## MHD Free Convective Flow along Vertical Oscillatory Plate with Radiative Heat Transfer in the Presence of Hall Current and Heat Source

**Uday Singh Rajput & Mohammad Shareef**

Department of Mathematics and Astronomy, University of Lucknow, Lucknow-226007, India

E-mail: rajputshareeflu@gmail.com

**Received March, 9 ^{th}, 2017, 1^{st} Revision February 20^{th}, 2019, 2nd Revision April 7^{th}, 2019, Accepted for publication May, 20^{th}, 2019.**

**Abstract. **MHD free convective flow with oscillations of an infinite non-conducting vertical flat surface through a porous medium with Hall current in a rotating system is studied here. The governing equations of the model are converted into dimensionless form. Analytical solution for velocity and temperature are obtained with the help of Laplace transform method. Graphs and tables are used to show the influence of various parameters on Temperature, Skin friction and velocity. It is observed that changes in plate oscillation, porous medium, radiation and Hall current cause significant effect on fluid motion. Further, the Skin friction near the surface is increased by radiation parameter. The results obtained have great implementations in the field engineering and science.

**Keywords: ***free convection; Hall Current; Heat Transfer; MHD; Porous medium.*

### References

[1] Agarwal, H.L., Ram, P.C. & Singh, V., *Combined Influence **of Dissipation **and Hall Effect **on Free Convective **in A Rotating Fluid**,* Indian J. Pure Appl. Math., **14**(3), pp. 314-32, 1983.

[2] Brewster, M.Q., *Thermal Radiative Transfer and Properties*, John Wiley & Sons, New York, 1992.

[3] Chamka, A.J., *MHD Flow **of A Uniformly Stretched Vertical Permeable Surface **in **the Presence **of Heat Generation/Absorption **and Chemical Reaction*, International Communication Heat Mass Transfer, **3****3**(3), pp. 413 – 422, 2003.

[4] Hosseinzadeh , Kh., Jafarian Amiri, A., Saedi Ardahaie, S., & Ganji, D.D., *Effect of **Variable **Lorentz **Forces on **Nanofluid **Flow in **Movable **Parallel **Plates **Utilizing **Analytical **Method*, Case Studies in Thermal Engineering, **1****0**, pp. 595–610, 2017.

[5] Hosseinzadeh , Kh., Afsharpanah, F., Zamani, S. Gholiniab, M. & Ganji, D.D., *A Numerical Investigation **on Ethylene Glycol-Titanium Dioxide Nanofluid Convective Flow **over **A Stretching Sheet **in Presence **of Heat Generation/Absorption*, Case Studies in Thermal Engineering, **12** , pp. 228–236, 2018.

[6] Ghadikolaei, S.S., Hosseinzadeh, Kh. & Ganji, D.D., *Analysis **of Unsteady MHD Eyring-Powell Squeezing Flow **in Stretching Channel **with Considering Thermal Radiation **and Joule Heating Effect **using AGM**,* Case Studies in Thermal Engineering , **10**, pp. 579–594, 2017.

[7] Ghadikolaei, S.S., Hosseinzadeh , Kh., Ganji, D.D. & Jafari B., *Nonlinear Thermal Radiation Effect **on Magneto Casson Nanofluid Flow **with Joule Heating Effect **Over **an Inclined Porous Stretching Sheet*, Case Studies in Thermal Engineering, **12**, pp 176–187, 2018.

[8] Greenspan, H.P., *The Theory of Rotating Fluids*, Cambridge University Press, London, 1968.

[9] Ismail, Z., Khan, I., Imran, A., Hussanan, A., & Sharidan Shafie,** ***MHD Double Diffusion Flowby Free Convection *

*past*

*an Infinite Inclined Plate*

*with Ramped Wall Temperature*

*in*

*a Porous Medium*, Malaysian Journal of Fundamental and Applied Sciences,

**10**(1), pp. 37-42, 2014.

[10] Jaimala, V. & Kumar, V., *Thermal Convection In A Couple-Stress Fluid In The Presence Of Horizontal Magnetic Field With Hall Currents*. Application and applied Mathematics, **8**(1), pp. 161-117, 2013.

