The heat transfer-flow characteristics of turbulent flow inside corrugated channels heated by constant heat flux are numerically investigated. The rate of heat transfer, pressure drop, and performance evaluation criterion is determined for smooth channel and various designs of corrugated channels at the Reynolds number ranged from 5000 to 60,000. The effect of rib arrangement distributions of inward, outward, and inward-outward ribs are examined. The various rib configurations of corrugated channels are also tested. In addition, the influences of rib roughness parameters (height, pitch, and width) and rib shapes (semicircular, trapezoidal, and rectangular) are researched. The Reynolds-averaged Navier-Stokes equations (RANS) are used to model the governing flow equations. The computational model is validated through a reasonable agreement between the present numerical results and the outcomes of related works. For different geometrical and operating conditions, the results revealed that the rate of heat exchange in corrugated channels exceeds higher than that of smooth ones but with additional pressure loss. Moreover, the rib arrangements, rib configuration, and rib roughness parameters exhibit a relatively significant effect on the performance of the corrugated channels. On the other hand, the influence of the rib shapes seems to be small.
- thermal-flow performance
- corrugated channel
- rib distribution
- rib configuration
- rib shapes
The reliable efficient heat exchangers transfer the maximum rate of heat with minimum friction losses. The rate of heat transfer of most fluids is restricted by their low thermal conductivity. Thus, the thermal systems adopt techniques of heat transfer enhancement to reduce the effect of this issue. There are three techniques of enhancing heat transfer, namely, active methods (require external power) , passive methods (fins, corrugation, ribs, etc.) , and compound techniques (simultaneous use of active and passive techniques) . Corrugation of tubes and channels is considered an efficient passive method to augment the rate of heat exchange. The thermal-flow features of turbulent flow in corrugated tubes are reported extensively in many articles (for example [4, 5, 6, 7, 8]).
Corrugated channels are widely utilized in industrial applications as they are the major components in plate heat exchangers. Naphon  conducted experiments to show the performance of a turbulent flow inside a two-sided corrugated channel with an in-line and staggered arrangements. He showed the important effect of corrugation on the augmentation of heat transfer and pressure loss. Eiamsa-ard and Promvonge  experimentally examined the thermal-hydrodynamic performance of the three types of ribbed-grooved ducts. They reported that the maximum rate of heat exchange and pressure drop exist in the ducts with a rectangular rib and a triangular groove. Elshafei et al.  conducted experiments to examine the thermal-hydraulic performance of corrugated channels under the influence of variations of phase shift and channel spacing. The corrugated channels exhibit a compound increase in heat transfer and pressure loss. Mohammed et al.  performed a computational model to investigate the effects of wavy tilt angle, channel height, and channel height on the flow-thermal fields in a corrugated channel. A three-dimensional numerical model to investigate the employing baffles on the heat transfer-flow in the corrugated channels was presented by Li and Gao . Increasing the baffle height enhances heat transfer effectively but leads to dramatic penalty in pressure drop. Pehlivan et al.  experimentally investigated the rate of heat exchange for sharp corrugation peak fins of corrugated channel for three different types and sinusoidal converging–diverging channels. It is reported that the rate of heat transfer increases with the corrugated angle. The numerical results showed that the wavy channel is an efficient method to increase the heat transfer. Ravi et al.  numerically studied the impact of different rib configurations on the heat transfer-flow characteristics of the turbulent flow inside corrugated channels. Shubham et al.  numerically investigated the thermal-hydrodynamic transport characteristics of non-Newtonian fluids in corrugated channels. It was found that using of shear thinning fluids is more convenient for maximum augmentation of thermal performance with a minimum penalty in pressure drop.
The present study offers a numerical model to investigate the thermal flow attributes of turbulent flow in corrugated channels. The performance of corrugated channels are examined under the effects of corrugation arrangement (inward, outward, and inward-outward rib distribution), corrugation configuration, corrugation roughness parameters (rib pitch, rib width, and rib height), and rib shapes (rectangular, trapezoidal, and semicircular). The comparisons between the predicted thermal flow performance of corrugated channels and that of smooth ones are fulfilled under a large range of Reynolds number (5000–60,000).
