Unsteady MHD Casson nanofluid transport over an inclined permeable cylinder in an anisotropic porous medium: effects of nonlinear radiation and Joule heating

Bukola Oluwatosin Falomo; Olugbenga John Fenuga; Israel Olutunji Abiala

doi:10.46481/jnsps.2026.3416

Authors

Bukola Oluwatosin Falomo
[email protected]

Department of Mathematics, University of Lagos, Lagos, Nigeria
Olugbenga John Fenuga
Department of Mathematics, University of Lagos, Lagos, Nigeria
Israel Olutunji Abiala
Department of Mathematics, University of Lagos, Lagos, Nigeria

Keywords:

Casson nanofluid, Inclined stretching cylinder, Anisotropic porous medium, Brownian motion, Homotopy perturbation method

Abstract

The present study investigates the coupled momentum, thermal, solutal, and magnetic transport characteristics of unsteady induced magnetohydrodynamic (MHD) Casson nanofluid flow over an inclined permeable cylindrical surface embedded in an anisotropic porous medium. The model incorporates several important physical mechanisms, including nonlinear thermal radiation, Joule heating, viscous dissipation, Brownian motion, thermophoresis, and higher-order chemical reaction kinetics. The governing nonlinear partial differential equations describing the conservation of mass, momentum, energy, nanoparticle concentration, and magnetic induction are transformed into a system of nonlinear ordinary differential equations through suitable similarity transformations derived using Lie group analysis. The resulting equations are solved using the semi-analytical homotopy perturbation method (HPM). The influence of key physical parameters on the velocity, temperature, nanoparticle concentration, and magnetic field profiles is analyzed through graphical and tabular results. The results indicate that increasing the magnetic parameter suppresses fluid motion due to the resistive Lorentz force while enhancing the thermal boundary layer thickness. The Casson parameter is found to significantly influence the velocity distribution, reflecting the non-Newtonian characteristics of the fluid. Thermal radiation and viscous dissipation increase the temperature field, whereas Brownian motion and thermophoresis strongly affect nanoparticle concentration profiles. Furthermore, anisotropic porous medium parameters and chemical reaction kinetics play important roles in controlling mass transfer rates. The study provides useful insights into magnetically controlled nanofluid transport in porous cylindrical geometries, which may assist in the design of advanced thermal systems in engineering applications.

Dimensions

REFERENCES

[1] S. U. S. Choi & J. A. Eastman, “Enhancing thermal conductivity of fluids with nanoparticles”, Proceedings of the ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA, 1995, pp. 99–105. https://doi.org/10.1115/IMECE1995-0926.

[2] J. Buongiorno, ``Convective transport in nanofluids'', Journal of Heat Transfer 128 (2006) 240. https://doi.org/10.1115/1.2150834.

[3] W. A. Khan & I. Pop, ``Boundary-layer flow of a nanofluid past a stretching sheet'', International Journal of Heat and Mass Transfer 53 (2010) 2477. https://doi.org/10.1016/j.ijheatmasstransfer.2010.01.032.

[4] F. Mabood, W. A. Khan & A. I. M. Ismail, ``MHD boundary-layer flow and heat transfer of nanofluids over a nonlinear stretching sheet'', Journal of Magnetism and Magnetic Materials 374 (2015) 569. https://doi.org/10.1016/j.jmmm.2014.09.013.

[5] Y. X. Li, M. H. Alshbool, Y. P. Lv, I. Khan, M. R. Khan & A. Issakhov, “Heat and mass transfer in MHD Williamson nanofluid flow over an exponentially porous stretching surface”, Case Studies in Thermal Engineering 26 (2021) 100975. https://doi.org/10.1016/j.csite.2021.100975.

[6] A. Zhu, H. Ali, M. Ishaq, M. S. Junaid, J. Raza & M. Amjad, ``Numerical study of heat and mass transfer for Williamson nanofluid over a stretching/shrinking sheet along with Brownian and thermophoresis effects'', Energies 15 (2022) 5926. https://doi.org/10.3390/en15165926.

