Análise da magnetohidrodinâmica com transferência de calor em canais de placas paralelas via transformação integral

Abstract

The main goal of the present work is related to the dynamics of the steady state, incompressible, laminar flow with heat transfer, of an electrically conducting and Newtonian fluid inside a flat parallel-plate channel under the action of an external and uniform magnetic field. For solution of the governing equations, written in the parabolic boundary layer and stream-function formulation, it was employed the hybrid, numericalanalytical, approach known as Generalized Integral Transform Technique (GITT). The flow is sustained by a pressure gradient and the magnetic field is applied in the direction normal to the flow and is assumed that normal magnetic field is kept uniform, remaining larger than any other fields generated in other directions. In order to evaluate the influence of the applied magnetic field on both entrance regions, thermal and hydrodynamic, for this forced convection problem, as well as for validating purposes of the adopted solution methodology, two kinds of channel entry conditions for the velocity field were used: an uniform and an non-MHD parabolic profile. On the other hand, for the thermal problem only an uniform temperature profile at the channel inlet was employed as boundary condition. Along the channel wall, plates are maintained at constant temperature, either equal to or different from each other. Results for the velocity and temperature fields as well as for the main related potentials are produced and compared, for validation purposes, to results reported on literature as function of the main dimensionless governing parameters as Reynolds and Hartman numbers, for typical situations. Finally, in order to illustrate the consistency of the integral transform method, convergence analyses are also effectuated and presented