On fluid flow and heat transfer of turbulent boundary layer of pseudoplastic fluids on a semi-infinite plate

Abstract

The boundary layer of a pseudoplastic fluid on a semi-infinite plate for a high generalized Reynolds number is analyzed. Based on the Prandtl mixing length theory, the turbulent region is divided into two regions. The coupled momentum and temperature equations, with a generalized thermal conductivity model, have made the process of finding the analytical solutions much difficult. By using the similarity transformation, the equations are converted to four ordinary differential equations constrained by ten boundary conditions. An interesting technique of scaling and translation of the calculation domain of one region into another is used to make the system of equations easier to solve. It is found that the fluid with a smaller power-law index, associated with a thinner velocity boundary layer thickness, processes a lower friction coefficient. Furthermore, the increase in the Reynolds number causes a thinner velocity boundary layer and a decreasing friction coefficient on the wall. Changes in temperature occur more slowly near the plate surface with a rise in the power-law index and a decrease in the Reynolds number.