A multi-dimensional heat conduction analysis: analytical solutions versus F.E. methods in simple and complex geometries with experimental results comparison

Computer codes are widely used to predict heat transfer fields. Modeling is accomplished in multidimensional media with homogenous or not homogenous thermal conductivity, with or without volume heat sources and enthalpy flux. This paper compares the analytical solution of temperature fields in a few physical cases such as aliment cakes, capacitors, gas turbine blades, tanks with infinite element computer results and experimental results. The analytical solution of heat transfer partial differential equations presented in this paper appears in the form of the sum of effects. One of them is an infinite series in term of eigenvalues that is easily managed through mathematical commercial codes available even for palmar calculations. A comparison with experimental results shows that the concept of analytical solution has application in many physical phenomena without going to the complexity of computer code modeling.