Fully-developed flow and temperature calculations for theologically complex materials using a mapped circular domain

This paper considers fully-developed flows in ducts of arbitrary shape unde r 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 conser vation equations, the analysis bads to direct determination of contour velo city curves, corresponding stresses and temperatures. Calculations are perf ormed in the mapped domain where simple meshes and efficient discretization schemes may be defined The thermal dependence is considered using a time-t emperature 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 an alytical solutions are found to be satisfactory The influence of temperatur e related to various physical and flow parameters is discussed.