Steady flow of some non-newtonian fluids through a porous medium by using adomian decomposition method

Abstract

Non-Newtonian fluids are employed in a wide range of industrial applications. Non-Newtonian fluids that shows characteristics of both elastic and viscous fluids as a result of shear stress, are referred to as viscoelastic fluids. Constitutive equations of the viscoelastic fluids, flow patterns and viscous response are important challenges that need to be considered when modelling the flow in a porous medium. The predominant idea of this thesis is to find the analytical solutions of viscoelastic fluid in a porous medium. The primary goal of this research is to create a one-dimensional simulation for three different kinds of viscoelastic fluids, namely, Johnson-Segalman, Powell-Eyring, and Sisko fluids, in a porous medium. Further, Darcy’s law is selected for simulating permeable media saturated by viscoelastic fluid. The effect of external magnetic field is an additional feature to the innovation of the constructed mathematical models. The system of nonlinear coupled partial differential equations supported by related boundary conditions are solved analytically by using the Adomian decomposition method (ADM). In the analysis, the impact of various physical parameters on velocity and temperature are scrutinized and the results are exhibited graphically. The wall shear stress versus governing constraints are also evaluated, and their results are summarised in the form of tables and graphs. The results demonstrated that for both isothermal and non-isothermal circumstances, the inclination angle causes a variation in shear stress. It is also observed that the viscosity and shear stress have a direct connection in the absence of a heating effect. Moreover, the viscosity of the non-isothermal state is sensitive to temperature variations for both lift and drainage problems. The findings validated the efficacy of the suggested technique, and the solutions are successfully approximated to the exact solutions.