# American Institute of Mathematical Sciences

• Previous Article
Conservation laws and symmetries of time-dependent generalized KdV equations
• DCDS-S Home
• This Issue
• Next Article
Numerical investigation of Cattanneo-Christov heat flux in CNT suspended nanofluid flow over a stretching porous surface with suction and injection
August  2018, 11(4): 595-606. doi: 10.3934/dcdss.2018034

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

 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  December 2016 Revised  May 2017 Published  November 2017

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 $v_0$.

Citation: Yasir Ali, Arshad Alam Khan. Exact solution of magnetohydrodynamic slip flow and heat transfer over an oscillating and translating porous plate. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 595-606. doi: 10.3934/dcdss.2018034
##### References:

show all references

##### References:
Velocity profile against $y$ for different values of $a$
Velocity against $y$ for different values of $M$
Velocity profile against $y$ for different values of $S$
Velocity profile against $y$ for different values of $G_r$
Velocity profile against $y$ for different values of $K_p$
Velocity profile against $y$ for different values of $P_r$
Velocity profile against $y$ for different values of $\upsilon_0$
Temperature profile against $y$ for different values of $\upsilon_0$
Temperature profile against $y$ for different values of $P_r$
Temperature profile against $y$ for different values of $S$
 [1] Azhar Ali Zafar, Khurram Shabbir, Asim Naseem, Muhammad Waqas Ashraf. MHD natural convection boundary-layer flow over a semi-infinite heated plate with arbitrary inclination. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 1007-1015. doi: 10.3934/dcdss.2020059 [2] Guofu Lu. Nonexistence and short time asymptotic behavior of source-type solution for porous medium equation with convection in one-dimension. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1567-1586. doi: 10.3934/dcdsb.2016011 [3] Edoardo Mainini. On the signed porous medium flow. Networks & Heterogeneous Media, 2012, 7 (3) : 525-541. doi: 10.3934/nhm.2012.7.525 [4] Matthias Erbar, Jan Maas. Gradient flow structures for discrete porous medium equations. Discrete & Continuous Dynamical Systems - A, 2014, 34 (4) : 1355-1374. doi: 10.3934/dcds.2014.34.1355 [5] Ansgar Jüngel, Ingrid Violet. Mixed entropy estimates for the porous-medium equation with convection. Discrete & Continuous Dynamical Systems - B, 2009, 12 (4) : 783-796. doi: 10.3934/dcdsb.2009.12.783 [6] Michela Eleuteri, Jana Kopfov, Pavel Krej?. Fatigue accumulation in an oscillating plate. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 909-923. doi: 10.3934/dcdss.2013.6.909 [7] Kaouther Ammar, Philippe Souplet. Liouville-type theorems and universal bounds for nonnegative solutions of the porous medium equation with source. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 665-689. doi: 10.3934/dcds.2010.26.665 [8] Anna Marciniak-Czochra, Andro Mikelić. A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium. Discrete & Continuous Dynamical Systems - S, 2014, 7 (5) : 1065-1077. doi: 10.3934/dcdss.2014.7.1065 [9] Yaqing Liu, Liancun Zheng. Second-order slip flow of a generalized Oldroyd-B fluid through porous medium. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 2031-2046. doi: 10.3934/dcdss.2016083 [10] Marie Henry, Danielle Hilhorst, Robert Eymard. Singular limit of a two-phase flow problem in porous medium as the air viscosity tends to zero. Discrete & Continuous Dynamical Systems - S, 2012, 5 (1) : 93-113. doi: 10.3934/dcdss.2012.5.93 [11] Wen Wang, Dapeng Xie, Hui Zhou. Local Aronson-Bénilan gradient estimates and Harnack inequality for the porous medium equation along Ricci flow. Communications on Pure & Applied Analysis, 2018, 17 (5) : 1957-1974. doi: 10.3934/cpaa.2018093 [12] Kashif Ali Abro, Ilyas Khan. MHD flow of fractional Newtonian fluid embedded in a porous medium via Atangana-Baleanu fractional derivatives. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 377-387. doi: 10.3934/dcdss.2020021 [13] María Anguiano, Francisco Javier Suárez-Grau. Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions. Networks & Heterogeneous Media, 2019, 14 (2) : 289-316. doi: 10.3934/nhm.2019012 [14] Zhiqiang Yang, Junzhi Cui, Qiang Ma. The second-order two-scale computation for integrated heat transfer problem with conduction, convection and radiation in periodic porous materials. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 827-848. doi: 10.3934/dcdsb.2014.19.827 [15] Changfeng Gui, Huaiyu Jian, Hongjie Ju. Properties of translating solutions to mean curvature flow. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 441-453. doi: 10.3934/dcds.2010.28.441 [16] Guillermo Reyes, Juan-Luis Vázquez. The Cauchy problem for the inhomogeneous porous medium equation. Networks & Heterogeneous Media, 2006, 1 (2) : 337-351. doi: 10.3934/nhm.2006.1.337 [17] Luis Caffarelli, Juan-Luis Vázquez. Asymptotic behaviour of a porous medium equation with fractional diffusion. Discrete & Continuous Dynamical Systems - A, 2011, 29 (4) : 1393-1404. doi: 10.3934/dcds.2011.29.1393 [18] Noreen Sher Akbar, Dharmendra Tripathi, Zafar Hayat Khan. Numerical investigation of Cattanneo-Christov heat flux in CNT suspended nanofluid flow over a stretching porous surface with suction and injection. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 583-594. doi: 10.3934/dcdss.2018033 [19] R.E. Showalter, Ning Su. Partially saturated flow in a poroelastic medium. Discrete & Continuous Dynamical Systems - B, 2001, 1 (4) : 403-420. doi: 10.3934/dcdsb.2001.1.403 [20] Paul Deuring, Stanislav Kračmar, Šárka Nečasová. Linearized stationary incompressible flow around rotating and translating bodies -- Leray solutions. Discrete & Continuous Dynamical Systems - S, 2014, 7 (5) : 967-979. doi: 10.3934/dcdss.2014.7.967

2018 Impact Factor: 0.545