A Discontinuous Galerkin Method for Thermal Simulation of Microchannel Cooling

This paper presents a numerical algorithm based on discontinuous Galerkin method (DGM) for thermal simulation of microchannel cooling. Under the assumptions of incompressible and fully developed flows, the governing equation is simplified and decoupled from temperature, and the analytical solution of velocity field is obtained. In the implementation of DGM, the heat flux is introduced as an auxiliary variable to reduce the Laplace operator to a divergence operator. The numerical flux is employed for the information exchange between neighboring elements, and the governing equations of conjugate heat transfer can be calculated by the DGM together with the auxiliary differential equation. The validity and accuracy of the proposed DGM are demonstrated by the numerical examples.