A numerical study on boundary layer flow of Carreau fluid and forced convection heat transfer with viscous dissipation and generalized thermal conductivity

Forced convective heat transfer and boundary layer flow of non-Newtonian fluid over a moving wedge is numerically studied. The non-Newtonian fluid is represented by Carreau fluid which is inelastic and characterizes shear-thinning and shear-thickening fluid. The thermal conductivity of fluid is no longer constant during heat transfer but is a function of temperature. The motion of the wedge surface is considered in the direction of mainstream or opposite. Both wedge and mainstream flows are assumed as a power of distance from the origin. Upon using similarity transformations, resultant equations are analyzed numerically using Chebyshev collocation and shooting methods for simulations of solutions. Most of the general features of solutions are identical to Newtonian fluid, the effects of Carreau fluid are to increase the velocity and heat transfer rate, and decrease the thicknesses. The present results of Carreau fluid and heat transfer unveil single and double solutions for the same system parameters and are shown to be a continuation of the Newtonian fluid. Also, the non-uniqueness of the solutions for the same set of parameters is classified as first and second solutions. Thus, there is a critical point beyond which no solution exists to model. In order to identify which of these solutions can be simulated practically, we perform linear stability analysis on velocity and temperature solutions. The eigenvalue analysis shows that the first solutions are always stable and the second solutions are amplified in time. Other interesting flows and heat transfer features are discussed in detail.