Pressure Drop and Heat Transfer in Turbulent Duct Flow: A Two-Parameter Variational Method

Abstract

A two-parameter variational method is introduced to calculate pressure drop and heat transfer for turbulent flow in ducts. The variational method leads to a Galerkin-type solution for the momentum and energy equations. The method uses the Prandtl mixing length theory to describe turbulent shear stress. The Van Driest model is compared with experimental data and incorporated in the numerical calculations. The computed velocity profiles, pressure drop, and heat transfer coefficient are compared with the experimental data of various investigators for fully developed turbulent flow in parallel plate ducts and pipes. This analysis leads to development of a Green’s function useful for solving a variety of conjugate heat transfer problems.