Laminar force convection heat transfer in some noncircular pipes

Abstract

In this study, solutions to forced, convection heat transfer problems in fully developed laminar flow are obtained for Newtonian fluids with constant properties. Internal flow for square, triangular and elliptical cross-sections have been solved. In addition, an approximate solution is presented for conduits with internal flow given by X4+ y4= a 4 . To solve the aformentioned problems, Complex Variable Techniques, Biharmonic Solutions, Variational and Finite Element Methods have been used. Biharmonic Solutions are directly applied to square and triangular pipes using the available solutions, in the plate theory. The Variational formulation of the governing equations are obtained. Based on this formulation velocity and temperature distributions are found in square pipes using the Ritz Method. Variational formulation is further used in corporation with the Finite Element Technique to determine approximate solutions for noncircular pipes. The Complex Variable Method is very suitable when applied to parallel plates, circular, triangular and elliptical pipes. It also gives considerable knowledge of heat transfer for the cross-section given by X4+ y4= a 4. Theoretical solutions for each of these geometries are then compared numerically by Finite Element Method.