Temperature distribution of MHD channel flows with finite width

The joule heating and the inner heat generation of viscosity dissipation of MHD channel flow were calculated, and the temperature distribution within rectangular cross section was obtained. The calculation was performed for the channel with conductive walls parallel to an external magnetic field and insulated walls perpendicular to the field. The calculus of variations was applied to solve a partial differential equation. At first, an equation of motion and an energy equation were presented for the steady flow of non-compressive conductive fluid. The temperature distribution of MHD channel flow was obtained for three models, namely (a) all the walls of the channel are electrically insulated, and the temperature of walls is isothermal, (b) walls parallel to a magnetic field are conductive, and those perpendicular to it are insulated, and (c) the insulated walls in the case (b) are also insulated thermally. As the results of calculation, it was found that the calculas of variations was useful for the present purpose, the temperature at the center of a channel rose with the increase of the ratio of height and width, and the isothermal line diagram in the channel of the model (c) showed interesting patterns for the rate of voltage utilization. (Kato, T.)