Abstract

A heat transfer problem was taken as an example to provide the analytical solutions of a one-dimensional conduction problem with two different kinds of boundary conditions. The theoretical solutions were obtained by using the method of separation of variables for solving partial differential equations. Temperature distribution in two simple cases were studied using the analytical solutions and were compared with corresponding numerical results. Reliability of the analytical results were shown by their excellent agreement with those numerical ones. The solutions presented in this note can be used for the verification of new numerical algorithms.

Keywords: Heat transfer; Conduction problem; Analytical solution; Boundary condition