1. Introduction
When the electronic components or other electronic devices work, they always generate heat. It is important to remove the heat to the surrounding to control the temperature in the range of the operating temperature. To remove the heat effectively and economically, the thermal engineers adopt forced convection to cool components and maintain the stability of the system using the heat sink to increase the area of heat dissipation. Therefore, to satisfy the demand, they have modified the shape of the heat sink, material, and manufacturing process.
Taking account of the lower levels of pressure loss using heat sink, many researchers employed fin array or dimpled surfaces or dimpled fin array for taking away heat from heat sources favorably. Zografos and Sunderland [
1] experimented on pin fin with different heat sources in line and staggered arrangement and discussed the adequate diameter of pin and pitch for better performance. The pin fin exhibited higher heat transfer than the plate fin under the same conditions. For different levels of Raleigh number (Ra) and geometry, they developed an empirical formula to predict the performance of the pin fin; it had a better performance as its pitch was 1/3. Ledezma and Bejan [
2] used numerical simulation and experiment to investigate the natural convection and forced convection induced by different shapes of fin and directions of fin with the distribution of temperature at different positions and Nu with different Ra levels. They discovered that the vertical fin cooled better than the horizontal one with different geometries, and forced convection had a better cooling effect than natural convection. Moreover, the study also discussed the effects of the slope of the side fin on heat transfer. The heat transfer rate obviously increased with increasing slopes. Goshayeshi et al. [
3] examined the influence of fins’ distance (S) on the temperature distribution of fins and boundary layer in natural convection by numerical analysis. Their results displayed that Nu increased with increasing Ra and S. According to these results, the heat resistance was at a minimum, and the best cooling performance occurred at S = 6.85. Chang et al. [
4] numerically explored natural convection of vertical fin channels, smooth nine-fin channel, smooth thirteen-fin channel, seven-fin channel with convex/concave dimples, and nine-fin channel with convex/concave dimples having the same fin base area and fin-channel volume. The nine-fin array with convex/concave dimples exhibited the greatest heat transfer enhancement among all the vertical fin channels. Afanasyev et al. [
5] investigated how shaped surface (spherical cavities) changed the friction factor as well as turbulent heat transfer by an experiment. Nine of ten plates were arranged in staggered fashion with spherical cavities at different geometries and densities, and the other one was a smooth plate. The depth of dimple to diameter of dimple ratio was about 0.04. They concluded that the spherical cavities’ surface raised heat transfer less than or equal to 30–40%. A slight reduction in the viscous sublayer thickness increased heat transfer because of concavities’ depth being consistent with the sublayer thickness. Such cavities produced a pressure drop along the wall determining the heat transfer mechanism. Chang et al. [
6] experimented on four sets of a combination of concave and convex fins in a single fin channel with Re = 1500–11000 to decide how Re and relative fin length to channel hydraulic diameter affected the heat transfer of the fin channel under dimple placement. The relative dimple depth to dimple diameter was 0.3. The local friction factor and centerline averaged mean friction factor increased with increasing Re or decreasing relative dimple depth to dimple diameter. The convex/convex dimpled fin channel offered the greater averaged Nu as well as thermal performance. Ligrani et al. [
7] experimentally investigated the flow velocity of a channel placing dimples on one surface, protrusions, and no protrusions for the same configurations with the dimples on the opposed surface. The depth of dimple to diameter of dimple ratio was 0.2. They found that the protrusions augmented the heat transfer because a separated shear layer attached again, and the strong secondary flow occurred owing to vertical fluid and vortex pairs driven out from each dimple. The friction factor value of the fin with dimples as well as protrusions on the opposite surface was higher than that of the one with dimples and no dimpled surface on the opposed wall. Fazli and Raisee [
8] evaluated the heat transfer coefficient of various ducts with repeated dimple/protrusion surfaces under turbulent flow. They found that using the nonlinear k-
model attained a greater recirculation zone within the dimple via larger impact and upward flow than the linear k-
model as well as the zonal k-
model.
