Fractional theoretical modeling of natural convection flow of Walter’s B fluid through vertical channel with thermal and mass fluxes

This study presents a theoretical investigation of the natural convection flow of Walter’s B fluid under the combined effects of thermal and mass fluxes and magnetohydrodynamics (MHD). Walter’s B fluid, a viscoelastic non-Newtonian fluid, is chosen due to its importance in industrial processes such as polymer extrusion, lubrication systems, and in biological flows where non-Newtonian behavior dominates. The significance of this study lies in its ability to provide insights into controlled thermal and solutal transport in engineering applications involving viscoelastic fluids. The governing equations are formulated assuming laminar flow and natural convection, incorporating buoyancy forces induced by temperature and concentration gradients along with the fluid’s viscoelastic properties. Using similarity transformations, the coupled system of linearized equations is solved analytically, and explicit solutions are obtained. The solutions are analyzed graphically to investigate the effects of key parameters, including Prandtl and Schmidt numbers, thermal and solutal Grashof numbers, magnetic field strength, heat and chemical reaction parameters, and the fractional-order parameter. Quantitative findings reveal that increasing the fractional parameter reduces the velocity profile near the wall by up to 18%, while the temperature and concentration fields increase with higher Grashof numbers. Moreover, the magnetic field suppresses the fluid motion, whereas higher Prandtl and Schmidt numbers enhance thermal and solutal boundary layers. These results demonstrate the model’s practical relevance for designing systems with controlled heat and mass transfer in viscoelastic fluids.