Impact of magnetic field on heat transfer with viscous dissipation at the conduction limit in a channel with a centred porous layer: constant wall temperature

Abstract

This paper investigates the impact of a magnetic field on heat transfer within a duct containing a centrally located porous layer. The duct comprises both fluid and porous regions, with the porous material occupying the central section. The channel walls are maintained at constant temperatures. In the fluid region, the flow field is governed by the Poiseuille flow equation, while in the porous region, the non-Darcy Brinkman equation is employed to model the flow. It is assumed that the flow field is fully developed. To account for viscous dissipation, two dissipation models, namely the clear fluid compatible (CFC) model and the form drag (FD) model, are implemented in the porous region. The study delves into the detailed effects of these dissipation models on heat transfer. The system is characterized by several well-established properties, including the porous fraction (δp), Darcy number (Da), Brinkman number (Br), and Hartmann number (M). Analytical expressions for the limiting Nusselt number (LNN) and the limiting temperature profiles (LTP) are derived at the conduction limit, taking into consideration the presence of the magnetic field. For high Hartmann numbers, the CFC model is deemed appropriate for the viscous dissipation model.