Effect of MHD mixed convection on a heat-generating element cooling inside a ventilated square cavity filled with Fe₃O₄–water ferrofluid

Abstract

This work groups a set of numerical results on the investigation of the external magnetic field effect on mixed convection in a ventilated square cavity with a heat source located in the middle of its bottom wall and filled with a ferrofluid. The behavior of the magnetic field was treated according to three different scenarios illustrated by magnetic Reynolds number value (R_m = 0.1, 0.001, and 0.00001). The dimensionless governing equations were solved numerically by the finite volume method and the SIMPLE algorithm was chosen for the treatment of coupling between the momentum and continuity equations using the QUICK scheme of Leonard. The numerical results for a large range of Hartmann numbers and volume fractions and for horizontal and vertical magnetic field directions are discussed in terms of streamlines, isotherms, Nusselt numbers, and maximal temperature of fluid and heat source. The results highlighted different scenarios showing the heat exchange rate enhancement and heat source cooling as a function of the magnetic field strength and direction and as a function of the internal fluid constitution and behavior. The diversity of these results as a function of the magnetic Reynolds number also underlines the limitation of theory based on low-R_m model in the treatment of MHD flows.

Keywords:

• Ferrofluid
• heat source
• magnetic diffusion
• MHD
• mixed convection