The coupled phenomena of radiative–magnetohyrodynamic (MHD) natural convection in a horizontal cylindrical annulus are numerically investigated. The buoyant flow is driven by the temperature difference between the inner and outer cylinder walls, while a circumferential magnetic field induced by a constant electric current is imposed. The hybrid approach of finite volume and discrete ordinates methods (FV-DOM) is developed to solve the nonlinear integro-differential governing equations in polar coordinate system, and accordingly, the influences of Hartmann number, radiation–convection parameter, and optical properties of fluid and wall on thermal and hydrodynamic behaviors of the “downward flow,” originally occurring without consideration of radiation and magnetic field, are mainly discussed. The results indicate that both the circulating flow and heat transfer are weakened by the magnetic field, but its suppression effect on the latter is rather small. Under the influence of magnetic field, the “downward flow” pattern has not been obtained from zero initial condition even for the case of weak radiation of NR = 0.1. Besides, the variation of radiative heat transfer rate with angular positions diminishes for the fluid with strong scattering or weak absorption.

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