RESUMO

The present paper deals with the characterization of the conjugated two-dimensional steady-state heat transfer problem in two parallel-plate micro-channel heat sinks. The fluid is assumed to be incompressible and with constant properties. Simultaneous hydrodynamic and thermal developing region is taken into consideration here. Axial conduction is also taken into account. An analysis is performed for constant wall temperature at the outer surfaces of the plates. The heat wave generated at these surfaces is crossing through the plates to reach the interface with the fluid in the micro-channel. Due to the fact that channel height (H) is of the same order of dimension of the plate thickness (E) in the micro-channel, the conduction in the plate cannot be assumed negligible. Therefore, the convective heat transfer in a micro-channel is conjugated with the conduction in the solid plates. The two-dimensional Navier-Stokes equations and the energy equation are solved by the finite-control-volume method. Detailed temperature profiles in the fluid and the solid, the fluid bulk temperature and the heat flux distributions on the fluid-solid interface are provided. The effects of the plate thickness and the solid to fluid thermal conductivities ratio (K = k_s/k_f) are studied for a water flow with a Reynolds number Re = 100. The results of different simulations are analyzed, and the axial distributions of the Nusselt number are deduced for each case. The results show that viscous heating of the fluid can significantly influence the heat transfer in the micro-channel heat sink. The thickness plate (E) may have an influence on both thermal developing length and the asymptotic Nusselt number value which corresponds to the fully developed flow. The bulk fluid temperature is shown to vary in a nonlinear form along the flow direction.