Soret and Dufour effects on convective heat and mass transfer over a stretching / shrinking surface

Mathematical Modelling of convective flow, heat, and mass transfer over a stretching or shrinking surface is studied to show the effects of Soret-Dufour by considering different types of fluids (Newtonian, non-Newtonian and Hybrid nanofluid). The mathematical models that have been investigated are as follows: Two-dimensional model of double-diffusive MHD Casson and Maxwell fluid flow over an exponentially permeable shrinking sheet, two-dimensional model of hybrid nanofluid flow past an exponentially permeable shrinking or stretching sheet, three-dimensional model of double-diffusive MHD Newtonian fluid flow and heat transfer over an exponentially stretching or shrinking sheet and the two-dimensional model of triple diffusive Sodium Chloride and Sucrose water over a nonlinear permeable shrinking sheet. The mathematical model is formed by a set of partial differential equations such as continuity, momentum, energy, and concentration. Similarity transformation is applied to transform the partial differential equations into ordinary differential equations. The MATLAB bvp4c program is the main mathematical program that is used to obtain the final numerical solutions for the reduced ordinary differential equations. The numerical results for the skin friction coefficient, local Nusselt number, local Sherwood number, and the profiles of velocity, temperature, and concentration are presented via plots to analyze the impact of governing parameters (buoyancy ratio, shrinking/ stretching, suction, mixed convection, magnetic field, Brownian motion, thermophoresis parameter, radiation parameter, Prandtl number, Soret number, Dufour number, Schmidt number, Deborah number, Eckert number, Lewis number) in the model. The MATLAB bvp4c program is also implemented to develop stability analysis when dual numerical solutions exist. Positive eigenvalue shows that the solution is stable and physically reliable. On the other hand, the negative eigenvalue represents the unstable solution and is rejected. In the presence of dual solutions, the first solution is accepted as the stable solution and the second solution is unstable. It is found that the temperature of the fluid increases with the increment of the Dufour number while fluids concentration is inclined with increased Soret number. Besides, all the governed parameters affected the variations of the fluid flow, heat transfer, mass transfer, and the profiles of velocity, temperature, and concentration.

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