Three-Dimensional Analysis of Fluid Flow and Heat Transfer in the Microchannel Heat Sink Using Additive-Correction Multigrid Technique

Heat generation from very large-scale integrated (VLSI) circuits increases with the advent of high-density integrated circuit technology. One of the promising techniques is liquid cooling by using microchannel heat sink. Numerical works on the microchannel heat sink in the literature are mostly two dimensional. The purpose of the present study is to develop a three-dimensional analysis procedure to investigate flow and conjugate heat transfer in the microchannel-based heat sink for electronic packaging applications. The micro-heat sink model consists of a 10 mm long silicon substrate, with rectangular microchannels, 57 μm wide and 180 μm deep, fabricated along the entire length. A finite volume numerical code with a multigrid technique, based on additive correction multigrid (AC-MG) scheme, that is a high-performance solver, was developed to solve the steady incompressible laminar Navier–Stokes (N–S) equations, over a colocated Cartesian grid arrangement. The results indicate that thermophysical properties of the liquid can significantly influence both the flow and heat transfer in the microchannel heat sink. Comparison of the numerical results with other published numerical results and experimental data available in the literature for Reynolds numbers less than 200 based on a hydraulic diameter of D_h = 86 μm and D_h/L_x<0.01, indicates that the assumption of hydrodynanmic, fully developed laminar flow is valid. The current research indicates that the AC-MG acceleration technique is highly efficient, reliable and robust, which makes it feasible for CPU-intensive computations, such as pressure Poisson equations. When compared to the discretized momentum equations, the pressure Poisson equations tend to be very stiff and ill-conditioned, i.e a_p ≡ Σ_nb a_nb Because of these reasons, solving the pressure Poisson equation is usually the CPU bottle-neck for the incompressible N–S equation system and AC-MG technique is required. With this acceleration technique the residuals of the large-scale algebraic equation system are guaranteed to be continuously driven down to the level of the computer machine round-off error and warrants strong conservations of mass and momentum satisfied over all the control volumes. In this cell centered multigrid algorithm both restriction and prolongation operators are based on piecewise constant interpolation. The accuracy of the prediction has been verified by comparing the results obtained with the numerical and analytical results from the open literature.