Unsteady MHD slip flow of non Newtonian power-law nanofluid over a moving surface with temperature dependent thermal conductivity

Asim Aziz,Wasim Jamshed

doi:10.3934/dcdss.2018036

Abstract

In this paper, unsteady magnetohydrodynamic (MHD) boundary layer slip flow and heat transfer of power-law nanofluid over a nonlinear porous stretching sheet is investigated numerically. The thermal conductivity of the nanofluid is assumed as a function of temperature and the partial slip conditions are employed at the boundary. The nonlinear coupled system of partial differential equations governing the flow and heat transfer of a power-law nanofluid is first transformed into a system of nonlinear coupled ordinary differential equations by applying a suitable similarity transformation. The resulting system is then solved numerically using shooting technique. Numerical results are presented in the form of graphs and tables and the effect of the power-law index, velocity and thermal slip parameters, nanofluid volume concentration parameter, applied magnetic field parameter, suction/injection parameter on the velocity and temperature profiles are examined from physical point of view. The boundary layer thickness decreases with increase in strength of applied magnetic field, nanoparticle volume concentration, velocity slip and the unsteadiness of the stretching surface. Whereas thermal boundary layer thickness increase with increasing values of magnetic parameter, nanoparticle volume concentration and velocity slip at the boundary.

Highlights

Class of fluids in which particles of nanometric size are disseminated in the base fluid is called a nanofluid
U and v are velocity components along the x and y directions respectively, t is the time, τxy is the shear stress component of nanofluid, ρnf is the density, σnf is the electrical conductivity, (Cp)nf is the specific heat capacity and κ∗nf is the thermal conductivity of nanofluid. τxy for the power-law model is taken as given by Bird et al [7]
In this paper a simplified model is presented to study the magnetohydrodynamic boundary layer slip flow and heat transfer characteristics of power-law nanofluid over an unsteady porous stretching sheet

Summary

Introduction

Class of fluids in which particles of nanometric size are disseminated in the base fluid is called a nanofluid. Bhaskar et al [4] carried out an analysis to investigate the influence of variable thermal conductivity and partial velocity slip on the hydromagnetic two-dimensional boundary layer flow of nanofluids over a porous sheet with a convective boundary condition. Sui et al [40] analyzed boundary layer heat and mass transfer with Cattaneo-Christov double-diffusion in upper-convected Maxwell nanofluid past a stretching sheet with slip velocity condition. To the best of authors knowledge no research is conducted to study the unsteady MHD slip flow and heat transfer of power-law nanofluids over a porous nonuniform stretching surface with temperature dependent thermal conductivity. In this present paper, we consider an unsteady, two-dimensional laminar flow with heat transfer of an incompressible electrically conducting power-law nanofluid over a porous stretching sheet.

Temperature Profile v

The surface temperature of the sheet is

Physical properties