American Journal of Mathematical and Computational Sciences
Manuscript Information

Reacting Flow of Temperature-Dependent Variable Permeability Through a Porous Medium in the Presence of Arrhenius Reaction
American Journal of Mathematical and Computational Sciences
Vol.4 , No. 1, Publication Date: Mar. 6, 2019, Page: 11-18
711 Views Since March 6, 2019, 221 Downloads Since Mar. 6, 2019

Authors

 [1] Benjamin Aina Peter, School of Engineering and Applied Sciences, Kamapala International University, Kampala, Uganda. [2] Amos Wale Ogunsola, Departmentof Pure and Applied Mathematics, University of Technology, Ogbomoso, Nigeria. [3] Anthony EjehItodo, School of Engineering and Applied Sciences, Kamapala International University, Kampala, Uganda. [4] Idowu Sabiki Adebola, Departmentof Mathematical Sciences, Olabisi Onabanjo University, Ago-Iwoye, Nigeria. [5] Mundu Muhamad Mustapha, School of Engineering and Applied Sciences, Kamapala International University, Kampala, Uganda.

Abstract

In this work, a reacting flow of temperature-dependent variable permeability through a porous medium has studied and analyzed. It is assumed that the viscosity is temperature-dependent. Absolute permeability is said to be the ability of a porous medium to transmit its fluid content under an applied pressure gradient. The permeability of a porous medium is an intrinsic property that measures its ability to transmit fluids or a medium that allow fluids to pass through it. It is determined by the macroscopic properties of the medium namely porosity, pore size distribution, tortuosity and specific surface. It is a well known fact that the value of permeability is independent of the type of fluid used in the porous medium where Newtonian fluids are used for measurements. Since a porous medium contains pores, the applications of thermal science to the system leads to an intuitive believe that the thermal expansion coefficient of the solid component will cause volumetric expansion with changes in temperature variation of the medium. The governing partial differential equations are transformed into ordinary differential equations in terms of a suitable similarity variable. Galerkin weighted residual method is employed to solve the resulting non-linear equations and the effects of various physical parameter s involve in the system of flow were reported graphically. Furthermore, the effect of variable permeability parameter on the velocity profile is investigated. Some special cases with their physical significance are discussed and compared with the existing published work.

Keywords

Unsteady Gravity Flow, Weighted Residual Method, Power-Law Fluid and Viscous Dissipation

Reference