ANALYSIS OF TWO-DIMENSIONAL HEAT DIFFUSION USING FEA AND THE FUNDAMENTAL COLLOCATION METHOD

Finite Element Analysis (FEA) and the Laplace Transform Based Fundamental Collocation Method (FCM) are used to solve the heat diffusion equation in two-dimensional regions having arbitrary shapes and subjected to arbitrary initial and mixed type boundary conditions. In the FEA method, the time derivative is replaced with a finite difference approximation. The resulting time dependent global equations are solved incrementally starting with the initial conditions. The FCM approach is applied in the Laplace transform domain to obtain temperatures in the s-domain, T(x,y,s). An inversion technique is used to retrieve the time domain solution, T(x,y,t). To compare applicability and accuracy of these methods, both techniques are applied to transient heat flow problems for which exact solutions are known.