Solving Transient Heat Transfer Problems by the Convolution Type Semi-Analytical DQ Method

Abstract

The convolution-type Gurtin variational principle is known as the only variational principle that is, from mathematics point of view, totally equivalent to the initial value problem system. In this paper, the governing equation of bars is first transformed to a new equation containing initial conditions by using convolution method. Then, a convolution-type semi-analytical DQ approach, which involves differential quadrature (DQ) approximation in space domain and an analytical series expansion in time domain, is proposed to obtain the transient response solution. The transient heat transfer examples show the proposed method is a very useful and efficient tool in transient heat transfer problems.