Approximate Methods for Calculating the Properties of Heated Laminar Boundary Layers in Water

A laminar boundary layer integral method (the method of Thwaites and Walz) is extended to handle variable fluid properties. This integral method uses simple correlations of universal parameters based on similar boundary layer flows. These universal parameters are correlated for water, which has a strongly temperature dependent viscosity, based on numerical solutions of heated water wedge flows. This extended integral method, in conjunction with the Lighthill high-Prandtl-number approximation for heat transfer, can be used to compute displacement thickness, momentum thickness, wall shear stress, Nusselt number, and higher derivatives of the velocity and temperature profiles at the wall for nonsimilar boundary layers. These parameters can be computed with a hand calculator. The extended integral method is tested for the highly nonsimilar Howarth retarded flow with surface temperature of 104 degrees F and ambient temperature of 32 degrees F; the method is accurate for this flow, except in the region near separation.