General solutions of the heat equation in finite regions

Abstract

Using a finite integral transform an analytical solution is found for a large class of heat transfer problems. This solution is obtained in form of infinite series and contains quasi-steady and transient terms. It is shown that the Ölçer's conductive heat transfer solution [2,3] is a special case of the general solution obtained. The latter can also be applied when studying heat transfer in laminar and turbulent flows of Newtonian and non-Newtonian fluids in pipes and ducts, temperature development in the entrance region of MHD channels and elsewhere.