International Journal of Research and Innovation in Applied Science (IJRIAS) | Volume VII, Issue VIII, July 2022 | ISSN 2454–6194
Hussaini Abdullahi1, I.J. Uwanta2 and E. Omokhuale3
1Department of Mathematics, Sokoto State University, Sokoto, Nigeria.
2Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria.
3Department of Mathematical Sciences, Federal University Gusau, Zamfara State, Nigeria.
Abstract: This manuscript addresses the impressions of Darcy-Forchheimer flow of hydromagnetic viscous incompressible fluid in a vertical infinite porous channel. The governing equations in dimensionless form is considered to the analysis. Implicit-finite difference scheme is employed to obtain the numerical solutions of the non-linear differential equations governing the flow. Relevance fluid flow quantities are found and portrayed graphically. Also, skin-friction, Nusselt number, and Sherwood number are numerically examined. It is understood that velocity, temperature, and concentration of the fluid change substantially with Forchheimer parameter, variable viscosity parameter, thermal conductivity parameter, and chemical reaction parameter.
Keywords: Forchheimer model, variable viscosity, thermal conductivity, implicit-finite-difference technique.
I. INTRODUCTION
Various industrial, environmental and engineering setups like chemical action reactors, heat ex-changers, geological setups, geothermic systems and many others require the convection through porous medium. The mechanical phenomenon, drag force and diffusion effects are dealt in Darcy-Forchheimer model. The model is employed to interpret the mechanical phenomenon in fluid flow and heat flux analysis. The velocity term with drag force constant is appended in momentum equation to convert the simple model into Darcy-Forchheimer model. Many applications like organic compound recovery method, soil physics, living tissue transformation, waste storage particularly gas wastes and plenty of others belong to this development. Numerous studies have been reported in this circumstance. Majeed et al [1] carried out Numerical study of Darcy-Forchheimer model with activation energy subject to chemically reactive species and momentum slip of order two. Darcy-Forchheimer flow of Maxwell Nanofluid flow over a linear stretching surface with nonlinear thermal radiation and activation energy was examined Sajid T et. al [2]. Analysis of results of Darcy-Forchheimer and Cattaneo-Christov of radiative three-dimensional Maxwell fluid flow over a vertical surface was studied by Khan and Nadeem [3]. Tarakaramu et al. [4]