The problem of the effect of an external magnetic field on fluid flow and heat transfer characteristics is relevant to several physical phenomena. In this paper, flow and heat transfer of an electrically-conductive fluid around a cylinder, wrapped with a porous ring and under the influence of a magnetic field, is studied numerically. The ranges of the Stuart (N), Reynolds (Re), and Darcy (Da) numbers are 0–7, 1–40, and 10−8–10−1, respectively. The Darcy–Brinkman–Forchheimer model was used for simulating flow in the porous layer. The governing equations provide a coupling between flow and magnetic fields. The governing equations, together with the relevant boundary conditions, are solved numerically using the finite-volume method (FVM). The effect of the Stuart, Reynolds, and Darcy numbers on the flow patterns and heat transfer rate are explored. Finally, two empirical equations for the average Nusselt number were suggested, in which the effect of a magnetic field and the Darcy numbers are taken into account. It was found that in the presence of a magnetic field, the drag coefficient and the critical radius of the insulation increases, while the wake length and Nusselt number decrease.

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