Combined effects of Joule heating and nonuniform 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 masstransfer for a viscous incompressible fluid through a vertical stretching surface embedded ina Darcy-Forchheimer porous medium in the presence of a non-uniform heat source/sink andfirst-order chemical reaction.The porous surface is subjected to a uniform transverse magneticfield.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 resultantsystem of non-linear ordinary differential equations has been solved numerically with the helpof the“MATLAB”BVP4C Solver.Results are presented graphically to analyze the effects ofvarious physical parameters discovered in the problem such as Hartmann number(M),Forchheimer number(Fr),Grashof number(Gr),solutal Grashof number(Gc),suction parameter(S),porosity parameter(el),dimensionless velocity slip(Sv),Prandtl number(Pr),dimensionless thermal slip(St),space-dependent heat source/sink parameter(eA
1),temperature-dependent heat source/sink(eB)1),Eckert number(Ec),Schmidt number(Sc),chemical reaction parameter(g),unsteadiness parameter(A),and dimensionless concentration slip(Sc)on non-dimensionalvelocity ec0ðhÞ,temperature zðhÞ,and concentration efðhÞprofiles.The influence of these parameters on skin-friction coefficient(C)f),Nusselt number(Nu)x),and Sherwood number(Sh)x)areexpressed in tabular form.It is observed that an enhancement in Fr and el results in the declination of the velocity profile.There is an enhancement in temperature with an increment in theeA)1 and eB)1.The physical representation of flow characteristics that appeared in the problem ispresented using various graphs to depict real-world applications in industrial and engineeringoperations.The results were compared to previous studies,revealing that the two are in goodagreement.The novelty of the present investigation is:To interpret the combined effects ofviscous dissipation and Joule heating on a vertical stretching surface embedded in a highlyporous medium modeled using the Darcy-Forchheimer model.The findings could be valuablein understanding the flow of oil,gas,and water through an oil or gas field reservoir,as well asgroundwater migration and filtering and purification procedures.