article · Journal of Applied Mathematics
Mathematical modelling describes how heat and mass transfer occur within an unsteady, two-dimensional flow of Williamson nanofluids over a permeable stretching sheet placed in a porous medium. The study evaluates the simultaneous effects of magnetic fields, thermal radiation, and chemical reactions. By applying similarity transformations, the governing partial differential equations were converted into ordinary differential equations and solved through the homotopy analysis method. Results demonstrate that boundary layer thicknesses for velocity, temperature, and concentration decline with distance from the surface. In addition, an increase in the Williamson parameter suppresses fluid velocity while elevating temperature and concentration levels near the sheet. Stronger magnetic fields, greater thermal radiation, or faster chemical reaction rates accelerate mass transfer, but these factors simultaneously decelerate heat transfer across the boundary layer.
Gaining precise mathematical insight into how non-Newtonian nanofluids move and exchange thermal energy under external magnetic and radiative forces informs foundational fluid dynamics. These analytical solutions help clarify the interplay between chemical reactions and heat transfer over permeable boundaries, providing baseline data for predicting transport phenomena in porous systems.
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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.
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DOI: 10.1155/2020/1890972
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