Finite Element Method Solution of Boundary Layer Flow of Powell-Eyring Nanofluid over a Nonlinear Stretching Surface

Wubshet Ibrahim,Gosa Gadisa

doi:10.1155/2019/3472518

Abstract

The nonlinear convective flow of Eyring-Powell nanofluid using Catteneo-Christov model with heat generation or absorption term and chemical reaction rate over nonlinear stretching surface is analyzed. The simultaneous nonlinear partial differential equations governing the boundary layer flow are transformed to the corresponding nonlinear ordinary differential equations using similarity solution and then solved using Galerkin finite element method (GFEM). The impacts of pertinent governing parameters like Brownian diffusion, thermophoresis, mixed convection, heat generation or absorption, chemical reaction rate, Deborah numbers, Prandtl number, magnetic field parameter, Lewis number, nonlinear stretching sheet, and Eyring-Powell fluid parameters on velocity field, temperature, and nanoparticle concentration are given in both figures and tabular form. The result shows that the rise in chemical reaction rate will improve mass transfer rate and reduce heat transfer rate and local buoyancy parameter has quit opposite effect. The attributes of local skin friction coefficient, Nusselt number, and Sheer wood number are investigated and validated with existing literatures.

Highlights

Due to wide application of non-Newtonian fluids in the advancement of modern technologies, many researchers engaged to explore the non-Newtonian fluid
We employed the Galerkin finite element method which is a prominent technique to solve nonlinear differential equations through the following five steps that are essential to realize what the approach of the FEM is: (i) Discretization of the domain into elements (ii) Element formulation which is called setup of differential equation in its weak form (iii) Assembly of element equations known as setup of global problem or obtaining equations for the entire system from the equations for one element (iv) Impose the appropriate boundary condition (v) Solve the system of equations
The nonlinear partial differential equations governing the laminar boundary layer flow were converted to the matching nonlinear ordinary differential equations (ODEs) using appropriate similarity transformation and passed through five necessary steps for solving differential equations using Galerkin finite element method (GFEM)

Summary

Introduction

Due to wide application of non-Newtonian fluids in the advancement of modern technologies, many researchers engaged to explore the non-Newtonian fluid. The investigators exposed that non-Newtonian fluids are applicable in polymer devolatilization and processing, heat exchangers, extrusion process, wire and fiber coating, chemical processing equipment, etc. Different researchers studied different non-Newtonian models by different solution method. Modeling of the viscoelastic properties of polymers has often been a very hot subject. The viscoelastic constitutive equations have been developed for the understanding of the numerous means of deformation and flow but unluckily have not offered us quantitative prophetic power. Few viscoelastic boundary layer flow problems can be solved with the suitable constitutive equations, but this is still an area of academic research with partial practical applications at the moment

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Conclusion