Thermodynamic optimization of radial MHD flow between parallel circular disks

Abstract

The radial flow between two parallel circular disks is investigated with the aim to determine the optimum convective heat transfer conditions at the external disk surfaces in order to minimize the intrinsic irreversibilities. A general situation is considered where the fluid is electrically conducting and may be under the influence of a transversal magnetic field. The velocity and electric current density fields are obtained analytically and used to solve the heat transfer equation under boundary conditions of the third kind. The analysis is in the absence of fluid inertia, under creeping flow conditions (Reynolds number ≪ 1). A perturbation approach in order to include the convective heat transfer effects in the flow is used. The Péclet number is assumed to be small. The analytic expressions for the velocity, electric current density and temperature fields are used to calculate explicitly the global entropy generation rate. When the convective heat transfer coefficients for each wall are different, this function displays a minimum for specific heat exchange conditions. The results are shown for both the hydrodynamic and the magnetohydrodynamic cases. It is also found that the mean Nusselt number at the upper wall shows a maximum value for a given value of the Hartman number, when the dimensionless heat transfer coefficients for each disk and the Péclet number are fixed. This mean Nusselt number for maximum heat transfer is near its value for minimum entropy generation conditions.