## MHD Fluid Flowing through a Vertical Porous Plate with the Influence of a Magnetic Field and an Angle of Inclination Using the Method of Reduced Differential Transformation

Liberty Ebiwareme *

Department of Mathematics, Rivers State University, Port Harcourt, Nigeria.

Kubugha Wilcox Bunonyo

Department of Mathematics and Statistics, Federal University Otuoke, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

In this study, the effects of the magnetic tilt angle and magnetic field on the velocity, temperature, and concentration distributions of a magnetohydrodynamic fluid flow are investigated in detail. The reduced differential transformation method (RDTM), a semi-analytical method, is used to arrive at the solution. With Taylor's series for analytic functions at the origin, the problem at hand is transformed specifically using this approach. The approximate analytical solutions for the dimensionless velocity, temperature, and concentration profiles of the relevant flow parameters are accurately approximated analytically using this method. Relevant factors including the magnetic field, Casson parameters, Grashof number, thermal radiation, Schmidt number, Prandtl number, radiation absorption, heat source, porosity parameters, magnetic tilt angle, tilt angle, and modified Grashof number are all taken into consideration for distinct profiles graphically. Increasing the Casson parameter, Grashof number, and modified Grashof number were found to increase velocity while decreasing tilt angle, magnetic field, porosity parameter, and radiation absorption. Similarly, increasing the heat source and radiation parameters increases temperature but decreases in the presence of Prandtl number, magnetic tilt angle, and porosity parameters. Comparing with the literature, we confirm the accuracy and reliability of the obtained solution.

Keywords: Reduced Differential Transformation Method (RDTM), Semi-infinite porous plate, MHD, angle of inclination, radiation absorption

**How to Cite**

*Asian Journal of Pure and Applied Mathematics*,

*5*(1), 179–193. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1819

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### References

Sugunamma V, Sandeep N, Mohan Krishna P, Bahunadam R. Inclined magnetic field and chemical reaction effects on flow over a semi-infinite vertical porous plate through porous medium. Commun Appl Sci. 2013;1(1),1:1-24.

Mohammad PM, Abdus Sattar M. Similarity solution for MHD flow through vertical porous plate with suction. J Comp Appl Mech. 2005;6(1):15-25.

Ebiwareme L, Bunonyo KW, Davies OA. Heat transfer analysis of magnetohydrodynamics fluid flow past an infinite vertical porous plate in the presence of suction: the Adomian Decomposition Method Approach. Am J Eng Res. 2023;12(2):146-60.

Ebiwareme L, Bunonyo KW. Analytical investigation of MHD Casson fluid flow past an inclined semi-infinite porous plate with radiation absorption and magnetic field effects. Int Res J Innov Eng Technol. 2023;7(3):36-49.

Prasad KV, Abel PS, Datti S. Diffusion of chemically reactive species of a non-Newtonian fluid immersed in a porous medium over a stretching sheet. Int J Non Linear Mech. 2003;3:651-7.

Soundalgekar VM, Deka UN. Effects of mass transfer on flow past an impulsively started infinite vertical plate with uniform heat flux and chemical reaction. Forsch.ingenieurwes. 1994;60:284-7.

Al-Odat MQ, Al-Azab TA. Influence of chemical reaction on transient MHD free convection over a moving vertical plate. Emirates J Eng Res. 2007;12(3):15-21.

Ahmed S. Effects of unsteady free convective MHD flow through a porous medium bounded by an infinite vertical porous plate. Bull Cal Math Soc. 2007;99(5):511-22.

Kumar A, S. MHD free convection and mass transfer flow with heat source and thermal diffusion. J Energy Heat Mass Transf. 2001;23:167-78.

Mohammed IS, Reddy RT, Roja P. Radiation effects on Unsteady MHD free convective Heat and Mass transfer flow of fluid past a vertical porous plate embedded in a porous medium with viscous dissipation. Int J Innov Res Sci Eng Technol. 2013;3(11):634-51.

Aydın O, Kaya A. MHD mixed convective heat transfer flow about an inclined plate. Heat Mass Transfer. 2009;46(1):129-36. DOI: 10.1007/s00231-009-0551-4

Shaik MI, Karna S. Influence of Thermo-diffusion, and Heat source on MHD free convective radiating dissipative boundary layer of chemically reacting fluid flow in a porous vertical surface. Adv Appl Math. 2016;1(1):17-28. DOI: 10.22606/jaam.2016.11003

Elbashbeshy EMA. Heat and Mass transfer along a vertical plate with variable surface temperature and concentration in the presence of magnetic field. 1997;34:515-22.

Ramana Reddy JV, Sugunamma V, Sandeep N. Effect of non-linear thermal radiation on MHD flow between rotating plates with homogenous-heterogenous reactions. Int J Eng Res Afr. 2016;20:130-43.

Idowu AS, Abdulwaheeed J, Funmilayo HO, Moses SD. Numerical solution for the thermal radiation effects on inclined magnetic field on MHD free convective heat transfer dissipative fluid flow past a moving vertical porous plate with variable suction. Am J Fluid Dyn. 2014;4(3):91-101.

