In this paper, analytic approximation to the heat and mass transfer characteristics of a two-dimensional time-dependent flow of Williamson nanofluids over a permeable stretching sheet embedded in a porous medium has been presented by considering the effects of magnetic field, thermal radiation, and chemical reaction. The governing partial differential equations along with the boundary conditions were reduced to dimensionless forms by using suitable similarity transformation. The resulting system of ordinary differential equations with the corresponding boundary conditions was solved via the homotopy analysis method. The results of the study show that velocity, temperature, and concentration boundary layer thicknesses generally decrease as we move away from the surface of the stretching sheet and the Williamson parameter was found to retard the velocity but it enhances the temperature and concentration profiles near the surface. It was also found that increasing magnetic field strength, thermal radiation, or rate of chemical reaction speeds up the mass transfer but slows down the heat transfer rates in the boundary layer. The results of this study were compared with some previously published works under some restrictions, and they are found in excellent agreement.

This work was carried out in collaboration between the two authors EH and BS. Author BS designed the study, wrote the protocol and wrote the first draft of the manuscript. Author EH deals with the calculation part, managed the analysis of the study and executed the program. Both authors read and approved the final manuscript.

The main purpose of this study is to give a mathematical analysis of heat and mass transfer in a boundary layer flow of Casson fluid over an inclined stretching cylinder in the presence of magnetic nanoparticles. The effects of Casson parameter, curvature of the cylinder, angle of inclination, Buoyancy force, external magnetic field, thermal radiation, Joule heating, viscous dissipation, heat source and chemical reaction are taken into account. Appropriate transformations are incorporated to convert the governing partial differential equations and the boundary conditions suitable for computation. The elegant optimal homotopy analysis method is used to obtain analytic approximations for the resulting system of nonlinear differential equations. The features of flow characteristics such as velocity, temperature and concentration profiles in response to the variations of the emerging parameters are simulated and examined in detail. Extensive analysis is also made to explore the influences of relevant constraints on the rates of momentum, heat and mass transfer near the surface of the cylinder. Among the many outputs of the study, it is found that increasing the non-Newtonian Casson parameter can slowdown the flow velocity and enhance the temperature and concentration profiles. It is also revealed that significant enhancement of wall friction and mass transfer rate can be achieved by increasing the curvature of the cylinder. Further, the analytic approximations obtained by implementing the optimal homotopy analysis method to the present model are in close agreements with previous studies under common assumptions.

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Heat and mass transfer in the boundary-layer flow of unsteady viscous nanofluid along a vertical stretching sheet in the presence of magnetic field, thermal radiation, heat generation, and chemical reaction are presented in this paper. The sheet is situated in the xz-plane and y is normal to the surface directing towards the positive y-axis. The sheet is continuously stretching in the positive x-axis and the external magnetic field is applied to the system parallel to the positive y-axis. With the help of similarity transformations, the partial differential equations are transformed into a couple of nonlinear ordinary differential equations. The new problem is then solved numerically by a finite-difference scheme known as the Keller-box method. Effects of the necessary parameters in the flow field are explicitly studied and briefly explained graphically and in tabular form. For the selected values of the pertinent parameters appearing in the governing equations, numerical results of velocity, temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number are obtained. The results are compared to the works of others (from previously published journals) and they are found in excellent agreement.