Evaluation of a new iterative solution procedure for conduction heat transfer problems

A recently developed method for solving simultaneous linear algebraic equations will be discussed in the context of heat transfer problems. This new technique is an iterative method which reduces the number of equations and then solves the reduced set by conventional methods. While the mathematical formulation of the new method described below dictates convergence, the rate of convergence is dependent upon using knowledge of the physical system to select successive trial solutions which can result in very rapid computer solutions for physical problems, in particular, transient heat transfer problems. The new method was compared with the Alternating Direction Explicit Procedure (ADEP) for a transient three-dimensional heat transfer problem. The new method was significantly faster than ADEP.