A steady MHD natural convection and heat transfer fluid flow through a vertical surface in the existence of hall current and radiation

A steady MHD natural convection and heat transfer fluid flow through a vertical surface in the existence of hall current and radiation

Rajib BiswasMunmun Mondal Ariful Islam 

Mathematics Discipline, Science, Khulna University, Khulna-9208, Bangladesh

Department of Chemical Engineering, University of Newcastle, NSW-2308, Australia

Corresponding Author Email: 
rajibkumath11@gmail.com
Page: 
331-356
|
DOI: 
https://doi.org/10.3166/I2M.17.331-356
Received: 
| |
Accepted: 
| | Citation

OPEN ACCESS

Abstract: 

MHD heat disposal fluid flow within a vertical surface in the attendance of Hall current is smeared in this recent paper. The leading partial differential equations (PDEs) are motamorposhosed into dimensionless coupled of partial differential equations (PDEs) by the as usual mathematical procedure of transformation and the resultant equations are numerically evaluated by applying the explicit finite difference method (EFDM). The numerical outcome of velocity (primary and secondary) and temperature profiles are computed with the helps of COMPAQ VISUAL FORTRAN (CVF) 6.6a for the variations of various non-dimensional parameters such as magnetic parameter (M), Grashof number (Gr), Prandtl number (Pr), Hall parameter (m), permeability of porous medium (Kp) and radiation parameter (Ra) which values are chosen after stability convergence test (SCT). Furthermore, the effects of different system parameters on skin friction, Nusselt and Sherwood number are exhibited graphically. In addition, the Streamlines and isotherms have been investigated for different interesting parameters in this article. At the end the acquired results are plotted by using TECPLOT-9 (graphics software) and these are cultivated with graphically.

Keywords: 

hall current, magnetic field, natural convection, radiation, MHD, EFDM

1. Introduction
2. Mathematical formulation
3. Calculation technique
4. Stability and convergence analysis
5. Results and discussion
6. Conclusions
  References

Ahmed N., Kalita D. (2011). Transient MHD free convection from an infinite vertical plate in a rotating system with mass transfer and hall current. Journal of Energy, Heat and Mass Transfer, Vol. 33, pp. 271-292.

Ahmed N., Khan U., Khan S. I., Bano S., Mohyud-Din S. T. (2017). Effects on magnetic field in squeezing flow of a casson fluid between parallel plates. Journal of King Saud University Science, Vol. 29, pp. 119-125. https://doi.org/10.1016/j.jksus.2015.03.006

Ahmmed S. F., Biswas R., Afikuzzaman M. (2018). Unsteady magnetohydrodynamic free convection flow of nanofluid through an exponentially accelerated inclined plate embedded in a porous medium with variable thermal conductivity in the presence of radiation. Journal of Nanofluids, Vol. 7, pp. 891-901. https://doi.org/10.5098/hmt.11.13

Ali E. S. M. (2004). A Text book of programming in FORTRAN. Third edition. https://www.springer.com/gp/book/9783319177007

Animasaun I. L., Adebile E. A., Fagbade A. I. (2016). Casson fluid flow with variable thermo-physical property along exponentially stretching sheet with suction and exponentiallydecaying internal heat generation using the homotopy analysis method. Journal of the Nigerian Mathematical Society, Vol. 35, pp. 11-17. https://doi.org/10.1016/j.jnnms.2015.02.001

Attia H. A. (2005, 2006, 2007). Unsteady couette flow with heat transfer considering the ion-slip has been investigated. European Journal of Scientific Research Recent, Vol. 44, pp. 971-987.

Balocco C., Petrone G. (2018). Heat and moisture transfer investigation of surface building materials. Mathematical Modelling of Engineering Problems, Vol. 5, No. 3, pp. 146-152. https://doi.org/10.18280/mmep.050303

Biswal S., Sahoo P. K. (1994). Hall effect on oscillatory hydromantic free convective flow of a visco-elastic fluid past an infinite vertical porous flat plate with mass transfer. Proc. Nat. Acad. Sci., Vol. 69A, pp. 46.

Biswas R., Afikuzzaman M., Mondal M., Ahmmed S. F. (2018). MHD free convection and heat transfer flow through a vertical porous plate in the presence of chemical reaction. Frontiers in Heat and Mass Transfer, Vol. 11, No. 13. https://doi.org/10.5098/hmt.11.13

Biswas R., Ahmmed S. F. (2018). Effects of Hall current and chemical reaction on MHD unsteady heat and mass transfer of Casson nanofluid flow through a vertical plate. Journal of Heat Transfer, Vol. 140, pp. 092402. https://doi.org/10.1115/1.4039909

Biswas R., Mondal M., Sarkar D. R., Ahmmed S. F. (2017). Effects of radiation and chemical reaction on MHD unsteady heat and mass transfer of Casson fluid flow past a vertical plate. Journal of Advances in Mathematics and Computer Science, Vol. 23, No. 2, pp. 1-16.

