Heat transfer and vortex shedding behind a square cylinder in a laminar channel flow under a magnetic field is conducted numerically. Computations were carried out for different Reynolds and Hartmann numbers ranging from 80 to 250 and from 0 to 4, respectively at a fixed blockage ratio = h/H = 1/4. The governing equations are solved with a control volume finite element method adapted to the staggered grid. From the investigation of the periodic flow fields, it is found that, through forced convection, both drag and lift coefficients are clearly damped by the magnetic field leading to the stabilization of the square cylinder. It has been found also that the application of a magnetic field to the vortex shedding flow can lead to a transition to symmetric flow. The critical Hartmann number Ha c characterizing this transition can be correlated by a linear relationship with the Reynolds number as: Ha c =0.0239. . A discussion about heat transfer under the magnetic field is also presented.
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