MHD Convective Casson Ferro-Fluid Flow Over Orthogonal Surfaces with Hall Current
DOI:
https://doi.org/10.53799/xbpw5p60Keywords:
Heat absorption/generation, Hall current, MHD Flow, Curvilinear surfaces, Ferro-fluid flow, Nonlinear Casson fluidAbstract
We consider MHD ferro Casson fluid flow across the orthogonal curvilinear surfaces. The unchanged magnetic field parallel to ζ-axis and perpendicular to surfaces, Hall current, heat absorption/generation and nonlinear Casson parameter also examined in our present paper. Pressure gradients and ferro-fluid buoyance forces are dependent on the free stream velocity. The set of governing equations in curvilinear coordinates is changed to a simultaneous dimensionless ordinary differential nonlinear equation by considering suitable nondimensional similarity functions and variable. The initial value from the boundary value has been finding by shooting method and then solving the dimensionless similarity equations by RK-6 method with constructing numerical program in FORTRAN language. Considering the different values of one parameter and other parameters are kept constant to find the numerical computation. Computational results of numerical solutions were exhibited in figures of momentum and energy by MATLAB and MS Excel softwires. Finally, we have highlighted the comparisons and found a great agreement to justify numerical results acceptable in our study.References
[1] A. G. Hansen, “Possible similarity solution of the laminar incompressible boundary layer equations,” ASME paper 57 A, pp79, 1957.
[2] Md. Zakerullah, and Kh. A. Maleque, “Similarity requirements for combined forced and free convective laminar boundary layer flow over vertical curvilinear surfaces,” J. Bangladesh academy of sciences, Vol-22(1), pp 79, 1998.:
[3] KA Maleque, “Similarity Requirements for Mixed Convective Boundary Layer Flow over Vertical Curvilinear Porous Surfaces with Heat Generation/Absorption", International Journal of Aerospace Engineering, vol. 2020, Article ID 7486971, 9 pages, 2020. https://doi.org/10.1155/2020/7486971.
[4] T. Cebeci, K. Kaups, and A. Moser, “Calculation of three-dimensional boundary Layer,” AIAA journal 14(8), pp. 1090, 1976.
[5] A. F. Blumberg, and H. J. Herring, “ Circulation modelling using orthogonal curvilinear coordinates,” In Elsevier oceanography series, vol-45, pp. 55, 1987.
[6] T. K. Hung, and T.D. Brown, “An implicit finite-difference method for solving the Navier-stokes equation using orthogonal curvilinear coordinates,” Journal of Computational Physics, Vol 23(4), pp. 343, 1977.
[7] Redzic, V. Dragan, “The operation in orthogonal curvilinear coordinates”, European Journal of Physics, vol 22(6), pp. 595, 2001.
[8] Mario Krzyk, and Matjaz Cetina, “Analysis of flow in a curved channel using the curvilinear orthogonal numerical mesh,”Journal of Mechanical Engineering, DOI:105545/sv-jme.2017.5183, Corpus ID:201799831, 2019.
[9] A. Shafiq, S. Nadeem, and Nurmuhammad, “Boundary layer flow over a curve surface imbedded in porous medium,” Communications in theoretical physics, Vol-71, pp-344, 2019,
[10] Kianoosh, Youseki and Fabrice Veron, “Boundary layer formulations in orthogonal curvilinear coordinates for flow over wind generated surface waves,” Journal of Fluid Mechanics, Vol-888, A11, 2020.
[11] E. Barakhovskaia, A. Glushchuk, P. Queeckers, and S. I. Carlo, “Stabilisation of condensate flow from curvilinear surfaces by means of porous media for space applications,” Experimental thermal and fluid science, vol-121, 1 February, 2021, 110283.
[12] A. Meneghetti, B.E.J. Bodmann, and M.T.M.B, Vilhena, “On viscous fluid flow in curvilinear coordinate system,” Integral methods in science and engineering (conference paper), 22 May. 2022.
[13] KA Maleque, “Combined fluid and ferrofluid buoyancy force, heat absorption and nonlinear ferro-viscosity effects on ferro-hydrodynamics fluid flow in orthogonal porous surface. Latin American Applied Research (LAAR), 54 (4), pp. 56, 2024.
[14] KA Maleque,, and MA Sattar, “Transient convective flow due to a rotating disc with magnetic field and heat absorption effects.” Journal of energy, heat, and mass transfer. Vol-25, pp-279, 2003.
