Thermosolutal convection in a porous domain with an internal heating element saturated by a temperature-dependent Carreau non-Newtonian fluid

Abstract

This study aims to investigate natural double-diffusive convection in a porous square enclosure containing an internal heating element and saturated with a temperature-dependent Carreau fluid. It focuses on the combined effects of Rayleigh number, Darcy number, heater dimensions and position and temperature-dependent viscosity on flow behavior, heat transfer and mass transfer. The governing equations are formulated using the Brinkman–Darcy porous model and Carreau rheology with temperature-dependent viscosity. The equations are solved numerically using a finite-difference stream function-vorticity formulation. Streamlines, isotherms, isoconcentrations and average Nusselt and Sherwood numbers are analyzed. Increasing Rayleigh and Darcy numbers strengthens buoyancy-driven circulation, thins thermal and solutal boundary layers and enhances heat and mass transfer. For strong temperature dependence of viscosity, increasing the Rayleigh number in the Right–Bottom configuration enhances heat and mass transfer by 78.9% and 332.0%, respectively, while increasing the Darcy number in the Center–Center configuration raises them by 34.9% and 189.8%. The left-top heater gives the highest transfer rates over most investigated ranges. Increasing heater dimensions improves transport, while temperature-dependent viscosity weakly affects heat transfer but enhances mass transfer, with Sherwood number increasing by up to 16.6%. This work clarifies the coupled effects of porous permeability, internal heater geometry, heater placement and temperature-dependent Carreau rheology on thermosolutal convection. The results provide useful physical insight for optimizing heat and mass transfer in porous systems involving non-Newtonian fluids.