Compressible laminar MHD flow inside a flat duct with heat transfer

This study is to present an analysis of two-dimensional, steady-state, laminar, compressible flow of an electrical conducting fluid inside a flat duct with a transversely applied magnetic field. The boundary-layer equations for the compressible MHD flow are solved by a new approach based on Morris and Smith's work on non-MHD flow. The compressible boundarylayer equations including the continuity, momentum, and energy equations are reduced to ordinary differential equations which are solved simultaneously by numerical integration. No restrictions are imposed on the Prandtl number. A very general form of viscosity variation with respect to temperature is used in the development of the general equations. A sample problem with the constant wall temperature, the Mach number of 0.8, and the Prandtl number of 0.01 is solved numerically. Investigations include the growth of the dynamic boundary and thermal boundary layers, the development of the velocity and temperature profiles, and the skin friction and heat transfer. The results show that the skin friction and heat transfer are increased with the increase of magnetic field strength. To obtain an estimate of the validity of the method, it is applied to the solution of incompressible flow problems for which some reliable solutions are available.