Fully‐developed flow and temperature calculations for rheologically complex materials using a mapped circular domain

This paper considers fully‐developed flows in ducts of arbitrary shape under thermal conditions of fluids obeying various constitutive equations. The numerical method is based on the transformation of the physical flow domain, assumed to be simply‐connected. By using mass, momentum and energy conservation equations, the analysis leads to direct determination of contour velocity curves, corresponding stresses and temperatures. Calculations are performed in the mapped domain where simple meshes and efficient discretization schemes may be defined. The thermal dependence is considered using a time‐temperature superposition principle. Newtonian, purely viscous, viscoelastic and yield stress fluids are investigated for several flow geometries, with realistic parameters and boundary conditions. Comparisons with existing analytical solutions are found to be satisfactory. The influence of temperature related to various physical and flow parameters is discussed.