Effects of Hall Current on Darcy-Forchheimer MHD Mixed Convective Flow Over a Vertical Surface with Rotation in Porous Medium

Keywords: Hall current, Rotation, Darcy Forchheimer, Mixed convection, Bvp4c

Abstract

The analysis of Darcy-Forchheimer MHD flow has been a concern of consideration for research scientists and engineers. This work examines the unsteady hydrodynamic mixed convective flow of an incompressible, viscous, electrically conducting fluid as well as the transfer of heat and mass in a vertical surface with the Hall current, rotation, and Darcy-Forchheimer effect. Through similarity transformation, the dimensionless unstable governing equation's exact solution is found. Then, using the Matlab method Bvp4c, the similarity ordinary differential equation was solved. When the exact solution and those produced by Elgazery and Stanford were compared to the numerical result for a few exceptional circumstances, there was a fair degree of agreement. Graphs are used to show the temperature, concentration, and fluid velocity. In contrast, skin friction, the Sherwood number, and the Nusselt number are calculated in tabular form.

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References

A.K.Sarma, and D. Sarma, ”Unsteady magnetohydrodynamic bioconvection Casson fluid flow in presence of gyrotactic microorganisms over a vertically stretched sheet,” Numerical Heat Transfer, Part A: Applications, 1-24 (2024). https://doi.org/10.1080/10407782.2024.2389338

Md.A. Samad, and M. Mansur-Rahman, ”Thermal radiation interaction with unsteady MHD flow past a vertical porous plate immersed in a porous medium,” Journal of Naval Architecture and Marine Engineering, 3(1), 7-14 (2006). https://doi.org/10.3329/jname.v3i1.924

S. Mukhopadhyay, and G.C. Layek, ”Radiation effect on forced convective flow and heat transfer over a porous plate in a porous medium,” Meccanica, 44(5), 587-597 (2009). https://doi.org/10.1007/s11012-009-9211-5

S. Mukhopadhyay, et al., ”Forced convective flow and heat transfer over a porous plate in a Darcy-Forchheimer porous medium in presence of radiation,” Meccanica, 47, 153-161 (2012). https://doi.org/10.1007/s11012-011-9423-3

Z. Khan, et al., ”Magnetohydrodynamic thin film flow through a porous stretching sheet with the impact of thermal radiation and viscous dissipation,” Mathematical Problems in Engineering, 2022(1), 1086847 (2022). https://doi.org/10.1155/2022/1086847

A.L. Panya, O.A. Akinyemi, and A.M. Okedoye, “MHD Darcy–Forchheimer slip flow in a porous medium with variable thermophysical properties,” Zenodo, 10(2), 30-43 (2023). https://doi.org/10.5281/zenodo.7646344

N.N. Reddy, V.S. Rao, and B.R. Reddy, ”Chemical reaction impact on MHD natural convection flow through porous medium past an exponentially stretching sheet in presence of heat source/sink and viscous dissipation,” Case studies in thermal engineering, 25, 100879 (2021). https://doi.org/10.1016/j.csite.2021.100879

B.C. Sakiadis, ”Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow,” AIChE Journal 7(1), 26–28 (1961). https://doi.org/10.1002/aic.690070108

L.J. Crane, ”Flow past a stretching plate,” Zeitschrift f¨ur angewandte Mathematik und Physik, 21, 645-647 (1970). https://doi.org/10.1007/BF01587695

M.K.Nayak, G.C. Dash, and L.P. Singh, ”Effect of chemical reaction onMHDflowof a visco-elastic fluid through porous medium,” J. Appl. Anal. Comput. 4(4), 367-381 (2014).

M.K.Nayak, G.C. Dash, and L.P. Singh, ”Steady MHD flow and heat transfer of a third grade fluid in wire coating analysis with temperature dependent viscosity,” International Journal of Heat and Mass Transfer, 79, 1087-1095 (2014). https://doi.org/10.1016/j.ijheatmasstransfer.2014.08.057

M.K. Nayak, G.C. Dash, and L.P. Singh, ”Heat and mass transfer effects on MHD viscoelastic fluid over a stretching sheet through porous medium in presence of chemical reaction,” Propulsion and Power Research, 5(1), 70-80 (2016). https://doi.org/10.1016/j.jppr.2016.01.006