[11] Kishore, P.M., Rajesh, V., Verma, S.V., *The Effects **of Thermal Radiation **and Viscous Dissipation **on MHD Heat **and Mass Diffusion Flow **past **an Oscillating Vertical Plate Embeded **in **a Porous Medium **with Variable Surface Conditions*,** **Theoret. Appl. Mech., **39**(2), pp. 99-125, 2012.

[12] Makinde, O.D. & Mhone, P.Y., *Heat Transfer **to MHD Oscillatory Flow **in **a Channel Filled **with Porous Medium*, Romania Journal of Physics, **50**(9–10), pp. 931–938, 2015.

[13] Mazumdar, B.S., Gupta, A.S. & Dattaa, N., *Flow **and Heat Transfer **in **the Hydrodynamic Ekman Layer **on **a Porous Plate **with Hall Effects*, Int. J. Heat Mass Transfer, **19**(5), pp. 523, 1976.

[14] Muthucumaraswamy, R., Dhanasekar, N. & Prasad, G.E., *Mass Transfer Effects **on Accelerated Vertical Plate **in** a Rotating Fluid **with First Order Chemical Reaction*, Journal of Mechanical Engineering and Sciences, **3**, pp. 346-355, 2012.

[15] Muthucumaraswamy, R., Dhanasekar, N. & Prasad, G.E., *Rotation Effects **on Unsteady Flow **Past **an Accelerated Isothermal Vertical Plate **with Variable Mass Transfer **in **the Presence **of Chemical Reaction **of First Order*, Journal of Applied Fluid Mechanics, **6**(4), pp. 485-490, 2013.

[16] Owen, J. M. & Rogers, R.H., *Flow and **Heat **Transfer in **Rotating **Disc **Systems*, Vol. I, Rotor – Stator Systems, John Wiley Sons, New York, 1989.

[17] Prasad, V.R., Bhaskar Reddy, N. & Muthucumaraswamy, R., *Radiation and **Mass **Transfer **Effects on **Two-dimensional **Flow **Past an **Impulsively **Started **Infinite **Vertical **Plate*, International Journal of Thermal Sciences **46**(12), pp. 1251–1258, 2007.

[18] Prasad, V.R., Bhaskar Reddy, N. & Vasu, B., *Radiation and Mass Transfer Effects on Transient Free Convection Flow of a Dissipative Fluid **Past Semi-Infinite Vertical Plate with Uniform Heat and Mass Flux*,* *Journal of Applied Fluid Mechanics, **4**(1), pp. 15-26, 2011.

[19] Rajput, U.S. & Kumar, G., *Effects of Radiation **and Porosity **of The Medium **on MHD Flow Past An Inclined Plate **in **the Presence **of Hall Current*, Computational Methods in Science and Technology, **23**(2), pp 93–103, Polish Academy of Science (PAN), 2017.

[20] Rajput, U.S. & Shareef, M., *Study of Soret and Ion **S**lip **E**ffects on MHD **F**low **N**ear **A**n Oscillating Vertical Plate in a Rotating System*, AAM: Intern. J., **13**(1), pp. 516-534, 2018.

[21] Soong, C.Y. & Ma., H.L. ,*Unsteady Analysis **of Non-**isothermal Flow **and Heat Transfer **between Rotating Co-**axial Disks*, *Int. J. Heat Mass Transfer*, **38**(10), pp. 1865–1878, 1995.

[22] Soong, C.Y., *Thermal Buoyancy Effects **in Rotating Non**-isothermal Flows*, International Journal of Rotating Machinery, **7**(6), pp. 435–446, 2001.

[23] Stewarton, K., *On the Impulsive Motion of **a Flat Plate in **a Viscous Fluid*, *Part 1*, Quart.J. Mech. Appl. Math., **4**(2), pp. 182-198, 1951.

[24] Stewarton, K., *On the Impulsive Motion of a Flat Plate in a Viscous Fluid**, Part 2*, Quart. J. Mech. Appl.Math., **22**(2), pp. 143-152, 1973.

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

ITB Journal Publisher, LPPM ITB, Center for Research and Community Services (CRCS) Building, 6th & 7th Floor, Jalan Ganesha 10, Bandung 40132, Indonesia, Phone: +62-22-86010080, Fax.: +62-22-86010051; E-mail: jmfs@lppm.itb.ac.id