SEMI-NUMERICAL METHOD FOR SOLVING UNSTEADY SQUEEZING MAGNETOHYDRODYNAMIC EYRING-POWELL FLUID MODEL WITH VARIABLE THERMOPHYSICAL PROPERTIES

adeyemi BEPO

doi:10.26740/vubeta.v3i3.52684

Authors

adeyemi BEPO Department of mathematics,ladoke akintola university of technology, ogbomoso, oyo state

DOI:

https://doi.org/10.26740/vubeta.v3i3.52684

Abstract

This study investigates the unsteady squeezing magnetohydrodynamic flow of an Eyring–Powell fluid between two parallel plates with variable thermophysical properties and Arrhenius chemical reaction effects. The governing continuity, momentum, energy, and concentration equations are transformed into dimensionless form and solved using a hybrid semi numerical approach based on Chebyshev polynomials combined with the Galerkin weighted residual technique,Gaussian quadrature ensures accurate evaluation of integral terms. The effects of electrical conductivity, thermal conductivity, mass diffusivity, magnetic field strength, and activation energy on velocity, temperature, and concentration are analyzed. Results show increase in electrical conductivity strengthens magnetic, producing a resistive Lorentz force that suppresses fluid velocity. Thermal conductivity improves heat transport within the channel, leading to higher temperature distribution and better thermal performance. Increasing Arrhenius activation energy reduces the chemical reaction rate, thereby increasing species concentration within the boundary layer due to reduced consumption of reacting particles. Variable mass diffusivity enhances species transport and enlarges the concentration boundary layer thickness. Quantities including skin friction coefficient, Nusselt number, and Sherwood number are evaluated to characterize momentum, heat, and mass transfer at the surfaces. Proposed Chebyshev–Galerkin demonstrates convergence and high accuracy, confirming its effectiveness for solving nonlinear fluid flow problems with variable properties.

References

[1] P. A. Davidson, An Introduction to Magnetohydrodynamics. Cambridge, U.K.: Cambridge University Press, 2001.

[2] J. A. Shercliff, A Textbook of Magnetohydrodynamics. Oxford, U.K.: Pergamon Press, 1965.

[3] O. D. Makinde, “MHD boundary layer flow with heat transfer,” Int. J. Therm. Sci., vol. 50, no. 7, pp. 1326–1332, 2011.

[4] M. Sheikholeslami, “Numerical simulation of MHD nanofluid flow and heat transfer,” Int. J. Heat Mass Transf., vol. 115, pp. 1203–1213, 2017.

[5] T. Hayat, S. Nadeem, and M. Imran, “Flow of an Eyring–Powell fluid over a stretching surface with heat transfer,” Int. J. Heat Mass Transf., vol. 55, no. 11–12, pp. 3031–3038, 2012.

[6] S. Abbasbandy and T. Hayat, “Solution of the MHD flow of Eyring–Powell fluid over a stretching sheet,” Phys. Lett. A, vol. 372, no. 5, pp. 731–734, 2008.

[7] S. Nadeem and R. Mehmood, “Effects of thermal radiation on MHD flow of a Powell–Eyring fluid,” J. Assoc. Arab Univ. Basic Appl. Sci., vol. 13, pp. 1–8, 2013.

[8] T. Hayat, M. Imtiaz, and A. Alsaedi, “MHD flow of Eyring–Powell fluid with nonlinear thermal radiation,” J. Mol. Liq., vol. 215, pp. 152–159, 2016.

[9] M. M. Rashidi, N. Freidoonimehr, and E. Momoniat, “Analytical solution of MHD boundary layer flow of non-Newtonian fluid,” Commun. Nonlinear Sci. Numer. Simul., vol. 19, no. 1, pp. 20–33, 2014.

[10] T. Hayat, M. Awais, and A. Alsaedi, “MHD flow of non-Newtonian fluid with heat transfer,” Appl. Math. Comput., vol. 217, no. 16, pp. 7066–7075, 2011.

[11] S. Nadeem, T. Hayat, and M. Imran, “Peristaltic flow of a non-Newtonian fluid in a channel,” Appl. Math. Mech., vol. 35, no. 1, pp. 1–16, 2014.

[12] M. Sheikholeslami and D. D. Ganji, “MHD squeezing flow of nanofluid between parallel plates,” Powder Technol., vol. 301, pp. 1102–1111, 2016.

[13] M. M. Rashidi, N. Freidoonimehr, and E. Momoniat, “Squeezing flow of a nanofluid between parallel plates,” J. Mol. Liq., vol. 216, pp. 699–706, 2016.

[14] M. Sheikholeslami, “Influence of magnetic field on squeezing flow of nanofluid,” Powder Technol., vol. 322, pp. 135–143, 2017.

[15] S. U. S. Choi and J. A. Eastman, “Enhancing thermal conductivity of fluids with nanoparticles,” in Proc. ASME Int. Mech. Eng. Congr. Expo., 1995.

