Journal of Computational Applied Mechanics

Effect of Varying Thermal Conductivity on MHD Micropolar Fluid Flow Based on Cattaneo-Christov Heat Flux Model over an Exponentially Extended Stretching Curved Surface

Document Type : Research Paper

Authors

1 Faculty of Science, Taibah University, Madinah Al Munawwarha Saudi Arabia

2 Department of Mathematics & Statistics, International Islamic University, Islamabad Pakistan

3 Department of Mathematics & Statistics, International Islamic University, Islamabad Pakistan

4 Center for Modeling & Computer Simulation, Research Institute, King Fahd University of Petroleum & Minerals, Dhahran-31261, Saudi Arabia

Abstract

This study investigates the magnetohydrodynamic (MHD) flow of a micropolar fluid over an exponentially extended stretching curved surface. The boundary layer flow along with temperature-dependent thermal conductivity is also taken into account. The Cattaneo-Christov heat flux model is used for energy equation. The curvilinear coordinates are used in the formation of flow equations. The governing non-linear partial differential equations (PDEs) are transformed into coupled non-linear ordinary different equations (ODEs) by appropriate transformations. The resulting ODEs are solved numerically using the ND-solve method in Mathematica. Graphs are plotted to explore the impacts of key parameters on microrotation, temperature, and velocity. Results show that increasing curvature leads to higher velocity and lower temperature, with potential applications in polymer processing and waste treatment. A comparison has been made with the existing literature as a limited case of present study to validate the results.

