Researchers have been conducting experiments to improve heat transfer rates and decrease fuel usage to improve heating system efficiency and reduce expenses. It has been demonstrated that incorporating solid nanoparticles into conventional liquids substantially increases thermal conductivity. This study emphasizes its potential usage in diverse heat exchange systems, including heat exchangers, radiators, and electronic cooling systems, highlighting its possible impact on enhancing thermal management in various engineering and industrial applications. This paper addresses the significance of Joule heating and viscous dissipation on the steady Couette–Hartmann flow of a nanoliquid between an asymmetrical channel having arbitrarily conductive walls and thickness. The generation of Hall current and induced magnetic fields (IMFs) is triggered by the existence of a robust magnetic field. The mathematical model is developed based on the underlying assumptions of energy conservation, momentum, and magnetic induction. The assumed models are represented by a set of interconnected ordinary differential equations that employ a suitable and comparable adjustment. The numerical solution to these equations is evaluated for approximate convergence using the Lobatto‐IIIa‐bvp4c‐solver integrated into the MATLAB software. This solver is constructed by means of a finite difference scheme.The implications of relevant evolving parameters on the velocity field (VF), IMF, nanoliquid temperature field (NTF), surface skin friction (SSF), and mass flow rate (MFR) are investigated. Graphical and tabular representations of the VF, IMF, NTF, SSF, and MFR of nanoliquid at the wall surface are shown for various relevant parameter values. It is quantified that rotation causes suppression in the main flow, which elevates the temperature of the nanoliquid. Heat diffusion causes the temperature to decrease, whereas viscous dissipation causes the nanoliquid temperature to increase. The numerical evaluation that captures the implications of Joule heating and viscous dissipation on the magnetohydrodynamic (MHD) steady Couette–Hartmann flow of a nanoliquid within an asymmetrical channel assuming arbitrarily conductive walls and thickness is the distinguishing feature of this research. In the majority of the research captured in this area, the channel wall is nonconducting or considered to be perfectly conducting for simplicity. However, the arbitrary wall conductance significantly alters the motion‐generated magnetic field, hence velocity and temperature. It is witnessed that the constant for wall conductivity brings growth in the motional IMF along the main flow. This research further investigates several unexplored variables, including wall conductance, energy dissipation, Hall effects, volumetric concentration, and rotation.
