A linearized analysis is presented for the magnetohydrodynamic entrance flow with combined forced and free convection in a vertical, constant wall temperature parallel-plate channel. Numerical results are obtained for slug velocity profile at the entrance and for various Hartmann and Grashof Numbers. The results agree well with the finite difference numerical solutions obtained elsewhere. They demonstrate that the velocity development and pressure gradient in the channel entrance region are greatly influenced by the Hartmann Number and the Grashof Number. Increasing Hartmann Number decreases velocity entrance length while increasing Grasho f Number increases it. Thermal development is also found to be dependent on the above mentioned parameters, but to a relatively minor extent.
Nomenclature
A m constant defined by equation ( 23) B 0 applied magnetic field C, constant defined by equation (13) E o constant electric field e nondimensional electric field parameter, Eo/UmB o Gr Grashof Number, flgL3 ( Tw -To)/V 2 L half-width of the channel M Hartmann Number, BoL(a/lz) Γ· Nu Nusselt Number, (g0/@)r= 1/(0w -0m) P pressure Pr Prandtl Number, v/ot p nondimensional pressure parameter, (P -Po + PogX)/Po U2 Re Reynolds Number, UmL/v