# American Institute of Mathematical Sciences

August  2018, 11(4): 617-630. doi: 10.3934/dcdss.2018036

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

 1 College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Rawalpindi, 46070, Pakistan 2 Department of Mathematics, Capital University of Science and Technology, Islamabad 44000, Pakistan

* Corresponding author: Asim Aziz

Received  December 2016 Revised  April 2017 Published  November 2017

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.

Citation: Asim Aziz, Wasim Jamshed. Unsteady MHD slip flow of non Newtonian power-law nanofluid over a moving surface with temperature dependent thermal conductivity. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 617-630. doi: 10.3934/dcdss.2018036
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##### References:
Geometry of the problem
Velocity profiles for different values of parameter $A$
Temperature profiles for different values of parameter $A$
Velocity profiles for different values of parameter $M$
Temperature profiles for different values of parameter $M$
Velocity profiles for different values of parameter $\phi$
Temperature profiles for different values of parameter $\phi$
Velocity profiles for different values of parameter $\delta$
Temperature profiles for different values of parameter $\delta$
Velocity profiles for different values of parameter $S$
Temperature profiles for different values of parameter $S$
Velocity profiles for different values of parameter $S$
Temperature profiles for different values of parameter $S$
Values of $-f''(0)$ for the variation of parameters and fixed $Pr= 6.2$, $\Delta = 1.0$ and $\phi = 0.0$
 $M$ $S$ $\delta$ $A$ $-f''(0)$ $-f''(0)$ $-f''(0)$ T.Hayat Khadeejah Present 0.25 1.0 1.0 0.2 0.60157 0.60157 0.60160 1.0 0.2 1.0 0.2 0.57563 0.57563 0.57560 1.0 0.5 1.0 0.2 0.602285 0.602265 0.60228
 $M$ $S$ $\delta$ $A$ $-f''(0)$ $-f''(0)$ $-f''(0)$ T.Hayat Khadeejah Present 0.25 1.0 1.0 0.2 0.60157 0.60157 0.60160 1.0 0.2 1.0 0.2 0.57563 0.57563 0.57560 1.0 0.5 1.0 0.2 0.602285 0.602265 0.60228
Thermophysical properties of the base fluid and nanoparticles
 Physical properties Base fluid Nanoparticles Water Cu $C_{p}(J/kgK)$ 4179 385 $\rho(kg/m^{3})$ 997.1 8933 $k(W/mK)$ 0.613 400 $\sigma (\Omega.m)^{-1}$ 0.05 $5.96\times10^{7}$
 Physical properties Base fluid Nanoparticles Water Cu $C_{p}(J/kgK)$ 4179 385 $\rho(kg/m^{3})$ 997.1 8933 $k(W/mK)$ 0.613 400 $\sigma (\Omega.m)^{-1}$ 0.05 $5.96\times10^{7}$
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