Parametric study on the effect of end walls on heat transfer and fluid flow across a micro pin-fin

Abstract Micro heat sinks have a broad applicability in many fields such as aerospace applications, micro turbine cooling, micro reactors, electronics cooling, and micro biological applications. Among different types of micro heat sinks, those with micro pin-fins are becoming popular due to their enhanced heat removal performance. However, relevant experimental data in current literature is still scarce to adequately explain their differences from their macro size counter parts. In previous studies in literature, it was shown that thermal and hydrodynamic characteristics of micro pin-fin heat sinks are strongly affected by height over diameter (H/D) ratio of pin-fins. To address the lack of information about this subject, the objective of this work is to show how velocity boundary layer around pin-fins and consequently, the thermal and hydrodynamic characteristics are affected when H/D ratio and local Reynolds number (Re) vary. To investigate end wall effects, a small portion of a typical micro pin-fin heat sink is modeled. This portion is represented by a simplified model, which consists of a single pin-fin positioned in a rectangular micro channel. This approach simplified the micro heat sink, which is simulated for only half of it by using a symmetry plane. Moreover, the transverse channel walls are kept as close as the minimum distance (1.5D) between pin-fins available in the literature. In this paper, the pin-fin height over diameter ratio, H/D, varies from 0.5 to 5, while Reynolds number and heat flux provided from the fluid interacting surfaces of the micro pin-fin are in the range of 20 ≤ Re ≤ 150 and 100 ≤ qin (W/cm2) ≤ 500, respectively. In this research, micro pin-fin heat sinks are three dimensionally modeled on a one-to-one scale with the use of commercially available software COMSOL Multiphysics 3.5a. Full and temperature dependent Navier–Stokes equations subjected to compressibility and energy equations are solved under steady state conditions. In order to validate the use of numerical models, simulation results are compared against theoretical predictions. The numerical results and theoretical predictions show a good agreement. After this validation, parametric analysis is performed using the three dimensional model developed with COMSOL Multiphysics 3.5a. The end wall effects are quantified, and this amount decreases with Re and H/D. It is revealed that end walls play an important role on the total fluidic force acting on the micro pin-fin and on the heat transfer coefficients. Moreover, the trends in the amount of end walls effects, the ratio of viscous over total forces on the pin-fin, friction factors, and Nusselt numbers change at various critical Reynolds numbers. It is also demonstrated that increasing H/D ratio leads to a less stable flow, higher fluidic forces on the micro pin-fin with an increased partial role of viscous forces relative to pressure forces, smaller friction factors, and higher heat transfer coefficients. There are maxima and minima in Nusselt number profiles for different H/D ratios. It is found that increasing Re has a positive role in Nusselt numbers, as well as a parallel effect with H/D on fluidic forces on micro pin-fin, friction factors, and heat transfer coefficients. Different than the effect of H/D, Re decreases the partial role of viscous forces relative to pressure forces.