic winter sceneries. They simulated snow fall over the ground, as well as the conductive, convective, and radiative thermal transfers according to the variations of air and dew point temperatures, the amount of snow, cloud cover, and day-night cycles.
The model also takes into account the phase changes such as snow melting into water or water freezing into ice and yielded good results and inferences. Lakatoš et. al. (2006) [102] used FEMLAB to simulate heat transfer and electromagnetic fields for the development of protected microcomputer prototypes. Heat field was extended and simulated from heat sources inside a monitor case along with electromagnetic fields in electronic systems. The temperature dependence on time was interpreted along with value of steady temperature. Elwassif et. al. developed and used a bio heat transfer model for getting information on the thermal effects of DBS using finite element models to investigate the magnitude and spatial distribution of DBS-induced temperature changes. “
4. Conclusions
Heat transfer studies comprise an important part of engineering analysis for any system ranging from automotive to process to energy applications. These are first hand analyses in any engineering problem/application related directly and/or indirectly with heat. Lately, modeling and simulation techniques and use of high-speed computers have greatly facilitated the thermal and heat transfer related analysis. More and more models are being developed, tested and used to ease out the calculations involved in the process also yielding direct results and even predicting future trends and auxiliary data. The present chapter deal with and explained in detail this field of engineering in a rational and practical way. Modeling and simulation of heat transfer phenomena as developed and applied is presented in various engineering applications. New and novel processes (investment casting, numerical machining, fuel cell technologies etc.) have also been discussed. The chapter draws attention to the use of modeling and simulation techniques and use of simulation packages (C++, MATLAB ® SIMULINK ®, Modelica, FLUENT, SolidCAST, COMSOL Packages, etc.) for solving heat transfer related problems of conventional and advanced processes, at the same time encouraging the reader to develop his/her own models for specific engineering problem/application.
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