Analysis of Cattaneo–Christov heat and mass flux in Williamson fluid flow with variable thermal conductivity and convective boundary conditions

Abstract In this article, we aim to investigate steady laminar incompressible Williamson fluid flow past a linearly stretching surface using the Cattaneo–Christov fluxes model theory, with the impacts of variable thermal conductivity, an inclined magnetic field, thermo‐solutal buoyancy forces, convective boundary conditions, and chemical reaction. This work is motivated to explore the heat and mass transport in Williamson fluid flow, having Cattaneo–Christov theory and the added physical influences, for its effective use in various engineering and industrial processes. The flow governing model that consists of partial differential equations (PDEs) is transformed via appropriate similarity transformations to nonlinear ordinary differential equations (ODEs). The numerical solutions of the ODEs are obtained to analyze the impacts of different physical parameters on temperature, concentration, and velocity profiles. Our findings indicate that the fluid velocity increases by enhancing the thermal Grashof number, while it decreases against the Williamson fluid parameter and inclination angle. Moreover, raising the thermal conductivity parameter, inclination angle, and thermal Biot number causes a rise in the temperature profile. A declining trend has been observed in the temperature profile via a higher thermal Grashof number and thermal relaxation time parameter. The concentration profile increases against the magnetic parameter and solutal Biot number, while a higher Schmidt number, chemical reaction rate parameter, and solutal relaxation time parameter contributed to its declining trend. We also evaluated the behavior of physical quantities against pertinent parameters, which implies that skin friction declines with inclination angle and Williamson fluid parameter, Nusselt number decreases against thermal conductivity parameter, and Sherwood number increases via chemical reaction rate parameter, Schmidt number, solutal Biot number, and solutal thermal relaxation time parameter. The conducted study has applications in various biomedical and industrial fields, including polymer extrusion, drug delivery, coating processes, geothermal energy systems, chemical reactors, and thermal management systems.