Steady-state flow of a power-law fluid between two coaxial cylinders taking into account the temperature dependence of the rheological parameters and the viscous dissipation

Abstract

The non-isothermal power-law fluid flow between two coaxial cylinders under the pressure drop providing a specified flow rate is studied with allowance for the viscous dissipation of the mechanical energy and dependence of the rheological parameters on temperature. The flow regime is assumed to be laminar. Mathematical formulation of the problem includes the dimensionless equations of motion and energy. The no-slip conditions are used on the channel walls while the temperature and the heat flux are assigned on the outer and inner walls, respectively. The stated problem is solved numerically with the use of the finite-difference method to discretize the equations. A tridiagonal matrix algorithm is applied to solve the obtained system of algebraic equations. The parametric investigation of the kinematic, dynamical, and thermo-physical characteristics of the flow is carried out.