The Second Fundamental Problem in Heat Transfer of Laminar Forced Convection

Abstract

This paper is concerned with the heat-transfer problem of laminar forced convection in noncircular pipes with arbitrary heat generation and prescribed heat flux at the wall. This class of boundary-value problems with Neumann conditions is approached by the method of conformal mapping. The solutions in terms of two analytic functions are established. This greatly enlarges the possibilities of analyses to many configurations which are otherwise not easily attainable. The example of an indented pipe of cardioid section is investigated in detail.