Galerkin method solution of a volume-averaged model for efficient conjugate heat transfer analysis

ABSTRACT

A numerical method is developed to efficiently model flow and conjugate heat transfer in heat sinks with arbitrary heat flux inputs. Volume averaging theory (VAT) is applied to the governing conservation equations to obtain a geometrically simplified model of the heat sink. The nonlinear momentum conservation equation is solved using finite difference, while the coupled energy partial differential equations are solved using a Galerkin method with modified Fourier series as basis function. Conduction in the base is significant, and its temperature distribution is obtained analytically. The predicted thermal and hydraulic performance parameters for water-cooled microchannel heat sinks are within 5% of experimental data. Results obtained with computational fluid dynamics (CFD) software were shown to provide similar accuracy, but require ~10³ times more CPU time.

Acknowledgments

We would like to genuinely thank the Kerze-Cheyovich endowment, and the late Dr. Novak Zuber who helped establish it, because they have enabled us to carry out this research study.