A computational analysis of heat transport irreversibility phenomenon in a magnetized porous channel Souad Marzougui and M. Bouabid High Institute of Applied Sciences and Technology, Industrial Chemistry and Processes Department, University of Gabes, Gabes, Tunisia Fateh Mebarek-Oudina Department of Physics, Faculty of Sciences, University of 20 août 1955-Skikda, Skikda, Algeria and Laboratoire des Matériaux et Génie Energétique (LMGE), University of 20 août 1955-Skikda, Skikda, Algeria Nidal Abu-Hamdeh Department of Mechanical Engineering, College of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia Mourad Magherbi High Institute of Applied Sciences and Technology, Industrial Chemistry and Processes Department, University of Gabes, Gabes, Tunisia, and K. Ramesh Department of Mathematics, Symbiosis Institute of Technology, Symbiosis International (Deemed University), Nagpur, India Abstract Purpose – The purpose of this paper is to evaluate the temperature, the Dirichlet conditions have been considered to the parallel horizontal plates. The model of generalized Brinkman-extended Darcy with the Boussinesq approximation is considered and the governing equations are computed by COMSOL multiphysics. Design/methodology/approach – In the current study, the thermodynamic irreversible principle is applied to study the unsteady Poiseuille–Rayleigh–Bénard (PRB) mixed convection in a channel (aspect ratio A = 5), with the effect of a uniform transverse magnetic field. Findings – The effects of various flow parameters on the fluid flow, Hartmann number (Ha), Darcy number (Da), Brinkman number (Br) and porosity (« ), are presented graphically and discussed. Numerical results for temperature and velocity profiles, entropy generation variations and contour maps of streamlines, are presented as functions of the governing parameter mentioned above. Basing on the generalized Brinkman- extended Darcy formulation, which allows the satisfaction of the no-slip boundary condition on a solid wall, it is found that the flow field and then entropy generation is notably influenced by the considering control parameters. The results demonstrate that the flow tends toward the steady-state with four various regimes, which strongly depends on the Hartman and Darcy numbers variations. Local thermodynamic irreversibilities are more confined near the active top and bottom horizontal walls of the channel when increasing the Da and decreasing the Hartmann number. Entropy generation is also found to be considerably affected by Brinkman number variation. Phenomenon in a magnetized porous channel Received 12 July 2020 Revised 21 September 2020 9 October 2020 Accepted 9 October 2020 International Journal of Numerical Methods for Heat & Fluid Flow © Emerald Publishing Limited 0961-5539 DOI 10.1108/HFF-07-2020-0418 The current issue and full text archive of this journal is available on Emerald Insight at: https://www.emerald.com/insight/0961-5539.htm