Luo et al. [
9] determined the optimum geometry parameters of pin fins and dimple/protrusion channel with respect to higher Nu and lower friction. They found that the Nu was large on the back of the dimple, whereas it was small on the front of the dimple. Sobhani et al. [
10] numerically investigated how dimple geometric parameters in the blade′s configuration of a vertical-axis wind turbine affected aerodynamic performance of turbine under turbulent flow. They reported that the efficiency increased up to 18% and average efficiencies of the turbine up to 25% for the airfoil with a dimple in comparison with the original airfoil. Jung and Kim [
11] numerically examined the effect of multi-jets impinging on the concave-dimples’ surface on the thermal performance of the diverter in a nuclear fusion reactor applying the shear stress transport turbulent modeling. They discovered that the heat transfer rate with concave-dimple array was raised up to 2.62%. In addition, the heat transfer rate as well as pressure drop rose with rising the dimple diameter and dimple height. Kim et al. [
12] evaluated the heat transfer rate of the heat exchangers with different dimple patterns employing the shear stress transport turbulence model. They observed that the lined and staggered patterns exhibited the greatest temperature variations at all Dean number levels. While the staggered patterns exhibited the greatest heat transfer performance, the lined pattern showed the second greatest performance. Zhou et al. [
13] studied how the dimple bionic structure inserted in the circumferential grooves’ surface influenced fluid resistance by comparing the drag coefficient of dimple bionic structure with that of smooth structure. They found that the dimple bionic structure could reduce fluid resistance because the dimple bionic structure decreased the pressure drop because of driving fluid to raise the velocity. Xie et al. [
14] numerically examined the thermal performance of a rectangular duct with internal-extruded dimples array mounted on the channel middle wall. Their results displayed that the dimple center with internal extrusion acquired the greatest thermal performance. Rao et al. [
15] experimentally and numerical studied the flow velocity and heat transport of a duct with dimples inserted transversely or transversely as well as streamwisely in the midst of the pin fins. The experimental results indicated that dimples inserted transversely between the pin fin-dimple channel increased heat transfer by 8.0% and decreased the friction factor by 18.0%; and dimples inserted transversely as well as streamwisely between the pin fins increased heat transfer by 20.0% and raised the friction factor by 6.0%. The numerical results illustrated the dimples substantially raised the near-wall turbulent kinetic energy, in particular dimples inserted transversely as well as streamwisely between the pin fins, and thus distinctly promoted the thermal convection in the duct. Sethi et al. [
16] explored how the arc angle ratio and roughness pitch ratio influenced heat transfer as well as the friction factor of rectangular channel. They concluded that the roughness pitch ratio of 10 achieved the maximum thermal performance. Lan et al. [
17] employed large eddy simulation (LES) to study how the boundary layer thickness of leading edge affected flow separation inside the dimple. Their results indicated that the upper part of horseshoe vortex was further away from the plate surface with an increase in the relative boundary layer thickness of the leading edge to dimple depth. Hairpin vortexes due to the wake behind dimple were generated by the horseshoe vortex. Dees et al. [
18] experimentally explored how the dimple configuration changed heat transport inside the suction area of a gas turbine blade. They found that all the dimple configurations augmented heat transfer by 20% in comparison with the smooth suction area. Mitsudharmadi et al. [
19] experimentally investigated how the rounded dimple arrays with various dimple depth ratios changed the turbulent flow field. The spanwise mean wall shear stress varied little with dimple depth and increased by 45% compared with the smooth surface. The deeper dimple was subject to flow separation different from the shallowest ones. Won et al. [
20] examined how dimple depth caused the flow pattern in a duct. When the dimple depth was large, it generated greater main vortex pairs with larger turbulence extents. Ejection frequencies of main vortex pair ranged from 7 to 9 Hz independent of dimple depth. Rao et al. [
21] experimentally explored how dimple depth changed pressure loss as well as heat transfer within a duct, where dimples were inserted transversely in the midst of the pin fins. The pin fin/dimple channels attained the maximum heat transport of 19.0%, and Nu rose as the dimple depth increased. Li et al. [
22] utilized LES to analyze how dimples and extrusions affected turbulent heat transport of a rectangular duct when Re was between 5600 and 22,000. Thermal performances rose greatly with an increase in Re or a decrease in the gap ratio; however, the flow pattern was only dependent on Re. The combined effect of vortical structure, the turbulent kinetic energy, and shedding frequency from dimples generated asymmetric profiles of Nu inside the wake in the rear of the dimple. Elyyan and Tafti [
23] performed LES for heat transfer in a duct with dimples and protrusions on opposite surfaces at Re levels of 220, 940, and 9300. Their results displayed heat transfer enhancement ratios of 0.99 at Re of 220, 2.9 at Re of 940, and 2.5 at Re of 9300. Friction coefficient enhancement ratios of 1.67 occurred at Re of 220, 4.82 at Re of 940, and 6.37 at Re of 9300. It could be found that dimples and protrusions might not be feasible heat transfer enhancement surfaces when the flow was steady and laminar. Sato et al. [
24] utilized LES to realize how the Prandtl number influenced heat and fluid flow in a dimpled channel at Re between 1000 and 10,600. The temperature gradient rose with increasing the Prandtl number because the fluid thermal diffusivity decreased. The thermal performance parameter had a maximum value of 1.22 for Re of 2000 and Pr of 3.0.
