Combined effects of Joule heating and non-uniform heat source/sink on unsteady MHD mixed convective flow over a vertical stretching surface embedded in a Darcy-Forchheimer porous medium

This paper deals with an unsteady magnetohydrodynamics (MHD) heat and mass transfer for a viscous incompressible fluid through a vertical stretching surface embedded in a Darcy-Forchheimer porous medium in the presence of a non-uniform heat source/sink and first-order chemical reaction. The porous surface is subjected to a uniform transverse magnetic field. The influence of velocity, thermal, and concentration slip is also investigated. The governing equations are coupled non-linear partial differential equations, which have been converted via similarity transformation into a set of ordinary differential equations. The resultant system of non-linear ordinary differential equations has been solved numerically with the help of the MATLAB BVP4C Solver. Results are presented graphically to analyze the effects of various physical parameters discovered in the problem such as Hartmann number (M), For-chheimer number (Fr), Grashof number (Gr), solutal Grashof number (Gc), suction parameter (S), porosity parameter ((lambda) over tilde), dimensionless velocity slip (S-v), Prandtl number (Pr), dimension-less thermal slip (S-t), space-dependent heat source/sink parameter ((A) over tilde (1)*), temperature-dependent heat source/sink ((B) over tilde (1)*), Eckert number (Ec), Schmidt number (Sc), chemical reaction parameter (gamma), unsteadiness parameter (A), and dimensionless concentration slip (S-c) on non-dimensional velocity (chi) over tilde'(eta), temperature zeta(eta), and concentration (phi) over tilde(eta) profiles. The influence of these parameters on skin-friction coefficient (C-f*), Nusselt number (Nu(x)*), and Sherwood number (Sh(x)*) are expressed in tabular form. It is observed that an enhancement in Fr and (lambda) over tilde results in the declination of the velocity profile. There is an enhancement in temperature with an increment in the (A) over tilde (1)* and (B) over tilde (1)*. The physical representation of flow characteristics that appeared in the problem is presented using various graphs to depict real-world applications in industrial and engineering operations. The results were compared to previous studies, revealing that the two are in good agreement. The novelty of the present investigation is: To interpret the combined effects of viscous dissipation and Joule heating on a vertical stretching surface embedded in a highly porous medium modeled using the Darcy-Forchheimer model. The findings could be valuable in understanding the flow of oil, gas, and water through an oil or gas field reservoir, as well as groundwater migration and filtering and purification procedures. (C) 2022 The Authors. Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd.

Automated summary

The paper discusses the unsteady magnetohydrodynamics heat and mass transfer for a viscous incompressible fluid through a vertical stretching surface embedded in a Darcy-Forchheimer porous medium. Various physical parameters and their effects were analyzed, with results presented graphically. The study's novelty lies in interpreting the combined effects of viscous dissipation and Joule heating on a vertical stretching surface in a highly porous medium.