[15] KA Maleque, “Effects of Binary Chemical Reaction and Activation Energy on MHD Boundary Layer Heat and Mass Transfer Flow with Viscous Dissipation and Heat Generation/Absorption.” International Scholarly Research Notices, Hindawi Publishing Corporation ISRN Thermodynamics Volume 2013, Article ID 284637, 9 pages, 2013. http://dx.doi.org/10.1155/2013/284637.
[16] Kh A Maleque (2014): A Binary Chemical Reaction on Unsteady Free Convective Boundary Layer Heat and Mass Transfer Flow with Arrhenius Activation Energy and Heat Generation/Absorption,” The Latin American Applied Research Journal (LAAR), Argentina, Vol -44(1) pp- 97, 2014. ISSN: 0327-0793,
DOI: https://doi.org/10.52292/j.laar.2014.425.
[17] KA Maleque, “Numerical solution of combined forced and free convective flow in porous curvilinear surfaces in presence of heat absorption/generation, Latin American Applied Research (LAAR)-An international journal 55 (1), pp. 95, 2025.
[18] MK Abdul, “The thermal absorption/generation on ferro-fluid combined convective flow over curvilinear porous surfaces,” AIUB journal of science and engineering (AJSE), vol 22, No. 3, pp 223, December, 2023. DOI: https://doi.org/10.53799/ajse.v22i3.546
[19] K. Ramesh, S. Jagadha, D. Gopal, S. H.S. Naik, and N. Kishan, “ One Dimensional Radiative Nanofluid Flow with Heat Generative Al2 O3-H2O and Cu-H2O Nanoparticles Reactions Chemically,” AIP Conf. Proc. 2943, December 2023; https://doi.org/10.1063/5.0190329.
[20] P. Jalili, S. Mousavi, B. Jalili, P. Pasha, and D. D. Ganji (2024): Thermal evaluation of MHD Jeffrey fluid flow in the presence of heat source and chemical reaction,” International journal of modern physics, vol. 38, No. 08, 2024, 450113,https://doi.org/10.1142/S0217979224501133
[21] RK. Dash, KN Metha, and G. Jayaraman, “ Casson fluid flow in a pipe filled with a homogenous porous medium, Int J Eng Sci; 34(10):1145-1156, 1996.
[22] Swati Mukhopadhyay, Prativa Ranjan De, Krishnendu Bhattacharyya, G.C. Layek, “Casson fluid flow over an unsteady stretching surface. Ain Shams Engineering Journal (Engineering Physics and Mathematics), 2013, 4, pp-933, 2013
[23] S. Nadeem , Rizwan UI Haq, Noreen Sher Akbar, Z. H. Khan, “ MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet.” Alexandria Engineering Journal, 2013, 52, 577-582, 2013
[24] H. Kataria, Patel HR, “Radiation and chemical reaction effects on MHD Casson fluid flow past an oscillating vertical plate embedded in porous medium.” Alexandria Engineering Journal, Vol. 55, issue 1, pp-583, March, 2016.
[25] Kh .A. Maleque, “MHD Non-Newtonian Casson fluid heat and mass transfer flow with exothermic/endothermic binary chemical reaction and activation energy,” American Journal of Heat and Mass Transfer, vol.3, pp. 166, 2016.
[26] Kh. A. Maleque, “Unsteady MHD Non-Newtonian Casson Fluid Flow due to a Porous Rotating Disk with Uniform Electric Field.” Fluid Mech Open Acc, vol. 3: pp-123, 2016a. doi:10.4172/fmoa.1000123
[27] Kh. A. Maleque, “Effect of Hall Current on MHD Non-Newtonian Unsteady Casson Fluid Porous Rotating Disk Flow with a Uniform Electric Field,” The Aiub Journal of Science and Engineering, vol. 16 (02), pp-51, 2017.
DOI: https://doi.org/10.53799/ajse.v16i2.79
[28] T. Anwar, P. Kumam, and W. Watthayu, “Unsteady MHD natural convection flow of Casson fluid incorporating thermal radiative flux and heat injection/suction mechanism under variable wall conditions,” Sci Rep 11, pp-4275, 2021. https://doi.org/10.1038/s41598-021-83691-2.
[29] S.S. Reddy, K. Govardhan K, G. Narender, and S. Mistra, “3D radiation flow of unsteady Casson fluid with viscous dissipation effect,” Iraqi Journal of Science, vol-64, No. 8, pp 4018, 2023. DOI:1024996/ijs.2023.64.8.26
[30] L.A. Lund, A. Asghar, G. Rasool, and U. Yashkun, “Magnetized casson SA-hybrid nanofluid flow over a permeable moving surface with thermal radiation and Joule heating effect,” Case Studies in Thermal Engineering, Vol 50, 103510, October, 2023. https://doi.org/10.1016/j.csite.2023.103510.