Chaware P., Sewatkar C. M. (2017). Effects of tangential and radial velocity on the heat transfer for flow through pipe with twisted tape insert-turbulent flow. International Journal of Heat and Technology, Vol. 35, No. 4, pp. 811-820. https://doi.org/10.18280/ijht.350417

Das S., Guchhait S. K., Jana R. N., Makinde O. D. (2016). Hall effects on an unsteady magneto-convection and radiative heat transfer past a porous plate. Alexandria Engineering Journal, Vol. 55, pp. 1321-1331.https://doi.org/10.1016/j.aej.2016.04.027

Garg R., Thakur H., Tripathi B. (2017). Nonlinear numerical analysis of convective-radiative fin using MLPG method. International Journal of Heat and Technology, Vol. 35, No. 4, pp. 721-729. https://doi.org/10.18280/ijht.350405

Hall E. (1879). On a new action of the magnet on electric currents. American Jurnal of Mathematics, Vol. 2, No. 3, pp. 287-292.

Hossain M. D., Samad M. A., Alam M. M. (2015). MHD free convection and mass transfer flow through a vertical oscillatory porous plate with hall, ion-slip currents and heat source in a rotating system. Procedia Engineering, Vol. 105, pp. 56-63. https://doi.org/10.1016/j.proeng.2015.05.006

Islam A., Biswas M. H. A., Karim M. R., Mohiuddin S. M. (2011). MHD micropolar fluid flow through a vertical porous medium. Academic Research International, Vol. 1, No. 3, pp. 380-393.

Kataria H. R., Patel H. R. (2016). Soret and heat generation effects on MHD casson fluid flow past an oscillating vertical plate embedded through porous medium. Alexandria Engineering Journal, Vol. 55, pp. 2125-2137. https://doi.org/10.1016/j.aej.2016.06.024

Kumar N. K., Masliyah J. H. (1986). Swirling flow and heat transfer in coiled and twisted pipes, Journal of American. Advanced Transport Process, Vol. 4, pp. 49-112. http://dx.doi.org/10.1155/2016/8235375

Makinde O. D. Khan Z. H., Ahmad R., Khan W. A. (2018). Numerical study of unsteady hydromagnetic radiating fluid flow past a slippery stretching sheet embedded in a porous medium. Physics of Fluids, Vol. 30, pp. 083601 (7pages). https://doi.org/10.1063/1.5046331

Makinde O. D., Khan W. A., Khan Z. H. (2017). Stagnation point flow of MHD chemically reacting nanofluid over a stretching convective surface with slip and radiative heat. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, Vol. 231, No. 4, pp. 695-703. https://doi.org/10.1177/0954408916629506

Makinde O. D., Mabood F., Ibrahim M. S. (2018). Chemically reacting on MHD boundary layer flow of nanofluid over a non-linear stretching sheet with heat source/sink and thermal radiation. Thermal Science, Vol. 22, No. 1B, pp. 495-506. https://doi.org/10.2298/TSCI151003284M

Pattnaik J. R., Dash G. C., Singh S. (2016). Diffusion- thermo effect with hall current on unsteady hydromagnetic flow past an infinite vertical porous plate. Alexandria Engineering Journal, Vol. 56, No. 1, pp. 13-25. https://doi.org/10.1016/j.aej.2016.08.027

Rajput K. R., Chad S. (2007). Heat and mass transfer (Multicolor edition). S. Chad and Company Ltd., pp. 373-387.

Rohsenow W. M., Harnett J. P., Cho Y. I. (1998). Handbook of heat transfer. 3rd edition. McGraw-Hill, New Year.

Sekhar K. R., Reddy G. V., Raju C. S. K., Ibrahim S. M., Makinde O. D. (2018). Multiple slip effects on magnetohydrodynamic boundary layer flow over a stretching sheet embedded in a porous medium with radiation and Joule heating. Special Topics & Reviews in Porous Media: An International Journal, Vol. 9, No. 2, pp. 117-132. https://doi.org/10.1615/SpecialTopicsRevPorousMedia.v9.i2.20

Shankar B., Yirga Y. (2013). Unsteady heat and mass transfer in MHD flow of nanofluids over stretching sheet with a nano-uniform heat source/sink. International Scholarly and Scientific Research and Innovation, Vol. 7, No. 12, pp. 1766-1774.

Sharma P. R. Choudhary S.,  Makinde O. D. (2018). MHD Slip flow and heat transfer over an exponentially stretching permeable sheet embedded in a porous medium with heat source. Frontiers in Heat and Mass Transfer, Vol. 9, pp. 1-7.

Sun C., Zuo Z. S., Lu W., Liu X. T., Guo X. L., Liu F. (2017). Visualization of the heat transfer character of dry slag discharge system. International Journal of Heat and Technology, Vol. 35, No. 4, pp. 793-798. https://doi.org/10.18280/ijht.350414

Tamoor M., Waqas M., Khan M. I., Alsaedi A., Hayat T. (2017). Magnetohydrodynamic flow of Casson fluid cylinder. Results in Physics, Vol. 7, pp. 498-502. https://doi.org/10.1016/j.rinp.2017.01.005

Venkateswarlu M., Makinde O. D. (2018). Unsteady MHD slip flow with radiative heat and mass transfer over an inclined plate embedded in a porous medium. Defect and Diffusion Forum, Vol. 384, pp. 31-48.

Wang L., Yang T. (2004). Bifurcation and stability of forced convection in curved ducts of square cross section. Int. J. Heat Mass Transfer. European Journal of Scientific Research Recent, Vol. 47, pp. 2971-2987. https://doi.org/10.1016/j.ijheatmasstransfer.2004.03.002