[7] N. Casson, ``A flow equation for pigment-oil suspensions'', in Rheology of Disperse Systems, Pergamon Press, Oxford, UK, 1959, pp. 84--102.

[8] S. S. Ghadikolaei, K. Hosseinzadeh, D. D. Ganji & B. Jafari, ``Nonlinear thermal radiation effect on magneto Casson nanofluid flow with Joule heating effect over an inclined porous stretching sheet'', Case Studies in Thermal Engineering 12 (2018) 176. https://doi.org/10.1016/j.csite.2018.04.009.

[9] A. S. Idowu, M. T. Akolade, J. U. Abubakar & B. O. Falodun, ``MHD free convective heat and mass transfer flow of dissipative Casson fluid with variable viscosity and thermal conductivity effects'', Journal of Taibah University for Science 14 (2020) 851. https://doi.org/10.1080/16583655.2020.1781431.

[10] K. R. Cramer & S.-I. Pai, Magnetofluid Dynamics for Engineers and Applied Physicists, Scripta Publishing Company, Washington, DC, USA, 1973.

[11] L. J. Crane, ``Flow past a stretching plate'', Zeitschrift f"ur Angewandte Mathematik und Physik 21 (1970) 645. https://doi.org/10.1007/BF01587695.

[12] A. K. Mishra, P. K. Pattnaik, S. R. Mishra & N. Senapati, ``Dissipative heat energy on Cu and Al$_2$O$_3$ ethylene-glycol-based nanofluid flow over a heated semi-infinite vertical plate'', Journal of Thermal Analysis and Calorimetry 145 (2021) 129. https://doi.org/10.1007/s10973-020-09666-z.

[13] T. Thumma, S. R. Mishra, M. A. Abbas, M. M. Bhatti & S. I. Abdelsalam, ``Three-dimensional nanofluid stirring with a non-uniform heat source/sink through an elongated sheet'', Applied Mathematics and Computation 421 (2022) 126927. https://doi.org/10.1016/j.amc.2022.126927.

[14] S. Panda, S. Ontela, S. R. Mishra & P. K. Pattnaik, ``Response surface methodology and sensitivity analysis for optimizing the heat-transfer rate in three-dimensional hybrid nanofluid flow through a permeable stretching surface'', Journal of Thermal Analysis and Calorimetry 148 (2023) 7369. https://doi.org/10.1007/s10973-023-12183-4.

[15] P. P. Humane, V. S. Patil & A. B. Patil, ``Chemical reaction and thermal radiation effects on magnetohydrodynamic flow of Casson--Williamson nanofluid over a porous stretching surface'', Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 235 (2021) 2008. https://doi.org/10.1177/09544089211025376.

[16] P. K. Pattnaik, S. R. Mishra, S. Panda, S. A. Syed & K. Muduli, ``Hybrid methodology for the computational behaviour of thermal radiation and chemical reaction on viscoelastic nanofluid flow'', Mathematical Problems in Engineering 2022 (2022) 2227811. https://doi.org/10.1155/2022/2227811.

[17] S. Tinker, S. R. Mishra, P. K. Pattnaik & R. P. Sharma, ``Simulation of time-dependent radiative heat motion over a stretching/shrinking sheet of hybrid nanofluid: stability analysis for dual solutions'', Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems 236 (2022) 19. https://doi.org/10.1177/23977914211069021.

[18] S. Baag & S. Panda, ``Free convection of conducting nanofluid past an expanding surface with heat source with convective heating boundary conditions'', International Journal of Ambient Energy 44 (2023) 880. https://ui.adsabs.harvard.edu/abs/2023IJAmE..44..880B/abstract.

[19] N. Gomathi & D. Poulomi, ``Entropy optimization on EMHD Casson--Williamson penta-hybrid nanofluid over porous exponentially vertical cone'', Alexandria Engineering Journal 108 (2024) 590. https://doi.org/10.1016/j.aej.2024.07.092.