2. Numerical model
The two-dimensional corrugated channel with a width (b) of 10 mm is described schematically in Figure 1. The water as heat transfer fluid enters the computational domain at a temperature of 27°C and intensity of turbulent of 5%. Also, 5% of turbulent intensity is considered at the exit. The end effects and viscous dissipation terms are ignored. The constant heat flux of 600 W/cm2 is applied on the channel wall. The consideration of an axisymmetric situation reduces the size of the numerical domain for saving computational time.
The flow-thermal behavior is modeled by the governing conservation equations (continuity, momentum, and energy) in a RANS technique as
in which are density, viscosity, fluctuated velocity, and turbulent shear stress, respectively.
The transport equations in k-e model are presented as 
The model constants
No-slip condition and constant wall heat flux are assumed as boundary conditions.
The thermal-hydrodynamic performance of the corrugated channels is assessed by dimensionless parameters which are the Nusselt number, friction factor, and performance evaluation criterion (
The average Nusselt number is presented as
The friction factor is defined as
The comparison between the enhancement in thermal performance and a penalty in the pressure drop is assessed by introducing the performance evaluation criteria (
The performance of corrugated channels is estimated according to different values of the Reynolds number which is introduced as
The ANSYS Fluent CFD package-based control volume method is adopted to discretize the governing equations and simulate thermal flow behavior of corrugated channels. The SIMPLE algorithm is utilized for solving the flow field. The diffusion terms and other resulting terms are discretized by employing the first-order upwind scheme. The residuals lower than 10−6 is chosen to achieve the convergence criterion for all variables. A fine grid discretization close to the wall is adopted. Also, the meshing system of 23,964 grids is sufficient for solution accuracy. On the other hand, the numerical code that is validated through a reasonable agreement is shown (Figure 2a) between the Nusselt number of the present work and the same number which is obtained from the well-known Gnielinski correlation . Furthermore, good agreement is indicated for the friction factor (Figure 2b) between the present work and the work of San and Huang .
3. Results and discussion
The flow-thermal features of turbulent flow in corrugated channels are evaluated numerically. The enhanced heat transfer and an accompanied pressure loss are assessed for corrugated channels under the influences of rib arrangement, rib configuration, rib roughness parameters, and rib shapes. The dimensionless parameters
3.1 The effect of rib arrangements
Corrugated channels exist in three layouts depending on rib arrangements, IOCC, ICC, and OCC, as described in Figure 1a. The variations of
3.2 The influence of rib configurations
Seven configurations of rib trapezoidal corrugated channels are denoted (B1, B2, C1, C2, C3, D1, and D2) which are presented in Figure 4a. Also, the smooth channel is indicated by A. The variation of the Nusselt number for all channels is depicted in Figure 4b. The increase in
3.3 The impact of rib roughness parameters
The roughness parameters of corrugated channels involve relative rib height (
3.4 The influence of rib shape
The heat transfer-flow behavior of IOCC channel, for example, is examined for rectangular, semicircular, and trapezoidal rib shapes. The different shapes of the rib are illustrated in Figure 6a, while the
The computational investigation of thermal-flow performance of turbulent flow in corrugated channels is carried out for the Reynolds number from 5000 to 60,000. The effects of rib arrangements, rib configurations, rib roughness parameters, and rib shapes are investigated. All layouts of corrugated channels showed a superior ability of exchange heat than that experienced by smooth channel. However, the pressure loss associated with corrugated channels is higher than that of the smooth ones. Furthermore, it is inferred that the arrangement of rib distribution, rib configuration, and rib roughness parameters has a pronounced effect on the thermal-flow performance of corrugated channels, while the influence of rib shapes seems to be small.
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