ASME International Mechanical Engineering Congress and Exposition, Anaheim, CA., November 16-17, 1998

Application of Block-Implicit Multigrid Approach to Heat Transfer Problems Involving Discrete Heating

L. Tang and Y. Joshi
CALCE Electronic Products and Systems Consortium
University of Maryland
College Park, MD 20742


Electronic systems are characterized by a large disparity in relevant length scales. Usually, very large number of grid points are needed, as a result, for accurate thermal modeling. With traditional iterative methods, the number of iteration and computing time for convergent results will significantly increase, as the number of gird points increases. On the other hand, design cycle for new electronic products are getting short. This makes searching for speedy solution techniques necessary. Primitive variables based SIMPLE and its variants are very popular among thermal engineers in electronics industries. However, the loose coupling between pressure and velocity makes their convergence rate slow. Symmetrically Coupled Gauss-Seidel (SCGS) technique handles the velocity and pressure in a coupled fashion and simultaneously updates the velocity and pressure that belong to the same control volume. In addition, use of multigrid technique can further speed up the convergence rate by cycling between coarser and finer grids to efficiently smooth all the errors with different wavelength. The superior performance of Multigrid Symmetrical Coupled Gauss-Seidel (MG-SCGS) on uniform heated or cooled situations is well documented. However, a literature review indicates that applications with discrete heat sources have not been investigated.

In the current study, SCGS based multigrid solution procedure was applied to two configurations with a discrete heat source mounted on a heat conducting board: (i) Natural convection cooled enclosure, (ii) mixed convection air cooled channel. The convergence rate for SIMPLER, SCGS, and MG-SCGS are compared for both cases. For the natural convection case, a discrete heat source was vertically mounted on one wall of a rectangular enclosure. The evaluation was carried out for different Rayleigh numbers. In addition, the effect of boundary conditions on the convergence rate was also considered. For the mixed convection case, a discrete heat source was horizontally placed on the bottom of a rectangular channel. By changing the inlet velocity and power levels of the component, the effect of the Reynolds and Rayleigh numbers on the performance of MG-SCGS was evaluated. Even with two grid levels involved, the decrease in CPU seconds is remarkable. With SCGS alone, CPU consumption is reduced by about 50%. With MG-SCGS, around 5 times decrease in CPU seconds is observed.


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