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

Article Contents

2018, Volume 11, Issue 4: 617-630. Doi: 10.3934/dcdss.2018036

This issue Previous Article Conservation laws and symmetries of time-dependent generalized KdV equations Next Article Symmetries and conservation laws of a KdV6 equation

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

Asim Aziz^1, , and
Wasim Jamshed^2, ,

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
* Corresponding author: Asim Aziz

Received: November 30, 2016

Revised: March 31, 2017

Published: August 2018

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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.

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Mathematics Subject Classification: Primary: 76R05, 76W05; Secondary: 76M60.

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Figure 1. Geometry of the problem

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Figure 2. Velocity profiles for different values of parameter $A$

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Figure 3. Temperature profiles for different values of parameter $A$

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Figure 4. Velocity profiles for different values of parameter $M$

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Figure 5. Temperature profiles for different values of parameter $M$

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Figure 6. Velocity profiles for different values of parameter $\phi$

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Figure 7. Temperature profiles for different values of parameter $\phi$

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Figure 8. Velocity profiles for different values of parameter $\delta$

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Figure 9. Temperature profiles for different values of parameter $\delta$

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Figure 10. Velocity profiles for different values of parameter $S$

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Figure 11. Temperature profiles for different values of parameter $S$

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Figure 12. Velocity profiles for different values of parameter $S$

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Figure 13. Temperature profiles for different values of parameter $S$

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Table 1. 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

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Table 2. 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 $5.96\times10^{7}$

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

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$M$	$S$	$\delta$	$A$	$-f''(0)$	$-f''(0)$	$-f''(0)$
				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

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	$5.96\times10^{7}$

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

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