A Numerical Study of Heat Transfer and Fluid Flow in a Channel with an Array of Pin Fins in Aligned and Staggered Configurations

Heat transfer and fluid flow in a channel with an array of pin fins is numerically investigated using a finite volume approach. Rectangular pin fins with circular cross sections are used in this investigation. The working fluid is air with constant physical properties. Steady, laminar flow with uniform velocity and temperature profiles approaches the pin fin array. Nine fin rows are stacked in aligned and staggered configurations, and fins are modeled as no-slip walls with uniform temperature boundary condition. The dimensionless spacing, $S^{*}$, defined as the ratio of the gap between the fin walls to the fin diameter, is varied between a value of 0.5 and 1. Nine different approaching velocities are considered in this study which resulted in Reynolds number values ranging between 5 and 160. In the aligned configuration, the calculated average fin Nusselt number showed its highest value at the first row of fins. It then decayed with increasing number of rows, N, a behavior that was consistently observed for every considered Reynolds number and for both spacing values $S^{*}$. In the staggered configuration, the same behavior was observed at low Reynolds number values. However, as Reynolds number is increased, the maximum average fin Nusselt number value moved to the second row of fins, a fact that was attributed to the speeding flow field by the first row of fins. The percentage decay of Nusselt number with respect to the number of fin rows N showed a large dependence on Reynolds number, the stacking configuration, and the dimensionless spacing, $S^{*}$. The pressure coefficient, $C_{p}$, showed a developing region close to the inlet and a fully developed region as the number of fin rows is increased. The fin array effectiveness, defined as the average Nusselt number to the aggregate pressure coefficient, for all fins in a single row in the streamwise direction, was shown to decrease in the direction of the flow. The staggered configuration showed a better performance than the aligned configuration, at fixed $S^{*}$, in the first few streamwise rows. Fin array configurations with large spacing ratio, $S^{*}$, showed a better performance than smaller spacing ones. For fin arrays with a large row number in the streamwise direction, the best performance was obtained in the case corresponding to the aligned configuration with the large spacing ratio, $S^{*} = 1$.