Numerical Simulation of Viscous Flow in Heterogeneous Media With Magnetic Effect

ABSTRACT The current article focuses on the characteristics of fluid flow resulting from the stretching of a sheet through a permeable medium. In real situations, the porous structure does not always need to be homogeneous, and hence, both homogeneous and heterogeneous media are taken into account, which relates to the geothermal reservoir model. The flow for a heterogeneous porous medium is examined under three different configurations, namely, linear, quadratic, and cubic functions for the stretching sheet. The physical flow system explored in the present study is framed mathematically, which results in a coupled nonlinear partial system of equations that are solved numerically through a finite difference method. The solutions are extracted for the four different permeable matrices, that is, when the medium is constant, varies linearly, quadratically, and exponentially. The numerical solution shows that the velocity of the fluid is relatively high in the cubical stretching of a sheet and lowest in the linearly varying one. A noteworthy disparity appears between the characteristics of the fluid flow through homogeneous and heterogeneous porous matrices. Particularly, the fluid movement is faster when the flow is through a homogeneous porous system than in a heterogeneous one. In addition, the streamlines and skin friction are also presented with the engineering interest. It is noticed that the friction rate is maximum in the exponentially varying porous medium, moderate in the linear case, and minimum in the quadratic case when the Reynolds number, magnetic strength, and stretching parameter are incremented. Further, the friction factor is found to be less in a homogeneous medium than in a heterogeneous case.