Ravi Kumar N, Vijaya RB. Heat and Mass transfer on MHD convective flow over an infinite vertical porous plate with the heat source and chemical reaction. J Heat Transf. 2021;50(8):8475-91. DOI: 10.1002/htj.22285

Kataria HR, Patel HR. Effects of chemical reaction and heat generation/absorption on magnetohydrodynamics (MHD) Casson fluid over an exponentially accelerated vertical plate embedded in porous medium with ramped wall temperature and ramped surface concentration. Propul Power Res. 2019;8(1):35-46. DOI: 10.1016/j.jppr.2018.12.001

Krishna MV, Ahamad NA, Aljohani AF. Thermal radiation, chemical reaction, Hall, and ion slip effects on MHD oscillatory rotating flow of micropolar liquid. Alexander Eng J. 2021;60:3467-84.

Patel HR. Effects of heat generation, thermal radiation, and Hall current on MHD Casson fluid flow past over an oscillating plate in porous medium. Multiphase Sci Technol. 2019;31(1):87-107.

Patel HR. Effects of cross diffusion and heat generation on mixed convective MHD flow of Casson fluid through porous medium with non-linear thermal radiation. Heliyon. 2019;5(4):e01555. DOI: 10.1016/j.heliyon.2019.e01555, PMID 31183425.

Alam MS, Rahman MM, Sattar MA. MHD free convective heat and mass transfer flow past an inclined semi-infinite heated surface of an electrically conducting and steady viscous incompressible fluid in the presence of a magnetic field and heat generation. Thamasat. Int J Sci Eng Technol. 2006;11(4):1-8.

Gnaneshwara RM, Bhaskar RN. Radiation, and mass transfer effect on an unsteady MHD free convection flow past a heated vertical porous plate with viscous dissipation. Int J Appl Math Mech. 2009;6(6):96-110.

Sandeep N, Sugunama V. Effect of inclined magnetic field on unsteady two-dimensional free convective flow through a porous bounded by a vertical porous surface. Asian J Explor Sci. 2013;22(3):275-84.

Sharma PR, Kumar N, Sharma P. Influence of Chemical reaction, and Radiation on unsteady MHD free convective flow and mass transfer through viscous incompressible fluid past a heated vertical plate immersed in porous medium in the presence of heat source. Appl Math Sci. 2011;5(46):2249-60.

Ramaiah P, Krishna PRK. Aligned magnetic field and Diffusion thermo effect on unsteady MHD free convective flow past an inclined surface. Int J Adv Sci Res Manag. 2019;4(7):210-21.

Ramaprasad JK, Balamurugan KS, Dharmaiah G. Unsteady MHD free convective heat and mass transfer flow past an inclined moving surface with heat absorption. JP J Heat Mass Transf. 2016;13(1):33-51.

Ebiwareme L, Bunonyo KW. Application of approximation technique for the effects of chemical reaction and radiation absorption of MHD fluid flowing past an inclined porous plate in the presence of inclined magnetic field. Int J Adv Appl Math Mech. 2023;11(1):30-41.

Ebiwareme L, Bunonyo KW, Davies OA. Homotopy perturbation method for MHD heat and mass transfer flow of convective fluid through a vertical porous plate in the presence of chemical reaction and inclined magnetic field. Eastline J Math Sci. 2023;13(1):209-233.

Ebiwareme L. Coupling of Laplace Differential Transform method with Pade Approximant for the Numerical solution of initial and boundary value problems. Int J Sci Manag. 2022;10(03):M-2022-373-385.

Abazari R, Soltanalizadeh B. Reduced Differential Transform method and its Application on Kawahara Equations. Thai J Math. 2013;11:199-216.

Jafari H, Jassim HK, Moshokoa SP. Reduced Differential Equation method for partial Differential Equations within local fractional derivative operators. Adv Mech Eng. 2016;8(4):1-6.

Alain Y, SW. Application of the reduced differential transform method to solve the Navier-Stoke’s Equation. Pure Appl Math J. 2022;11(6):96-101.

Saravanan A, Magesh N. A comparison between the Reduced Differential Transform method and the Adomian Decomposition method for the Newell-Whitehead-Segel Equation. Int J Egypt Math Soc. 2013;21(3):259-65. DOI: 10.1016/j.joems.2013.03.004

Keskin Y, Oturanc G. Reduced differential transform method for solving linear and nonlinear wave equations. Iran J Sci Technol. 2010;34(2).

Haghbin A, Hesam S. Reduced differential transform method for solving seventh order Sawada-Kotera equations. J Math Computer Sci. 2012;05(1):53-9. DOI: 10.22436/jmcs.05.01.06

Abazari R, Kilicman A. Numerical study of two-dimensional Volterra integral equation by RDTM with DTM. Admin Appl Anal. 2013;10:929-34.

Keskin Y, Oturanc G. Reduced Differential Transform method: A new approach to fractional partial differential Equations. Nonlinear Sci Lett A. 2010;1:207-18.

Ebiwareme L. Application of Semi-analytical iteration techniques for the numerical solution of linear and nonlinear Differential Equations. Int J Math Trends Technol. 2021;67(2):146-58. DOI: 10.14445/22315373/IJMTT-V67I2P521

Kenmogne F. Generalizing of differential transform method for solving nonlinear differential equations. J Appl Comp Math. 2015;4:196. DOI: 4172/2168-9679.1000196