Porosity effect on unsteady MHD free convection flow of Jeffrey fluid past an oscillating vertical plate with ramped wall temperature

Nor Athirah Mohd Zin, Ahmad Qushairi Mohamad, Ilyas Khan, Sharidan Shafie

Abstract


The unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid embedded in porous medium past an oscillating vertical plate generated by thermal radiation with ramped wall temperature is investigated. The incompressible fluid is taken electrically conducting under the action of transverse magnetic field towards the flow. Constitutive relation of Jeffrey fluid is employed to model the governing equations in terms of partial differential equations with some physical conditions. The transformed dimensionless governing equations are solved analytically using Laplace transform technique. The impact of various pertinent parameters namely material parameter of Jeffrey fluid , dimensionless parameter of Jeffrey fluid , phase angle , Hartmann number , permeability parameter , Grashof number , Prandtl number , radiation parameter  and dimensionless time  on velocity and temperature distributions are presented graphically and discussed in details. It is observed that, the permeability parameter tend to retard the fluid velocity for ramped wall temperature but enhance the velocity for an isothermal plate. Besides that, this study shows, the amplitude of velocity and temperature fields for ramped wall temperature are always lower than isothermal plate. A comparison with the existing published work is also provided to confirm the validity of the present results and an excellent agreement are found. 


Keywords


Unsteady; Jeffrey Fluid; MHD; Porous Medium; Oscillating Vertical Plate; Laplace Transform Technique

Full Text:

PDF

References


Aaiza, G., Khan, I., Shafie, S. (2015). Energy transfer in mixed convection mhd flow of nanofluid containing different shapes of nanoparticles in a channel filled with saturated porous medium. Nanoscale Research Letters. 10(490): 1-14.

Al- Khafajy, D. G. S. (2016). Effects of heat transfer on MHD oscillatory flow of Jeffrey Fluid with variable viscosity through porous medium. Advances in Applied Science Research. 7(3): 179-186.

Ali, A., Asghar, S. (2014). Analytic solution for oscillatory flow in a channel for Jeffrey Fluid. Journal of Aerospace Engineering. 27: 644-651.

Ali, F., Khan, I., Shafie, S. (2014). Closed form solutions for unsteady free convection flow of a second grade fluid over an oscillating vertical plate. PLoS ONE. 9(2): 1-15.

Bhaskar Reddy, G., Sreenadh, S., Hemadri Reddy, R., Kavitha, A. (2015). Flow of a Jeffrey Fluid between torsionally oscillating disks. Ain Shams Engineering Journal. 6: 355-362.

Cortell, R. (2014). Fluid flow and radiative nonlinear heat transfer over a stretching sheet. Journal of King Saud University-Science. 26: 161-167.

Das, R. K., Neog, B. C. (2015). MHD flow past a vertical oscillating plate with radiation and chemical reaction in porous medium. IOSR Journal of Mathematics. 11(1): 46-50.

Gao, C., Jian, Y. (2015). Analytical solution of magnetohydrodynamic flow of Jeffrey Fluid through a circular microchannel. Journal of Molecular Liquids. 211: 803-811.

Ghara, N., Das, S., Maji, S. L., Jana R. N. (2012). Effect of radiation on MHD free convection flow past an impulsively moving vertical plate with ramped wall temperature. American Journal of Scientific and Industrial Research. 3(6): 376-386.

Gul, A., Khan, I., Shafie, S., Khalid, A. and Khan, A. (2015). Heat transfer in MHD mixed convection flow of a ferrofluid along a vertical channel. PLoS ONE. 10(11): 1-14.

Hayat, T., Mustafa, M. (2010). Influence of thermal radiation on the unsteady mixed convection flow of a jeffrey fluid over a stretching sheet. Z. Naturforsch. 65a: 711-719.

Hayat, T., Iqbal, Z., Mustafa, M., Alsaedi, A. (2014). Unsteady flow and heat transfer of jeffrey fluid over a stretching sheet. Thermal Science. 18(4): 1069-1078.

Hayat, T., Khan, M., Fakhar, K., Amin, N. (2010). Oscillatory rotating flows of a fractional Jeffrey Fluid filling a porous space. Journal of Porous Media. 13(1): 29-38.

Idowu, A. S., Jimoh, A., Ahmed, L. O. (2015a). Effect of heat and mass transfer on MHD oscillatory flow of jeffrey fluid in a porous channel with thermal conductivity and soret. Journal of Research in National Development. 13(2):Chapter 30.

Idowu, A. S., Jimoh, A., Ahmed, L. O. (2015b). Impact of heat and mass transfer on MHD oscillatory flow of Jeffrey Fluid in a porous channel with thermal conductivity, dufour and soret. Journal of Applied Sciences and Environmental Management. 19(4): 819-830.

