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
Abstract
The present work is devoted to study a viscous, incompressible, and electrically conducting fluid on an MHD fluid flowing past a semi-infinite porous plate in the presence of chemical reaction and inclined magnetic parameter. The governing equations are expressed in non-dimensional form and the resulting nonlinear equations are solved employing the Homotopy perturbation method for the nondimensional velocity, temperature, and concentration profiles. The effects of various controlling parameters such as Casson parameter, Hartmann number, inclined magnetic parameter, porosity parameter, Grashof number, angle of inclination, Prandtl number, Eckert number, radiation parameter, Schmidt number and thermal radiation parameters are presented graphically and discussed in detail. It was found that, velocity profile is enhanced in the presence of Casson, magnetic field and inclined angle parameters whereas it declined with positive increase in the porosity, Grashof and inclined angle numbers. Similarly, increase in Prandtl, Eckert, radiation and inclined angle numbers lead to increase in the temperature distribution of the fluid, while it deceased as the magnetic field parameter increased. The effect of increased thermal radiation parameter is proportional to the concentration profile, whereas it declines for increase in values of Schmidt number.
References
V. Gupta, Engineering Elements of Heat and Mass Transfer, Second Edition, New Age International Publishers, New Delhi, 2021.
M. Anghel, M. A. Hossain and S. Zeb, Combined heat and mass transfer of free convection past an inclined flat plate, Journal of Applied Mechanics and Engineering 2 (2001), 473-497.
C. H. Chen, Heat and mass transfer in MHD flow by natural convection from a permeable inclined surface with variable wall temperature and concentration, Acta Mechanica 172 (2004), 219-235. https://doi.org/10.1007/s00707-004-0155-5
S. Sivasankaran, P. Bhuvaneswari, P. Kandaswamy and E. K. Ramasami, Lie group analysis of natural convection heat and mass transfer in an inclined surface, Nonlinear Analysis: Modelling and Control 11(1) (2006), 201-212. https://doi.org/10.15388/na.2006.11.2.14759
L. Ebiwareme, K. W. Bunonyo and O. A. Davies, Heat transfer analysis of magnetohydrodynamics fluid flow past an infinite vertical porous plate in the presence of suction: the Adomian decomposition approach, American Journal of Engineering Research 12(2) (2023), 146-160.
L. Ebiwareme, K. W. Bunonyo and N. N. Tasie, Analytical investigation of MHD Casson fluid flow past an inclined semi-infinite porous plate with radiation absorption and magnetic field effects, International Research Journal of Innovation in Engineering and Technology 7(4) (2023), 45-55.
N. F. M. Noor, S. Abbasbandy and I. Hashim, Heat and mass transfer of thermophoretic MHD flow over an inclined radiate isothermal permeable surface in the presence of heat source/sink, International Journal of Heat and Mass Transfer 55(7-8) (2012), 2122-2128. https://doi.org/10.1016/j.ijheatmasstransfer.2011.12.015
Joaqu´ın Zueco Jord´an, Numerical study of an unsteady free convective magnetohydrodynamic flow of a dissipative fluid along a vertical plate subject to a constant heat flux, International Journal of Engineering Science 44 (2006), 1380-1393. https://doi.org/10.1016/j.ijengsci.2006.08.006
A. Selim, M. A. Hossain, D. A. S. Rees, The effect of surface mass transfer on mixed convection flow past a heated vertical flat permeable plate with thermophoresis, International Journal of Thermal Sciences 42(10) (2003), 973-982. https://doi.org/10.1016/s1290-0729(03)00075-9
N. Sandeep and V. Sugunamma, Effects of inclined magnetic field on unsteady free convective flow of dissipative fluid past a vertical plate, World Applied Sciences Journal 22(7) (2013), 975-984.
P. R. Sharma, N. Kumar and P. Sharma, 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, Applied Mathematical Sciences 5(46) (2011), 2249-2260.
N. Mahaptra, G. C. Dash, S. Panda and M. Acharya, Effects of chemical reaction on free convection flow through a porous medium bounded by a vertical surface, Journal of Engineering Physics and Thermophysics 83 (2010), 130-140. https://doi.org/10.1007/s10891-010-0327-1
N. Vedavathi, G. Dharmaiah, K. S. Balamurugan and G. Chanran Kumar, Chemical reaction, radiation and Dufour effects on Casson magnetohydrodynamics fluid flow over a vertical plate with heat source/sink, Global Journal of Pure and Applied Mathematics 12(1) (2016), 191-200.
