Analytical solution for a class of flat plate conjugate convective heat transfer problems

Analytical solutions for three different flat plate conjugate heat transfer cases are presented. The cases are as follows: transient heat transfer of a thin plate with uniform heat generation; the Luikov problem in which one plate surface is kept in a constant temperature and the other one is cooled by forced convection; and a modified Luikov problem with heat generation on one surface and convection on both surfaces of the plate. All the cases are solved for both laminar and turbulent flows with Pr ≥ 1. The solutions in the paper are based on the superposition principle and analytical expressions are used to couple the temperature and the heat flux distributions on the surface of the plate. The results of the Luikov problem and transient plate are also compared to other solutions presented earlier in the literature.