Torregrosa et al. [
25] investigated the turbulent flow and the pressure coefficient fluctuations downstream for a plate with surface-mounted obstacle. The surface-mounted obstacle generated great turbulent structures to excite unsteady flow and the pressure coefficient fluctuations downstream. Hocine et al. [
26] employed Reynolds stress models and LES to analyze the turbulent flow past a D-pattern non-streamlined body. The k-ω turbulence model best captured the intensive shear layer on the upper area of the D-pattern among all the Reynolds stress modellings. The LES with a suitable orthogonal decomposition could extract the mean flow feature as well as the coherent structure. Alam et al. [
27] applied LES to study a turbulent flow past the block array of a similar building. The presented stress modelling including the strain and rotation tensors was accurate for analyzing vertical distributions of variance and average, and unsteady coherent structures. Lu et al. [
28] employed LES to investigate how cube-obstacles influenced turbulent channel flow. The von Karman constant decreased as roughness height rose. The surface cube-obstacles caused greater quasi-streamwise vortices and stronger discharge. Saeedi et al. [
29] performed LES to explore turbulent flow characteristics of a flat plate with a square cylinder mounted on a wall. The greatest level of the mean dissipation rate was near the recirculation region. The peak relative sub-grid scale (SGS) viscosity over the kinematic viscosity dropped when the distance from the cylinder rose. The ratio distribution spanwisely expanded more broadly because the turbulent wake grew. Hao et al. [
30] utilized LES to explore thermal convection in a pin fin array by formerly examining eddy-viscosity turbulences. Reynolds stresses predicted by LES showed different characteristics in these different flows, which were not reflected in those predicted by the shear stress transport model. The analysis provided some perception to correct the Reynolds stress tensor. Toubiana et al. [
31] compared LES and the Reynolds stress model for turbulent flow in staggered plate arrays. Employing the results of LES realized the development of the turbulence structure with Re and estimated the effectiveness of every turbulence model prediction. The k-ω modelling underestimated the turbulent kinetic energy, while the k-ε model overestimated it. Paniagua et al. [
32] compared three subgrid-scale models for turbulent heat transfer inside a surface-mounted cylindrical pin array on a plate. The three modellings could predict the bulk unsteady flow generated by vortex shedding behind the pin array. A subgrid-scale model with the invariants of the strain rate tensor better predicted the pressure profile near pins, while the surface-adjusting local eddy viscosity modelling gained the velocity field in better accordance with experimental data. Chen et al. [
33] developed a phase-averaging approach to study momentum, vorticity structure, and turbulent heat transfer behind a round cylinder. The presented model described the structures similar to rib in taking away heat in detail and highlighted the half of the spanwisely expanded vortex. Yang et al. [
34] used the dynamic subgrid-scale model to simulate the turbulent duct flow with square rib on the surface. The Re was 3210 according to the average velocity above the block and its height. Their results showed better agreement with direct numerical simulation than with LES at the same factors, verifying the value of subgrid-scale model from simulating complex turbulent heat transfer. Franke et al. [
35] utilized LES to simulate the turbulence that passed a round cylinder with Re equal to 3900 by a grid centered finite volume scheme for resolving the compressible Navier–Strokes equations. They compared the results with the computational results of Ma et al. [
36] and experimental results of Ong et al. [
37]. Their study dealt with data by the time averaging method, and the results were close to the reference data. Their study also discussed the subgrid-scale stresses as well as Reynolds stresses modeling.
From the preview studies, fin array still has the advantages of low cost and simplicity. There are some studies about the effect of shape, pitch, height, and thickness of a fin in the vertical or horizontal direction in natural and forced convection. Most articles studied heat transfer of a single dimpled channel or a dimpled plate with changed dimple depth or placed location and direction. However, there are few studies about flow interactions of convex/concave dimples between fin channels under turbulent forced convection. This study is aims to explore how Re and dimple height affect turbulent heat transfer of nine-fin array with alternately convex/concave dimples by using LES. The purpose of this study is to examine temperature and flow field using LES to find the effects of dimple height and to discuss the effects on time-mean drag coefficient and averaged time-mean Nu. At which dimple height the maximum averaged time-mean Nu occurs is to be determined. The enthalpy flow rates of the inlet, the top outlet, and the back outlet are also explored to identify the trend of dimple height with averaged time-mean Nu.