The double integral method applied to heat conduction problems

Abstract

This paper presents the application of the double integral method (DIM) to solve problems of transient one-dimensional conduction heat transfer. This method is a mathematical technique that transforms the non-linear boundary value problem into an initial value problem, whose solution can often be expressed in a closed analytical form. The partial differential equations are integrated twice, the first integration being performed within the domain and the second along the phenomenological distance. This double integration allows the gradient vector at the surface to be approximated using the simple integral method (SIM). Thus improvements can be attained by changing the derivative at the boundary by an integral relation, since the process of differentiation amplifies any difference between the assumed temperature profile and the exact solution. In this the work results obtained were are compared with exact and approximate analytical solutions found in the literature