A liquid metal forced-convection fully-developed flow inside a square duct whose surfaces are electrically insulated and subjected to a constant temperature in a transverse magnetic field, is solved numerically using the spectral method. The axial momentum, induction, and non-linear energy equations are solved by expanding the axial velocity, induced magnetic field, and temperature in double Chebyshev series and are allocated at Gauss points. The resulting system of equations are solved numerically by Gauss elimination for the expansion coefficients. The velocity and the magnetic field coefficients are directly solved for, while the temperature coefficients are solved for iteratively. As expected, the velocity profile is flattened in the direction of the magnetic field, but it is more round in the direction normal to it. Also the friction factor and Nusselt number increase with the magnetic field due to the flatness of velocity profile. Some results are compared with previous work done for circular tube. It is noticed that the effect of magnetic field on square duct flow is slightly lower from that one for circular pipe flow.

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