Abstract
A three-dimensional numerical method based on the superposition principle for the solution of the heat diffusion equation is derived for Cartesian coordinates and tested for three different boundary conditions: a constant heat flux density, a convective-type surface heat flux, and a sudden cooling of the surface to a constant temperature, In addition, this three-dimensional numerical method is compared with the popular three-dimensional Brian's alternating direction implicit (ADI) method. The method based on the superposition principle has the same degree of accuracy in most cases as the method normally used for these types of calculations. In addition, its algorithm is considerably simpler to formulate and easier to program, and it requires about half the computing time needed to solve the problem when using Brian's ADI method. On the other hand, Brian's ADI method is unconditionally stable, but the method based on the superposition principle is not.
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