Mohammed Nasir UddinThis email address is being protected from spambots. You need JavaScript enabled to view it. and Md. Yeakub Ali
Department of Mathematics Chittagong University of Engineering & Technology,Chattogram-4349,Bangladesh
Received: January 28, 2024 Accepted: April 13, 2024 Publication Date: June 11, 2024
Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.
In this regard, we have investigated similarity solution of unsteady convective MHD flow of viscous incompressible fluid over an inclined porous surface with ohmic heating and viscous dissipation. Here, surface temperature and concentration may be considered as a variable according to the Power-law. The problem is assigned by the systems of nonlinear partial differential equation. We have introduced similarity variables on the governing equation to convert it non-linear ordinary differential equation by means of the similarity transformation. The possible four similarity cases have been derived for various possibilities and one of the cases is established elaborately for searching quantitative results. The shooting method is also used to obtain numerical solutions from the nonlinear partial differential equation. Fluid properties are derived graphically and numerically for different physical parameters arising from ohmic heating and viscous dissipation effects regarding this study. The Skin friction coefficient falls down about by 1.86%, Sherwood number rises about by 1.65% and Nusselt number falls down about by 4.88% due to the enhancing values of unsteadiness parameter varies from 0.5 to 10. Again, Skin friction coefficient falls down about by 3.03%, Sherwood number falls down about by 25.88% and Nusselt number rises about by 2.61% for the enhancing values of the inclination from 20◦ to 60◦ . This research can be applied in the surface water desalination plants, plasma studies and smart healthcare systems.
Keywords: Similarity Solution, Buoyancy ratio, Ohmic heating, viscous dissipation and Soret number
[1] A. Sinha, J. Misra, and G. Shit, (2016) “Effect of heat transfer on unsteady MHD flow of blood in a permeable vessel in the presence of non-uniform heat source" Alexandria Engineering Journal 55(3): 2023–2033.
[2] Y. J. Kim, (2001) “Unsteady MHD convection flow of polar fluids past a vertical moving porous plate in a porous medium" International Journal of Heat and Mass Transfer 44(15): 2791–2799.
[3] E. Sparrow and R. Cess, (1961) “The effect of a magnetic field on free convection heat transfer" International Journal of Heat and Mass Transfer 3(4): 267–274.
[4] T. Watanabe and I. Pop, (1994) “Thermal boundary layers in magnetohydrodynamic flow over a flat plate in the presence of a transverse magnetic field" Acta Mechanica 105: 233–238.
[5] L. Erickson, L. Fan, and V. Fox, (1966) “Heat and mass transfer on moving continuous flat plate with suction or injection" Industrial & Engineering Chemistry Fundamentals 5(1): 19–25.
[6] P. Sharma and G. Singh, (2009) “Effects of variable thermal conductivity and heat source/sink on MHD flow near a stagnation point on a linearly stretching sheet":
[7] H. Andersson, (1992) “MHD flow of a viscoelastic fluid past a stretching surface" Acta Mechanica 95(1): 227–230.
[8] M. Chowdhury and M. Islam, (2000) “MHD free convection flow of visco-elastic fluid past an infinite vertical porous plate" Heat and Mass transfer 36(5): 439–447.
[9] C. Israel-Cookey, A. Ogulu, and V. B. Omubo-Pepple, (2003) “Influence of viscous dissipation and radiation on unsteady MHD free-convection flow past an infinite heated vertical plate in a porous medium with timedependent suction" International journal of heat and mass transfer 46(13): 2305–2311.
[10] M. Subhas Abel, A. Joshi, and R. Sonth, (2001) “Heat Transfer in MHD Visco-elastic Fluid Flow over a Stretching Surface" ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik: Applied Mathematics and Mechanics 81(10): 691–698.
[11] M. Seddeek, (2002) “Effects of radiation and variable viscosity on a MHD free convection flow past a semiinfinite flat plate with an aligned magnetic field in the case of unsteady flow" International journal of heat and mass transfer 45(4): 931–935.
[12] M. M. Hossain, A. R. Laskar, and M. A. Bhuiyan, (2023) “Effect of chemical reaction on unsteady MHD convective transport passing a vertical porous sheet" Journal of Engineering Science 14(1): 85–93.
[13] R. Nyabuto, R. O. Amenya, and J. A. Okelo, (2021) “Unsteady Viscous Dissipative Flow of Salty Water in the Presence of a Magnetic Field in a Semi-Infinite Porous Medium":
[14] B. Gebhart. Buoyancy-induced flows and transport. Hemisphere Pub, 1988.
[15] M. Nayak, G. Dash, and L. Singh, (2015) “Unsteady radiative MHD free convective flow and mass transfer of a viscoelastic fluid past an inclined porous plate" Arabian Journal for Science and Engineering 40: 3029–3039.
[16] E. Elbashbeshy, (1997) “Heat and mass transfer along a vertical plate with variable surface tension and concentration in the presence of the magnetic field" International Journal of Engineering Science 35(5): 515–522.
[17] A. J. Chamkha and A.-R. A. Khaled, (2001) “Similarity solutions for hydromagnetic simultaneous heat and mass transfer by natural convection from an inclined plate with internal heat generation or absorption" Heat and Mass Transfer 37(2): 117–123.
[18] M. Hasanuzzaman, S. Akter, S. Sharin, M. M. Hossain, A. Miyara, and M. A. Hossain, (2023) “Viscous dissipation effect on unsteady magneto-convective heatmass transport passing in a vertical porous plate with thermal radiation" Heliyon 9(3):
[19] I. Ejaz and M. Mustafa, (2022) “A comparative study of different viscosity models for unsteady flow over a decelerating rotating disk with variable physical properties" International Communications in Heat and Mass Transfer 135: 106155.
[20] C.-H. Chen, (2004) “Heat and mass transfer in MHD flow by natural convection from a permeable, inclined surface with variable wall temperature and concentration" Acta Mechanica 172(3): 219–235.
[21] M. Umamaheswar, S. Varma, and M. Raju, (2013) “Unsteady MHD free convective visco-elastic fluid flow bounded by an infinite inclined porous plate in the presence of heat source, viscous dissipation and ohmic heating" International journal of advanced science and technology 61: 39–52.
[22] S. Mukhopadhyay, G. C. Layek, and R. S. R. Gorla, (2010) “Radiation effects on MHD combined convective flow and heat transfer past a porous stretching surface" International Journal of Fluid Mechanics Research 37(6):
[23] M. A. Bkar PK, M. Hasanuzzaman, M. M. Hossain, D. Mondal, et al., (2024) “Effects of Thermal Radiation and Variable Porosity on Unsteady Magnetoconvective Heat-Mass Transport Past a Vertical Perforated Sheet" Journal of Engineering 2024:
[24] D. Yadav, J. Lee, and H. H. Cho, (2016) “Throughflow and quadratic drag effects on the onset of convection in a Forchheimer-extended Darcy porous medium layer saturated by a nanofluid" Journal of the Brazilian Society of Mechanical Sciences and Engineering 38: 2299–2309.
[25] D. Yadav and J. Wang, (2019) “Convective Heat Transport in a Heat Generating Porous Layer Saturated by a Non-Newtonian Nanofluid" Heat Transfer Engineering 40(16): 1363–1382. DOI: 10.1080/01457632.2018.1470298.
[26] D. Yadav, S. B. Nair, M. K. Awasthi, R. Ragoju, and K. Bhattacharyya, (2024) “Linear and nonlinear investigations of the impact of chemical reaction on the thermohaline convection in a permeable layer saturated with Casson fluid" Physics of Fluids 36(1):
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