K. Vafai, and C.L. Tien, ”Boundary and inertia effects on convective mass transfer in porous media”, International Journal of Heat and Mass Transfer, 25(8), 1183–1190 (1982). https://doi.org/10.1016/0017-9310(82)90212-5

J.T. Hong, Y. Yamada, and C.L. Tien, ”Effects of non-Darcian and nonuniform porosity on vertical-plate natural convection in porous media,” J. Heat Transfer. 109(2), 356-362 (1987). https://doi.org/10.1115/1.3248088

R.Y. Jumah, A. Fawzi, and F. Abu-Al-Rub, ”Darcy-Forchheimer mixed convection heat and mass transfer in fluid saturated porous media,” International Journal of Numerical Methods for Heat and Fluid Flow, 11(6), 600–618 (2001). https://doi.org/10.1108/09615530110399503

A.J. Chamkha, ”Hydromagnetic natural convection from an isothermal inclined surface adjacent to a thermally stratified porous medium,” International Journal of Engineering Science, 35(10-11), 975–986 (1997). https://doi.org/10.1016/S0020-7225(96)00122-X

N.S. Elgazery, ”The effects of chemical reaction, Hall and ion-slip currents on MHD flow with temperature dependent viscosity and thermal diffusivity,” Communications in Nonlinear Science and Numerical Simulation, 14(4), 1267–1283 (2009). https://doi.org/10.1016/j.cnsns.2007.12.009

M. Kinyanjui, J.K. Kwanza, and S.M. Uppal, ”Magnetohydrodynamic free convection heat and mass transfer of a heat generating fluid past an impulsively started infinite vertical porous plate with Hall current and radiation absorption,” Energy conversion and management, 42(8), 917–931 (2001). https://doi.org/10.1016/S0196-8904(00)00115-1

S. Shateyi, S.S. Motsa, and P. Sibanda, ”The Effects of Thermal Radiation, Hall Currents, Soret, and Dufour on MHD Flow by Mixed Convection over a Vertical Surface in Porous Media,” Mathematical Problems in Engineering, 2010, 627475 (2010). https://doi.org/10.1155/2010/627475

A.K. Singh, ”Hall effects onMHDfree-convection flow past an accelerated vertical porous plate,” Astrophysics and Space Science, 102, 213-221 (1984). https://doi.org/10.1007/BF00650168

D. Sarma, and K.K. Pandit, ”Effects of thermal radiation and chemical reaction on steady MHD mixed convective flow over a vertical porous plate with induced magnetic field,” International journal of fluid Mechanics Research, 42(4), 315-333 (2015). https://doi.org/10.1615/InterJFluidMechRes.v42.i4.30

M.D.A. Sattar, and H. Kalim, ”Unsteady free-convection interaction with thermal radiation in a boundary layer flow past a vertical porous plate,” J. Math. Phys. Sci. 30(1), 25-37 (1996).

R. Nandkeolyar, M. Das, and S. Precious, ”Exact solutions of unsteady MHD-free convection in a heat-absorbing fluid flow past a flat plate with ramped wall temperature,” Boundary Value Problems, 2013, 1-16 (2013). http://dx.doi.org/10.1186%2F1687-2770-2013-247

A.J. Chamkha, ”MHD-free convection from a vertical plate embedded in a thermally stratified porous medium with Hall effects,” Applied Mathematical Modeling, 21(10), 603-609 (1997). https://doi.org/10.1016/S0307-904X(97)00084-X

E.M. Abo-Eldahab, and A.M. Salem, ”Hall effects on MHD free convection flow of a non-Newtonian power-law fluid at a stretching surface,” International communications in heat and mass transfer, 31(3), 343-354 (2004). https://doi.org/10.1016/j.icheatmasstransfer.2004.02.005

S. Siddiqa, M.A. Hossain, and R.S.D. Gorla. ”Hall current effects on magnetohydrodynamic natural convection flow with strong cross-magnetic field,” International journal of thermal sciences, 71, 196-204 (2013). https://doi.org/10.1016/j.ijthermalsci.2013.04.016

Published
2025-03-03
Cited
How to Cite
Roy, S., Sarma, D., Sarma, A. K., & Mudoi, S. (2025). Effects of Hall Current on Darcy-Forchheimer MHD Mixed Convective Flow Over a Vertical Surface with Rotation in Porous Medium. East European Journal of Physics, (1), 112-121. https://doi.org/10.26565/2312-4334-2025-1-10