Steady magnetohydrodynamic flow in a diverging channel with suction or blowing

An analysis is made of steady two-dimensional divergent flow of an electrically conducting incompressible viscous fluid in a channel formed by two non-parallel walls, the flow being caused by a source of fluid volume at the intersection of the walls. The fluid is permeated by a magnetic field produced by an electric current along the line of intersection of the channel walls. The walls are porous and subjected to either suction (k > 0) or blowing (k < 0) of equal magnitude on both the walls. It is found that when the Reynolds number for the flow is large and the magnetic Reynolds number is very small, boundary layers are formed on the channel walls such that a sufficient condition for the existence of a unique boundary layer solution (without separation) in the case of suction is N > 2, N being the magnetic parameter. When k = 0, boundary layer exists without separation only when N > 2. Further, it is found that the necessary and sufficient condition for the existence of a unique solution for boundary layer flow (without separation) even in the presence of blowing (k < 0) is N > 2. For given value of k, velocity at a point increases with increase in N. It is also shown that when N > 2, blowing makes the boundary layer thinner. A similarity solution for steady temperature distribution in the divergent flow is also presented when the channel walls are held at variable temperature. It is found that for fixed value of wall suction, temperature at a point decreases with increase in N. It is further shown that when N > 2, steady distribution of temperature exists even in the case of blowing at the walls.