Similarity Solutions of a non-Newtonian Fluid’s Momentum and Thermal Boundary Layers: Cross Fluid Model

Abstract

The steady, incompressible and laminer flow of a non-Newtonian fluid that fits the Cross-fluid model over a flat plate is investigated. Dimensionless momentum and energy equations in partial differential form are derived to examine the variation of fluid velocity and temperature. The equations are simplified by the boundary layer theory based on the assumption that the change occurs in a narrow region, then scaling symmetries are calculated. By means of symmetries, equations in a partial form are reduced to an ordinary form by computing similarity variables and functions. The sbvp2.0 package developed for the Matlab environment based on collocation methods was used for the numerical solutions of the equations. In the light of analytical approach and solutions, the heat transfer is investigated by the Nusselt number. The study reveals that increases in Weissenberg number and power-law index, as non-Newtonian properties, are in charge of the thinner boundary layers, thus causing less friction and effective convection. As a result of numerical parts of the study, sbvp2.0 package is recomended for stiff equations with high nonlinearity, especially arising from boundary layer flows.