Antti Lehtinen, Reijo Karvinen

Frontiers in Heat and Mass Transfer (FHMT) 2 - 043004 (2011)

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 P r & 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.
Keywords: flat plate, conjugate heat transfer, Luikov problem, fractional calculus