A local adaptive differential quadrature method for solving multi-dimensional heat transport equation at the microscale

Abstract

In this article, we employed the local adaptive differential quadrature method to solve multi-dimensional heat transport equation at the microscale. The local adaptive differential quadrature method was employed to tackle the boundary conditions by using both localized interpolation basis functions and exterior grid points. We found that accurate numerical solution can be obtained by using a small number of gird points for boundary treatments. The governing equation of heat transport was employed to describe the thermal behavior of microstructures, which was of vital importance in microtechnology applications. Four examples showed the effectiveness and accuracy of our algorism in providing excellent estimates of unknown temperature from the given data. We found that the proposed scheme is applicable to the heat transport equation at the microscale.

Keywords

Heat transport equation local adaptive differential quadrature method microscale

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