Idowu, A. S., Joseph, K. M., Daniel, S. (2013). Effects of heat and mass transfer on unsteady MHD oscillatory flow of Jeffrey Fluid in a horizontal channel with chemical reaction. IOSR Journal of Mathematics. 8(5): 74-87.

Joseph, K. M., Magaji, A. S., Peter, A., Tijani, N. Z. (2016). Effect of variable suction on unsteady MHD oscillatory flow of Jeffrey Fluid in a horizontal channel with heat and mass transfer. Journal of Scientific and Engineering Research. 3(3): 599-610.

Kavita, K., Ramakrishna Prasad, K., Aruna Kumari B. (2012). Influence of heat transfer on MHD oscillatory flow of Jeffrey Fluid in a channel. Advances in Applied Science Research. 3(4): 2312-2325.

Khalid, A., Khan, I., Khan, A., Shafie, S. (2015a). Unsteady MHD free convection flow of casson fluid past over an oscillating vertical plate embedded in a porous medium. Engineering Science and Technology, an International Journal. 18: 309-317.

Khan, I. (2015). A note on exact solutions for the unsteady free convection flow of a Jeffrey Fluid. Zeitschrift für Naturforsch. 70(6): 272-284.

Khan, I., Ali, F., Sharidan, S., Norzieha, M. (2010). Exact solutions for accelerated flows of a rotating second grade fluid in a porous medium. World Applied Sciences Journal. 9: 55-68.

Khan, M., Iftikhar, F., Anjum, A. (2011). Some unsteady flows of a Jeffrey Fluid between two side walls over a plane wall. Zeitschrift für Naturforsch. 66a: 745 – 752.

Khan. M. (2007). Partial slip effects on the oscillatory flows of a fractional Jeffrey Fluid in a porous medium. Journal of Porous Media. 10(5): 473-487.

Mabood, F., Abdel-Rahman, R., Lorenzini, G. (2016). Numerical study of unsteady Jeffrey fluid flow with magnetic field effect and variable fluid properties. Journal of Thermal Science and Engineering Applications. 8: 1- 9.

Mekheimer, K. S., Husseny S. Z-A., Ali A. T., Abo-Elkhair R. E. (2011). Lie Point Symmetries and Similarity Solutions for an Electrically Conducting Jeffrey Fluid. Physica Scripta. 83: 1-7.

Nadeem, S., Tahir, B., Labropulu, F., Akbar, N. S. (2014). Unsteady oscillatory stagnation point flow of a Jeffrey Fluid. Journal of Aerospace Engineering. 27: 636-643.

Narahari, M., Ishak, A. (2011). A radiation effects on free convection flow near a moving vertical plate with newtonian heating. Journal of Applied Sciences. 11(7): 1096-1104.

Pantokratoras, A., Fang, T. (2013). Sakiadis flow with nonlinear Rosseland thermal radiation. Physica Scripta. 87: 1-5.

Qayyum, A., Awais, M., Alsaedi, A., Hayat, T. (2012). Unsteady squeezing flow of Jeffrey Fluid between two parallel disks. Chinese Physics Letters. 29(3): 1-4.

Samiulhaq, Ahmad, S., Vieru, D., Khan, I., Shafie, I. (2014a). Unsteady magnetohydrodynamic free convection flow of a second grade fluid in a porous medium with ramped wall temperature. PLoS ONE. 9(5): 1-9.

Samiulhaq, Khan, I., Ali, F., Shafie, S. (2014b). Free convection flow of a second grade fluid with ramped wall temperature. Heat Transfer Research. 45(7): 579-588.

Sree, H. K., Sudheer Kumar, M., Vijayatha, D. (2016). MHD heat transfer oscillatory flow Jeffrey Fluid in an inclined channel filled with porous medium. Chemical and Process Engineering Research. 44: 26-30.

Sukumar, M., Krishna Murthy, M., Varma, S. V. K., Rajinikanth, K. (2016). Slip effects on MHD flow of Jeffrey Fluid over an unsteady shrinking sheet with wall mass transfer. Middle-East Journal of Scientific Research. 24(6): 1920-1925.




DOI: http://dx.doi.org/10.11113/mjfas.v13n2.532

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Nor Athirah Mohd Zin, ahmad Qushairi Mohamad, Ilyas Khan, Sharidan Shafie

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.


Copyright © 2016 Penerbit UTM Press, Universiti Teknologi Malaysia. Disclaimer: This website has been updated to the best of our knowledge to be accurate. However, Universiti Teknologi Malaysia shall not be liable for any loss or damage caused by the usage of any information obtained from this website. AmazingCounters.com