In this paper we report on combined Dufour and Soret effects on the heat and mass transfer in a Casson nanofluid flow over an unsteady stretching sheet with thermal radiation and heat generation. The effects of partial slip on the velocity at the boundary, convective thermal boundary condition, Brownian and thermophoresis diffusion coefficients on the concentration boundary condition are investigated. The model equations are solved using the spectral relaxation method. The results indicate that the fluid flow, temperature and concentration profiles are significantly influenced by the fluid unsteadiness, the Casson parameter, magnetic parameter and the velocity slip. The effect of increasing the Casson parameter is to suppress the velocity and temperature growth. An increase in the Dufour parameter reduces the flow temperature, while an increase in the value of the Soret parameter causes increase in the concentration of the fluid. Again, increasing the velocity slip parameter reduces the velocity profile whereas increasing the heat generation parameter increases the temperature profile. A validation of the work is presented by comparing the current results with existing literature

In this article, we use the Buongiorno model to study the three‐dimensional tangent hyperbolic nanofluid flow over a stretched sheet. The study investigates the impact of velocity slip on the flow and heat transfer features in a tangent hyperbolic nanofluid. For a better fit with experimental observations. We assume that the nanoparticle mass flux at the boundary is zero as opposed to a prescribed concentration at the surface. Using appropriate transformations, we reduce the partial differential equations that describe the momentum, energy, and concentration transport to ordinary differential equations. Numerical solutions of the equations are obtained using the spectral method. Graphical illustration of the physical influence of various parameters on the flow features, the skin friction coefficient, and the local Nusselt number is given. The results indicate, that particle Brownian motion has a negligible impact on the rate of heat transfer. The impact of the modified Weissenberg number, a measure of the ratio of elastic to viscous forces, causes a reduction in the fluid velocity. The results are shown to be good agreement with those in related studies in the literature.

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In this paper, we have investigated the unsteady mixed convection flow and heat transfer in a nanofluid with buoyancy, thermal radiation and double diffusive effects over a vertical plate which is assumed to be moving in the free stream direction in a porous medium. The plate is maintained at a constant wall temperature while the nanoparticle flux at the boundary is zero. The free stream velocity is time dependent, an assumption that leads to non-similar differential equations. The equations are solved using the bivariate spectral quasilinearization method, a method used to solve this kind of problem for the first time. The thermal radiation parameter enhances the temperature profile, while the nanoparticle concentration profile is enhanced by the thermophoresis parameter but reduced by an increase in the Brownian motion parameter. The unsteadiness of the flow leads to an increase in the momentum boundary layer thickness and a decrease in the temperature and concentration boundary layer thickness. The skin friction coefficient is reduced by the unsteady parameter, while it increases the rate of heat transfer. We present a comparison of result with those in existing literature.