This paper deals with the transient analysis of a two dimensional pin fin that contains tip convection and is subjected to time and space dependent heat flux at the fin base. A method of combining the Laplace transformation and finite difference is applied to analyze the problem. The general solution of the governing equation is first solved in the transform domain. The numerical transient solutions of temperature increments in the real domain are then obtained by using the matrix similarity transformation and Fourier series technique. Comparing with existing analytical solutions, the results presented here show high accuracy. The computational procedures established in this paper are also applicable to other types of boundary conditions, such as variable convection heat transfer coefficient. (C) 2004 Elsevier Ltd. All rights reserved.