[20] M. Sadighi, S. E. Ghasemi & M. Hatami, ``Magnetohydrodynamic nanofluid flow over a stretching surface with thermal radiation and chemical reaction'', Case Studies in Thermal Engineering 41 (2023) 103345. https://doi.org/10.1016/j.csite.2023.103345.

[21] S. Irshad, S. Jahan, J. M. Machado, P. '{S}liwi'nski, K. Kk{e}dzia & A. Z. Jan, ``MHD Casson flow across a stretched surface in a porous material: a numerical study'', Multiscale and Multidisciplinary Modeling, Experiments and Design 8 (2025) 36. https://doi.org/10.1007/s41939-024-00628-8.

[22] T. A. Walelign, ``Casson nanofluid flow over a stretching surface with thermal radiation and magnetic-field effects'', Results in Engineering 23 (2025) 101850. https://www.researchgate.net/publication/354983698.

[23] K. A. Abbas, K. M. Naveed, N. A. Ahammad, M. Ashraf, K. Guedri & A. M. Galal, ``Flow investigation of second grade micropolar nanofluid with porous medium over an exponentially stretching sheet'', Journal of Applied Biomaterials & Functional Materials 2022 (2022) 20. https://doi.org/10.1177/22808000221089782.

[24] V. Makkar, V. Poply & N. Sharma, ``Radiative MHD non-Newtonian chemically reactive nanofluid flow with a heat source induced by a nonlinear stretching cylinder'', Trends in Sciences 19 (2022) 6314. https://doi.org/10.48048/tis.2022.6314.

[25] E. M. A. Elbashbeshy, ``Heat transfer over a stretching surface with variable surface heat flux'', Journal of Physics D: Applied Physics 31 (1998) 1951. https://doi.org/10.1088/0022-3727/31/16/002.

[26] N. Bachok, A. Ishak & I. Pop, ``Flow and heat transfer over a stretching/shrinking sheet in a nanofluid'', Advances in Mechanical Engineering 2 (2010) 681345.

[27] N. A. Mat Noor, S. Shafie & M. A. Admon, ``Unsteady MHD flow of Casson nanofluid with chemical reaction, thermal radiation and heat generation/absorption'', MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics 35 (2019) 33. https://doi.org/10.11113/matematika.v35.n4.1262.

[28] H. A. Attia, ``Hiemenz flow through a porous medium of a non-Newtonian Rivlin--Ericksen fluid with heat transfer'', Journal of Applied Science and Engineering 12 (2009) 359. http://163.13.100.126/articles/jase-200909-12-3-15.pdf.

[29] K. G. Kumar, B. J. Gireesha & M. G. Reddy, ``MHD flow and heat transfer of Casson nanofluid over a stretching sheet with Joule heating and thermal radiation'', Journal of Molecular Liquids 276 (2019) 653. https://www.researchgate.net/publication/343417335.

[30] A. Adeniyan, F. Mabood & S. S. Okoya, ``Effect of heat radiating and generating second-grade mixed-convection flow over a vertical slender cylinder with variable physical properties'', International Communications in Heat and Mass Transfer 121 (2021) 105110. https://doi.org/10.1016/j.icheatmasstransfer.2021.105110.

[31] T. M. Kabir & T. Abdulganiyu, ``Homotopy perturbation method for analyzing the effect of viscous dissipation on steady natural-convection Couette flow with convective boundary conditions'', International Journal of Fluid Mechanics & Thermal Sciences 10 (2024) 45. https://doi.org/10.11648/j.ijfmts.20241003.11.

[32] A. J. Shkarah, S. W. Noori, D. A. Lafta, A. M. Lafta & M. M. Mansour, ``Application of the homotopy perturbation method to the Jeffery--Hamel flow of nanofluids between two non-parallel planar walls'', Results in Engineering 28 (2025) 107805. https://doi.org/10.1016/j.rineng.2025.107805.