Variable thermal conductivity and viscosity effects on non-isothermal flow of a non-newtonian fluid

This study investigates the effect of variable thermal conductivity andvariable viscosity on the flow characteristics and flow rates of an inelastic fluidflowing steadily in a channel under a constant pressure gradient. The flow is assumednon-isothermal and viscous heating terms are included in the analysis. Theexponential dependence of viscosity on temperature is modeled through Arrheniuslaw and shear rate dependence is modeled through Carreau rheological equationwhile it is assumed that the thermal conductivity varies linearly with temperature.Flow governing motion and energy balance equations are coupled and the solution tothis non-linear boundary value problem is found iteratively facilitating aPseudospectral method based on the Chebyshev polynomial expansions. Effect ofvariable thermal conductivity and viscosity as well as the effect of power law indexand material time constant of the Carreau model; Brinkman and Peclet numbers ofthe flow on the velocity and temperature profiles are presented. Moreover, theinfluence of the above parameters on the flow rate is also calculated.Keywords: Pseudospectral method, Variable Viscosity, Variable ThermalConductivity, Poiseuille flow.