Title: Computational heat transfer of MHD mixed convection in a vertical pipe: thermal non-equilibrium approach

Authors: Saurabh Kapoor; Durgaprasad Nayak

Addresses: Department of Science and Mathematics, Regional Institute of Education (NCERT), Bhubaneswar, India ' Department of Mathematics, Regional Institute of Education, Utkal University, Bhubaneswar, India

Abstract: This study investigates fully developed mixed convective flow in a vertical porous pipe under local thermal non-equilibrium (LTNE) conditions, incorporating magnetic field and heat source effects. The non-Darcy-Brinkman-Forchheimer (NDBF) model is employed, with equations solved via the Chebyshev spectral collocation method. Validation against existing solutions shows excellent agreement. We analyse the influence of the magnetic parameter (M), heat source parameters (Q_f, Q_s), interphase heat transfer coefficient (H), and conductivity ratio (γ) on flow and thermal profiles. Results indicate that increasing M flattens the velocity profile, which exhibits inflection points at lower values. Higher Q_f induces backflow and raises both fluid and solid temperatures. Notably, increasing H enhances heat transfer from the fluid to the solid phase; consequently, fluid temperatures decrease while solid-phase temperatures rise. These findings offer valuable insights for optimising MHD flows in porous media for engineering and industrial applications.

Keywords: porous medium; convection; magnetic field; heat source parameter; spectral collocation method; thermal non-equilibrium.

DOI: 10.1504/IJESMS.2026.155175

International Journal of Engineering Systems Modelling and Simulation, 2026 Vol.17 No.4, pp.238 - 250

Received: 17 Jun 2025
Accepted: 13 Oct 2025
Published online: 28 Jul 2026 *

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