[16] A. Pantokratoras, “Variable viscosity effects on boundary layer flow,” Appl. Math. Model., vol. 28, no. 5, pp. 431–440, 2004.

[17] M. A. Seddeek, “Effects of radiation and variable viscosity on MHD flow,” Int. Commun. Heat Mass Transf., vol. 29, no. 3, pp. 379–388, 2002.

[18] T. Hayat, Z. Iqbal, and A. Alsaedi, “Impact of variable thermal conductivity in MHD flows,” Appl. Math. Mech., vol. 34, no. 2, pp. 123–138, 2013.

[19] M. M. Rashidi and N. Freidoonimehr, “Effects of chemical reaction on MHD flow,” J. Taiwan Inst. Chem. Eng., vol. 45, no. 4, pp. 1658–1664, 2014.

[20] T. Hayat, S. A. Shehzad, and A. Alsaedi, “Effects of activation energy on MHD flow with chemical reaction,” J. Mol. Liq., vol. 221, pp. 245–253, 2016.

[21] O. D. Makinde, “MHD flow with heat and mass transfer,” Int. J. Therm. Sci., vol. 50, no. 7, pp. 1326–1332, 2011.

[22] J. P. Boyd, Chebyshev and Fourier Spectral Methods, 2nd ed. New York, NY, USA: Dover, 2001.

[23] C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics. Berlin, Germany: Springer, 1988.

[24] R. Peyret, Spectral Methods for Incompressible Flows. New York, NY, USA: Springer, 2002.

[25] L. N. Trefethen, Spectral Methods in MATLAB. Philadelphia, PA, USA: SIAM, 2000.

[26] D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods. Philadelphia, PA, USA: SIAM, 1977.

[27] M. Sheikholeslami, “Numerical modeling of MHD nanofluid flow with entropy generation,” Phys. Fluids, vol. 32, 2020.

[28] T. Hayat, A. Alsaedi, and M. Khan, “MHD flow of non-Newtonian fluids with thermal radiation,” J. Mol. Liq., vol. 318, 2020.

[29] S. Nadeem et al., “Impact of activation energy on MHD nanofluid flow,” Case Stud. Therm. Eng., vol. 28, 2021.

[30] M. Imran et al., “Numerical study of Eyring–Powell fluid with heat transfer,” Results Eng., vol. 10, 2021.

[31] S. A. Obalalu, A. B. Adeyemi, and F. O. Akinola, “Numerical solution of Eyring–Powell MHD squeezing flow,” Journal of Applied Fluid Mechanics, vol. 10, no. 3, pp. 245–261, 2017.

[32] S. S. Ghadikolaei, M. N. Reza, and D. D. Ganji, “Analysis of unsteady MHD Eyring–Powell squeezing flow in stretching channel with thermal radiation and Joule heating,”Case Studies in Thermal Engineering, vol. 10, pp. 579–594, 2017. ScienceDirect

[33] S. A. Obalalu, A. R. Ismail, and S. Khan, “Chebyshev collocation method for solving boundary layer problems,” Applied Mathematics and Computation, vol. 315, pp. 512–525, 2018.

[34] Alao, et al.: Weighted residual method for the squeezing flow between parallel walls plates, Americal International Journal of Research in Science, Technology, Engineering and Mathematics ISSN: 2328-3491, Sciences,4:476484.doi:10.30538/oms 2020.013 2017

[35] Akolade, M. T., and Idowu, A. S. (2025). Radiation convection flow of Eyring–Powell Prandtl Eyring nanofluid over a convectively heated surface with thermo-chemical flux interactions. Multiscale and Multidisciplinary Modeling, Experiments and Design, 8(2), 140. https://doi.org/10.1007/s41939-025-00735-0

[36] Afaq, H., Azhar, E. and Kamran, A. (2025). Modeling and analysis of heat transfer in Eyring–Powell fluids with magnetic and viscous dissipation: Applications to MHD systems. Multiscale and Multidisciplinary Modeling, Experiments and Design, 8, 168. https://doi.org/10.1007/s41939-025-00741-2

[37] Abel, M. S., and Mahesha, N. J. A. M. M. (2008): Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation. Applied Mathematical Modelling, 32(10), 1965-1983.

[38] Acosta‐Zamora, K. P., and Núñez, J. (2022): On the solutions of fluid flow problems with a Chebyshev collocation method using Mathematica. Computer Applications in Engineering Education, 30(4), 1222-1235.

[39] Alhazmi et al. A multi-layer neural network-based evaluation of MHD radiative heat transfer in Eyring–Powell fluid model. Heliyon, 11(3). https://www.cell.com/heliyon/fulltext/S2405-8440(25)00180-X 2025

[40] Alghamdi, et al. Double layered combined convective heated flow of Eyring–Powell fluid across an elevated stretched cylinder using intelligent computing approach. Case Studies in Thermal Engineering, 54, 104009. https://doi.org/10.1016/j.csite.2024.104009 2024