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**Exact solution of magnetohydrodynamic slip flow and heat transfer over an oscillating and translating porous plate.**
*(English)*
Zbl 1386.76156

Summary: 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 \(\upsilon_0\).

### MSC:

76S05 | Flows in porous media; filtration; seepage |

76R10 | Free convection |

76W05 | Magnetohydrodynamics and electrohydrodynamics |

### Keywords:

natural convection; hydromagnetic flow; porous medium; oscillating and translating plate; heat source
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\textit{Y. Ali} and \textit{A. A. Khan}, Discrete Contin. Dyn. Syst., Ser. S 11, No. 4, 595--606 (2018; Zbl 1386.76156)

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