[31] P. Jalili, A. A. Azar, B. Jalili, D.D. Ganji, “Study of nonlinear radiative heat transfer with magnetic field for non-Newtonian Casson fluid flow in a porous medium,” Results of Physics, vol 48, 106137, 2023. https://doi.org/10.1016/j.rinp.2023.106371.
[32] Pop, I., “The effect of Hall currents on hydromagnetic flow near an accelerated plate”. (English) Zbl 0229.76074, J. Math. Phys. Sci., Madras 5, pp. 375, 1971
[33] Gupta, A.S, “Hydromagnetic flow past a porous flat plate with hall effects. Acta Mechanica 22, pp. 281, 1975. https://doi.org/10.1007/BF01170681
[34] Nanigopal Datta, and Rabindra Nath Jana, “Oscillatory Magnetohydrodynamic Flow past a Flat Plate with Hall Effects, J. Phys. Soc. Jpn. 40, pp. 1469-1474, 1976. https://doi.org/10.1143/JPSJ.40.1469
[35] Ram, P. C., “Hall Effects on the Hydromagnetic Free Convective Flow and Mass Transfer Through a Porous Medium Bounded by an Infinite Vertical Porous Plate with Constant Heat Flux”. International journal of energy research, 12, 227, 1988. https://doi.org/10.1002/er.4440120205
[36] Sattar, Md. A., “Unsteady hydromagnetic free convection flow with hall current mass transfer and variable suction through a porous medium near an infinite vertical porous plate with constant heat flux”. International journal of energy research, 18(9), pp-771, 1994.
https://doi.org/10.1002/er.4440180902
[37] Ahmed L. Aboul-Hassan, Hazem Ali Attia, “Flow due to a rotating disk with Hall effect” Physics Letters A 228, pp. 286, 1997. https://doi.org/10.1016/S0375-9601(97)00086-8
[38] KA Maleque, MA Sattar, “The effects of variable properties and Hall current on steady MHD laminar convective fluid flow due to a porous rotating disk”, International Journal of Heat and Mass Transfer 48 (Nov.), 4963-4972,, 2005 ISSN: 0017-9310.
[39] KA Maleque, “Effects of combined temperature-and depth-dependent viscosity and Hall current on an unsteady MHD laminar convective flow due to a rotating disk”. Chemical Engineering Communications(Taylor and Francis), 197(4), 506-521, 2009. ISSN 0098-6445.
[40] Z. Uddina, and M. Kumarc, “Hall and ion-slip effect on MHD boundary layer flow of a micro polar fluid past a wedge, Scientia Iranica B . 20 (3), pp. 467, 2013.
[41] D. Srinivasacharya and Md. Shafeeurrahman, “ Hall and ion slip effects on mixed convection flow of nanofluid between two concentric cylinders, Journal of the Association of Arab Universities for Basic and Applied Sciences, vol 24, pp. 223, 2017.
[42] Veera Krishna M, “Hall and ion-slip effects on MHD free convective rotating flow bounded by the semi-infinite vertical porous surface”. Heat Transfer ,2020; 49(4): 1920–1938, 2020. https://doi.org/10.1002/htj.21700
[43] Jitendra Kumar Singh, Suneetha Kolasani, and Gauri Shenker Seth, “Scrutiny of induced magnetic field and Hall current impacts on transient hydromagnetic nanofluid flow within two vertical alternative magnetized surfaces”. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, Vol 237 (4), pp.1595, 2023. https://doi.org/10.1177/09544089221119255
[44] P. R. Nachtsheim, and P. Swigert,“Satisfaction of asymptotic boundary conditions in numerical solution of system of nonlinear of boundary layer type,” NASA TN-D3004, 1965.
[45] H. Schlichting, “Boundary layer theory,”, McGraw-Hill Book Company, New York, Sixth Edition pp-151, 1968.
[46] E. M. Sparrow, R. Eichorn, and L. J. Gregg, “Combined forced and free convection in a boundary layer flow,” Phys. Fluids, Vol-2, pp-319, 1959.
[47] Vasile Marinca, R. Daniel Ene, and B. Marinca, “Analytical approximate solution for Falkner-Skan equation,” The scientific world Journal (Hindawi publishing corporation), Volume 2014, Article ID: 617453, 2014. https://doi.org/10.1155/2014/617453
Downloads
Published
Issue
Section
License
Copyright (c) 2026 AIUB Journal of Science and Engineering
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
AJSE contents are under the terms of the Creative Commons Attribution License. This permits anyone to copy, distribute, transmit and adapt the work non-commercially provided the original work and source is appropriately cited.