Keywords

Main Subjects

[1] M. M. Bhatti, A. Zeeshan, F. Bashir, S. M. Sait, R. Ellahi, Sinusoidal motion of small particles through a Darcy-Brinkman-Forchheimer microchannel filled with non-Newtonian fluid under electro-osmotic forces, Journal of Taibah University for Science, Vol. 15, No. 1, pp. 514-529, 2021/01/01, 2021.
[2] F. Ishtiaq, R. Ellahi, M. M. Bhatti, S. Z. Alamri, Insight in Thermally Radiative Cilia-Driven Flow of Electrically Conducting Non-Newtonian Jeffrey Fluid under the Influence of Induced Magnetic Field, Mathematics, Vol. 10, No. 12, pp. 2007, 2022.
[3] A. A. Khan, B. Zahra, R. Ellahi, S. M. Sait, Analytical Solutions of Peristalsis Flow of Non-Newtonian Williamson Fluid in a Curved Micro-Channel under the Effects of Electro-Osmotic and Entropy Generation, Symmetry, Vol. 15, No. 4, pp. 889, 2023.
[4] R. Ellahi, The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions, Applied Mathematical Modelling, Vol. 37, No. 3, pp. 1451-1467, 2013/02/01/, 2013.
[5] F. Ishtiaq, R. Ellahi, M. M. Bhatti, S. Sait, Convective heat transfer with Hall current using magnetized non-Newtonian Carreau fluid model on the cilia-attenuated flow, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 34, 07/16, 2024.
[6] S. M. Sait, R. Ellahi, N. Khalid, T. Taha, A. Zeeshan, Effects of thermal radiation on MHD bioconvection flow of non-Newtonian fluids using linear regression based machine learning and artificial neural networks, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 35, No. 5, pp. 1587-1609, 2025.
[7] M. S. Nadeem, A. Zeeshan, A. Majeed, S. M. Sait, R. Ellahi, Cavitating bubbly flow of non-Newtonian second grade fluid through nozzles: Application of reduction of cavitation damage and noise, International Journal of Modern Physics B, Vol. 39, No. 11, pp. 2550085, 2025.
[8] R. Ellahi, A. Zeeshan, S. Shafique, S. M. Sait, A. u. Rehman, Electroosmotic slip flow in peristaltic transport of non-Newtonian third-grade MHD fluid: RSM-based sensitivity analysis, International Journal of Heat and Mass Transfer, Vol. 247, pp. 127121, 2025/09/01/, 2025.
[9] A. C. Eringen, Simple microfluids, International Journal of Engineering Science, Vol. 2, No. 2, pp. 205-217, 1964/05/01/, 1964.
[10]              A. C. Eringen, Theory of Micropolar Fluids, Journal of Mathematics and Mechanics, Vol. 16, No. 1, pp. 1-18, 1966.
[11]              C. Eringen, 1970, Foundations of Micropolar Thermoelasticity, Springer Vienna,
[12]              A. A. Khan, S. M. Sait, R. Ellahi, Reflection of Harmonic Waves in a Nonlocal Rotating Micropolar Medium with Constant Magnetic Field under Three-phase-lag Theory with Temperature Dependent Elastic Model, Journal of Computational Applied Mechanics, Vol. 56, No. 2, pp. 331-344, 2025.
[13]              M. Turkyilmazoglu, Flow of a micropolar fluid due to a porous stretching sheet and heat transfer, International Journal of Non-Linear Mechanics, Vol. 83, pp. 59-64, 2016/07/01/, 2016.
[14]              Seyed M. Hashem Zadeh, S. A. M. Mehryan, M. A. Sheremet, M. Izadi, M. Ghodrat, Numerical study of mixed bio-convection associated with a micropolar fluid, Thermal Science and Engineering Progress, Vol. 18, pp. 100539, 2020/08/01/, 2020.
[15]              A. Sid Ahmed, B. Ayoub, B. M. Najib, B. A. Manal, Conjugate Mixed Convection of a Micropolar Fluid Over a Vertical Hollow Circular Cylinder, International Journal of Applied Mechanics and Engineering, Vol. 29, No. 1, pp. 1-18, 2024.
[16]              N. S. Elgazery, N. Y. Abd Elazem, Insights into viscosity/thermal conductivity of a micropolar nanofluid flow near a horizontal cylinder, Journal of Nanofluids, Vol. 13, No. 2, pp. 614-624, 2024.
[17]              M. Ghobadi, Y. S. Muzychka, A Review of Heat Transfer and Pressure Drop Correlations for Laminar Flow in Curved Circular Ducts, Heat Transfer Engineering, Vol. 37, No. 10, pp. 815-839, 2016/07/02, 2016.
[18]              A. Afsar Khan, R. Batool, N. Kousar, Examining the behavior of MHD micropolar fluid over curved stretching surface based on the modified Fourier law, Scientia Iranica, Vol. 28, No. 1, pp. 223-230, 2021.
[19]              T. Muhammad, K. Rafique, M. Asma, M. Alghamdi, Darcy–Forchheimer flow over an exponentially stretching curved surface with Cattaneo–Christov double diffusion, Physica A: Statistical Mechanics and its Applications, Vol. 556, pp. 123968, 2020/10/15/, 2020.
[20]              A. K. Kempannagari, R. R. Buruju, S. Naramgari, S. Vangala, Effect of Joule heating on MHD non-Newtonian fluid flow past an exponentially stretching curved surface, Heat Transfer, Vol. 49, No. 6, pp. 3575-3592, 2020.
[21]              Q.-H. Shi, T. Shabbir, M. Mushtaq, M. I. Khan, Z. Shah, P. Kumam, Modelling and numerical computation for flow of micropolar fluid towards an exponential curved surface: a Keller box method, Scientific Reports, Vol. 11, No. 1, pp. 16351, 2021/08/11, 2021.
[22]              K. A. Kumar, V. Sugunamma, N. Sandeep, S. Sivaiah, Physical Aspects on MHD Micropolar Fluid Flow Past an Exponentially Stretching Curved Surface, Defect and Diffusion Forum, Vol. 401, pp. 79-91, 2020.
[23]              R. Ellahi, A. Zeeshan, N. Shehzad, S. Z. Alamri, Structural impact of kerosene-Al2O3 nanoliquid on MHD Poiseuille flow with variable thermal conductivity: Application of cooling process, Journal of Molecular Liquids, Vol. 264, pp. 607-615, 2018/08/15/, 2018.
[24]              A. A. Khan, S. Naeem, R. Ellahi, S. M. Sait, K. Vafai, Dufour and Soret effects on Darcy-Forchheimer flow of second-grade fluid with the variable magnetic field and thermal conductivity, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30, No. 9, pp. 4331-4347, 2020.
[25]              A. Kanwal, A. A. Khan, S. M. Sait, R. Ellahi, Heat transfer analysis of magnetohydrodynamics peristaltic fluid with inhomogeneous solid particles and variable thermal conductivity through curved passageway, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 34, No. 4, pp. 1884-1902, 2024.
[26]              A. Khan, S. Noor, R. Ellahi, S. Sait, THERMAL ANALYSIS OF TWO-PHASE MHD FLOW DUE TO CILIARY MOVEMENT WITH VISCOUS DISSIPATION IN THE PRESENCE OF HEAT SOURCE/SINK, Journal of Enhanced Heat Transfer, 01/01, 2025.
[27]              A. M. Megahed, M. G. Reddy, W. Abbas, Modeling of MHD fluid flow over an unsteady stretching sheet with thermal radiation, variable fluid properties and heat flux, Mathematics and Computers in Simulation, Vol. 185, pp. 583-593, 2021/07/01/, 2021.
[28]              A. A. Khan, S. Ilyas, T. Abbas, R. Ellahi, Significance of induced magnetic field and variable thermal conductivity on stagnation point flow of second grade fluid, Journal of Central South University, Vol. 28, No. 11, pp. 3381-3390, 2021/11/01, 2021.
[29]              S. Z. Alamri, A. A. Khan, M. Azeez, R. Ellahi, Effects of mass transfer on MHD second grade fluid towards stretching cylinder: A novel perspective of Cattaneo–Christov heat flux model, Physics Letters A, Vol. 383, No. 2, pp. 276-281, 2019/01/12/, 2019.
[30]              A. A. Khan, I. Saleem, R. Ellahi, S. M. Sait, K. Vafai, On magnetohydrodynamics Powell–Eyring fluid with Cattaneo–Christov heat flux over a curved surface, International Journal of Modern Physics B, Vol. 37, No. 19, pp. 2350190, 2023.
[31]              J. Mehboob, R. Ellahi, S. M. Sait, N. S. Akbar, Optimizing bioconvective heat transfer with MHD Eyring–Powell nanofluids containing motile microorganisms with viscosity variability and porous media in ciliated microchannels, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 35, No. 2, pp. 825-846, 2025.
[32]              A. Zeeshan, N. Khalid, R. Ellahi, M. Khan, S. Z. Alamri, Analysis of nonlinear complex heat transfer MHD flow of Jeffrey nanofluid over an exponentially stretching sheet via three phase artificial intelligence and Machine Learning techniques, Chaos, Solitons & Fractals, Vol. 189, pp. 115600, 2024.
[33]              R. Ellahi, S. Alamri, A. Majeed, Effects of MHD and slip on heat transfer boundary layer flow over a moving plate based on specific entropy generation, Journal of Taibah University for Science, Vol. 12, pp. 1-7, 06/14, 2018.
[34]              A. M. Alqahtani, Zeeshan, W. Khan, Amina, S. A. Alhabeeb, H. A. El-Wahed Khalifa, Stability of magnetohydrodynamics free convective micropolar thermal liquid movement over an exponentially extended curved surface, Heliyon, Vol. 9, No. 11, 2023.
Journal of Computational Applied Mechanics
Volume 56, Issue 4
October 2025
Pages 776-790
  • Receive Date: 15 July 2025
  • Accept Date: 16 July 2025