The general mathematical problem of MHD thermal entrance regions is formulated for a parallel plate channel by including Joule heating, viscous dissipation, and the effect of axial conduction. The associated eigenvalue problem is solved by the B. G. Galerkin method and the results are presented for constant wall temperature and constant wall heat flux conditions. It is shown that the particular method has distinct computational advantages over the classical form of solutions. The constant wall temperature case is investigated by employing the solutions of the eigenvalue problem and it is concluded that the axial conduction has considerable effect on the temperature development for low values of Peclet number.
The Solution of Temperature Development in the Entrance Region of an MHD Channel by the B. G. Galerkin Method
LeCroy, R. C., and Eraslan, A. H. (May 1, 1969). "The Solution of Temperature Development in the Entrance Region of an MHD Channel by the B. G. Galerkin Method." ASME. J. Heat Transfer. May 1969; 91(2): 212–220. https://doi.org/10.1115/1.3580130
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