Exact solution of magnetohydrodynamic slip flow and heat transfer over an oscillating and translating porous plate

Yasir Ali; Arshad Alam Khan

doi:10.3934/dcdss.2018034

Article Contents

2018, Volume 11, Issue 4: 595-606. Doi: 10.3934/dcdss.2018034

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Exact solution of magnetohydrodynamic slip flow and heat transfer over an oscillating and translating porous plate

Yasir Ali^1, and
Arshad Alam Khan^2,

1.
National University of Sciences and Technology, College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan
2.
National University of Sciences and Technology, School of Natural Science, H-12 Islamabad, Pakistan

Received: November 30, 2016

Revised: April 30, 2017

Published: August 2018

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Abstract

Objective of this paper is to study natural convection MHD flow past over a moving porous plate with heat source in the porous medium. The motion of the plate is translating as well as oscillating and embedded in the porous medium. The exact solution of the governing equations, of the flow and heat transfer for this model is obtained. To study heat flux for our model we use Nusselt number. Comparisons of effects of magnetic parameter $M$, translation $a$ and heat source parameter $S$ on velocity and temperature profile is given. The effects of some other physical parameters like Prandtl number $P_r$, Grashof number for heat transfer $G_r$, Permeability parameter $K_p$, is presented graphically on the distributions of velocity and temperature. It is concluded that the fluid motion in the boundary layer increases with increase of $a$, $S$, $G_r$ and $K_P$. Whereas opposite behavior is observed for $M$ and $P_r$. The heat source parameter increases the temperature of fluid and on the other hand cooling effects occur due to $P_r$ and $v_0$.

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Mathematics Subject Classification: Primary: 76S05, 76R10; Secondary: 76W05.

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Figure 1. Velocity profile against $y$ for different values of $a$

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Figure 2. Velocity against $y$ for different values of $M$

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Figure 3. Velocity profile against $y$ for different values of $S$

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Figure 4. Velocity profile against $y$ for different values of $G_r$

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Figure 5. Velocity profile against $y$ for different values of $K_p$

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Figure 6. Velocity profile against $y$ for different values of $P_r$

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Figure 7. Velocity profile against $y$ for different values of $\upsilon_0$

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Figure 8. Temperature profile against $y$ for different values of $\upsilon_0$

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Figure 9. Temperature profile against $y$ for different values of $P_r$

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Figure 10. Temperature profile against $y$ for different values of $S$

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