In the present work, a novel modeling method based on the so-called porous medium approach and its application to an analysis of fluid flow and heat transfer in microstructures are presented.
This paper covers two types of microstructures, one microstructure of straight fin shape and the other microstructure of pin fin shape. The former is a typical example of microstructures having straight flow passages inside and the latter is a typical example of microstructures having tortuous and periodic flow passages inside. The microstructure is modeled as a porous medium through which fluid flows. The local volume-averaged momentum and energy equations for heat and fluid flow in microstructures are obtained using the local volume-averaging method. For microstructures of straight fin shape, the Navier-Stokes equations and the energy equation are locally volume-averaged in the spanwise direction due to the periodic structure in that direction. To solve the local volume-averaged governing equations, the permeability K and the interstitial heat transfer coefficient he which are related to the viscous shear stress caused by sides of fins and the heat transfer from sides of fins, respectively are determined analytically through an approximation. For this the pressure drop and heat transfer characteristics of sides of fins under consideration are assumed to be approximated as those found for the Poiseuille flow between two parallel plates that are subject to a constant heat flux. On the other hand, for microstructures of pin fin shape, the Navier-Stokes equations and the energy equation are locally volume-averaged in a unit cell of the microstructure. To solve the local volume-averaged governing equations, the permeability K, the Ergun constant $C_E$ which is related to the form drag caused by fins, and the interstitial heat transfer coefficient $h_l$ are determined empirically due to the complicated fluid flow and heat transfer in the microstructure.
To validate the porous medium approach, pressure and temperature distributions in scaled-up heat sinks of straight fin shape and pin fin shape measured in the experimental part of this study and Tuckerman’s experimental data on flow and thermal performance of microstructures of straight fin shape and pin fin shape are compared with those obtained from the porous medium approach. Through these comparisons, it is verified that the porous medium approach is a promising analysis tool for heat and fluid flow in microstructures.
The porous medium approach is expected to be a useful analysis tool in many engineering applications such as microscale heat sinks, PCRs, and Bio-chips where heat and fluid flow in a microstructure is essential.
