A porous model for the square pin-fin heat sink situated in a rectangular channel with laminar side-bypass flow

Abstract

This work illustrates the compact heat sink simulations in forced convection flow with side-bypass effect. Conventionally, the numerical study of the fluid flow and heat transfer in finned heat sinks employs the detailed model that spends a lot of computational time. Therefore, some investigators begin to numerically study such problem by using the compact model (i.e. the porous approach) since the regularly arranged fin array can be set as a porous medium. The computations of the porous approach model will be faster than those of the detailed mode due to the assumption of the volume-averaging technique. This work uses the Brinkman–Forchheimer model for fluid flow and two-equation model for heat transfer. A configuration of in-line square pin-fin heat sink situated in a rectangular channel with fixed height ( H = 23.7 mm), various width and two equal-spacing bypass passages beside the heat sink is successfully studied. The pin-fin arrays with various porosities ( ε = 0.358–0.750) and numbers of pin-fins ( n = 25–81), confined within a square spreader whose side length ( L) is 67 mm, are employed. The numerical results suggest that, within the range of present studied parameters (0.358 ⩽ ε ⩽ 0.750, 25 ⩽ n ⩽ 81 and 1 ⩽ W/ L ⩽ 5), the pin-fin heat sink with ε = 0.750 and n = 25 is the optimal cooling configuration based on the maximum ratio of Nusselt number to dimensionless pumping power ( Nu/(Δ P × Re 3)). Besides, based on medium Nu/(Δ P × Re 3) value and suitable channel size, W/ L = 2–3 is suggested as the better size ratio of channel to heat sink.