Numerical Solution of Skin Friction in Porous Medium Using Brinkman Forchheimer Model Under Fuzzy Environment

Abstract

Abstract Fluid flow and transport processes through porous structures are a topic of great interest in various scientific and technical fields. In this paper an attempt has been made to fuzzify the boundary conditions and the differential equation governed by the flow of a steady incompressible viscous fluid flow through a porous medium confined between two horizontal walls using the Brinkman Forchheimer model. The 𝛼−𝑐𝑢𝑡 technique is used to show the validation for the uncertainty of the equation of the motion Numerical solution is carried out by developing computer codes for the Fuzzified boundary value problem. The effect of the permeability parameter 𝜎 and Ergun number 𝐸𝑟 is being discussed under fuzzy Environment. We observe that the uncertainty in the solution of the said problem is due to the effect of the permeability parameter 𝜎, but not for the parameter Ergun number 𝐸𝑟. Finally, we compare the corresponding values of the skin friction between crisp and Fuzzified values under the justifying range of the parameters. We have found that velocity decrease for the increase’s values of 𝜎.