Conjugate heat transfer and entropy generation optimization of MHD flow in a microchannel
G. Ibánez [1], S. Cuevas [2]

Universidad Politecnica de Chiapas, Eduardo J. Selvas S/N. Col. Magisterial. Tuxla Gutierrez, Chiapas 29010, Mexico, [2] Centro de Investigatcion en Energia, UNAM, A.P. 34, Temixco, Morelos 62580, Mexico

Abstract: Entropy generation due to steady-state conjugate heat transfer of a magnetohydrodynamic flow in a microchannel between two parallel electrically conducting walls of finite thickness is investigated. The heat transfer equations in the solid walls and in the fluid are solved simultaneously using thermal boundary conditions of the third kind at the outer surfaces of the walls and continuity of temperature and heat flux across the fluid-wall interfaces. We assume that a nonzero constant, longitudinal pressure gradient is applied in the x direction of the microchannel. The analytic solutions for the velocity, temperature and electric current density fields of the system are used to calculate the global entropy generation rate explicitly. In dimensionless terms, this function depends on the convective heat transfer coefficients (Biot numbers) of each surface, Bi, Peclet number, Pe, constant axial temperature gradient, dθ/dx, thermal conductivity ratio wall to fluid, γ, dimensionless wall thickness ratio, δ, Hartmann number, M, dimensionless wall conductance ratio, c, and dimensionless ambient temperature, θa. We have taken into account irreversibilities caused by viscous dissipation, heat flow and electric conduction in the fluid and due to heat flow and electric conduction in the walls. It is found that there is an optimum Biot number for both the lower and upper surfaces where the global entropy generation rate displays a minimum for specific operation conditions of the system. Also, we observe that the rate of global entropy reaches minimum values for specific values of dθ/dx, M and c, respectively, when the other parameters are fixed. Moreover, the effects of the externally applied magnetic field on the heat transfer within the MHD microchannel are studied. It is found that there is a magnetic field strength that minimizes the heat transfer.