On the integral transform solution of low-magnetic MHD flow and heat transfer in the entrance region of a channel

The main goal of the present study is to show the procedure, application and main features of the hybrid numerical/analytical approach known as GITT (Generalized Integral Transform Technique) by solving a magnetohydrodynamic channel flow with heat transfer, sustained by a pressure gradient and subjected to a uniformly applied and undisturbed transversal magnetic field. Although not the primary objective, application of this novel method provides a critical review of previously published numerical results on developing channel flows with uniform or non-uniform velocity and temperature profiles at the channel inlet. This is bounded by non-conducting horizontal walls at constant temperature and lateral walls that are electrically perfect conductors (open or short-circuited). Transport properties, namely, fluid viscosity, thermal and electrical conductivities, are taken as either constant or thermally-dependent, exponential-type, functions. Due to the hybrid numerical-analytical nature of the integral transform approach, benchmark results for velocity and temperature fields and the main correlated potentials are produced as a function of the primary dimensionless governing parameters, such as Hartmann, Prandtl and Eckert numbers, as well as the electrical parameter, for typical situations.