Non-linear thermal radiative Williamson nanofluid flow with viscous dissipation and Joule heating

In this work, we analyzed unsteady viscous incompressible two-dimensional magnetohydrodynamics (MHD) Williamson nanofluid flow with effects of non-linear thermal radiation, viscous dissipation, Joule heating, thermo-solutal buoyancy forces, suction/injection, heat source/sink, and convective boundary conditions. The dimensionless variables are used to non-dimensionalize the governing equations of the Williamson nanofluid flow model into dimensionless non-linear partial differential equations (PDEs). Numerical solutions are obtained and the results are presented and examined for the effects of different governing parameters on the velocity, temperature, and concentration fields, and also on physical quantities Nusselt number, Sherwood number, and skin friction coefficient. The velocity profile observed increasing trend against the Reynolds number, thermal Grashof number, and solutal Grashof number while it is decreasing against the higher magnetic parameter. The temperature of the fluid increases for higher radiation parameter, temperature ratio parameter, Eckert number, thermal Biot number, and thermal Grashof number. The fluid concentration profile increases against the Schmidt number, thermophoresis parameter, and solutal Biot number while it declines for the thermal Biot number and Brownian motion parameter. The accuracy of our results are confirmed by comparing the Nusselt number against the radiation parameter with previous results in the literature. • We have examined unsteady two-dimensional MHD Williamson nanofluid flow. • Effects of non-linear thermal radiation and Joule heating are considered. • The heat mass transfer problem is solved numerically, and results are plotted. • Nusselt number, Sherwood number, and skin friction coefficient are studied in plots. • The impacts of various parameters are studied and discussed.