Solving heat conduction problems in Mathematica environment

The aim of this paper is to demonstrate benefits of applying innovative symbolic computation tools to solving heat conduction problems that often arise in engineering practice. Wolfram Research's Mathematica 4.0 application was used, For demonstration purposes a transient nonlinear problem in a 2D square area. was chosen, as a frequently encountered one in thermal design of microelectronics, although the approach is readily extensible to a wide range of problems. The paper further extends the insights and developments.