J. Ramaprasad, K. S. Balamurugan and G. Dharmaiah, Unsteady MHD convective heat and mass transfer flow past an inclined moving surface with heat absorption, JP Journal of Heat and Mass transfer 13(1) (2016), 33-51. https://doi.org/10.17654/hm013010033
D. Srinivas Reddy, Impact of chemical reaction on MHD free convection heat and mass transfer from vertical surfaces in porous media considering thermal diffusion and diffusion thermo effects, Advances in Applied Science Research 7(4) (2016), 235-242.
V. Marinca and N. Herisanu, Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches, Springer, New York, 2018.
A. George, Solving Frontier Problems of Physics: The Decomposition method, Fundamental Theories of Physics, Springer Science Business Media, 1994.
S. S. Ray and A. K. Gupta, Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations, Taylor and Francis Group, LLC, USA, 2018. https://doi.org/10.1201/9781315167183-8
E. Esmailzadeh, Y. Davood and A. Hassan, Analytical Methods in NonlinearOscillations: Approaches and Applications, Soil Mechanics and its Application, 252, Springer Nature B. V., 2019.
J. H. He, Homotopy perturbation technique, Computational Methods and Applied Mechanical Engineering 178(3) (1999), 257-262.
J. H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal of Nonlinear Mechanics 35 (2000), 37-43. https://doi.org/10.1016/s0020-7462(98)00085-7
J. H. He, Homotopy perturbation method: a new nonlinear analytical technique, Applied Mathematics and Computation 135(1) (2003), 73-79. https://doi.org/10.1016/s0096-3003(01)00312-5
S. J. Liao, An approximate solution technique not depending on small parameters: a special example, International Journal of Nonlinear Mechanics 30(3) (1995), 371-380. https://doi.org/10.1016/0020-7462(94)00054-e
J. H. He, Addendum: New interpretation of homotopy perturbation method, International Journal of Modern Physics B 20 (2006), 2561-2568. http://doi.org/10.1142/S0217979206034819
J. H. He, The homotopy perturbation method for nonlinear oscillators with
discontinuities, Applied Mathematics and Computation 151(1) (2004), 287-292. https://doi.org/10.1016/s0096-3003(03)00341-2
J. H. He, Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B 20(10) (2006), 1141-1199. https://doi.org/10.1142/s0217979206033796
T. Ozis and D. Agirseven, He’s homotopy perturbation method for solving heat-like and wave-like equations with variable coefficients, Physics Letters A 372 (2008), 5944-5950. https://doi.org/10.1016/j.physleta.2008.07.060
L. Ebiwareme and K. W. Bunonyo, A new homotopy perturbation-Sumudu transform method applied to physical models, International Research Journal of Modernization in Engineering Technology and Science 4(11) (2022).
L. Ebiwareme, K. W. Bunonyo and F. P. Kormane, Study of chemical ion transport through the soil using combined variational iteration and homotopy perturbation methods, International Journal of Innovation in Engineering and Science Research 6(2) (2022).
L. Ebiwareme, I. Davies and S. Esaenwi, Variational Homotopy Perturbation Study of the Dengue Disease Model with incubation period, International Journal of Multidisciplinary Research and Growth Evaluation 3(02) (2022).
M. Tahmina Akter and M. A. Mansur Chowdhoury, Homotopy perturbation method for solving nonlinear partial differential equation, IOSR Journal of Mathematics 12(5) 2016, pp. 59-69.
S. M. Moghimi, D. D. Ganji, H. Bararnia, M. Hosseini and M. Jalaal, Homotopy perturbation method for nonlinear MHD Jefferey-Hamel problem, Computers and Mathematics with Applications 61 (2011), 2213-2216. https://doi.org/10.1016/j.camwa.2010.09.018
R. A. Mustapha and A. M. Salau, Comparative solution of heat transfer analysis for squeezing flow between parallel disks, Iconic Research and Engineering Journal 4(10) (2021), 136-142.
A. El Harfouf, A. Wakif and S. Hayani Mounir, Analytical resolution on squeezing unsteady nanofluid flow problem between two parallel plates a solution by using a semianalytical method: The Homotopy Perturbation Method (HPM), Applied Journal of Environmental Engineering Science 6(3) (2020), 325-337. https://doi.org/10.48422/IMIST.PRSM/ajees-v6i3.22440
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