Heat transfer in micro-channels filled with porous media under local thermal non- equilibrium conditions without and with dissipation

by B. Buonomo1, O. Manca1, G. Lauriat2

1Dipartimento di Ingegneria Industriale e dell'Informazione, Seconda Università degli Studi di Napoli, Via Roma 29, Aversa (CE) 81031, Italy

2 Laboratoire Modélisation et Simulation Multi Echelle, UMR 8208 CNRS, Université Paris-Est Marne-la-Vallée, Bâtiment Lavoisier, 5 Boulevard Descartes, F-7454 Marne-la-Valee Cedex 2, France

In the last years, research interest was developing on microchannels and microtubes filled with porous medium due to their applications in micro filtration, fractionation, catalysis and microbiology, as underlined in. However, forced convection in porous channels and tubes in rarefied conditions or in porous microchannels and microtubes still needs to be investigated, especially because some phenomenological aspects related to local thermal non-equilibrium in porous microducts received little attention. Therefore, improvement of the analytical solutions according to the geometrical and thermal conditions should be considered. It should be also underlined that these analytical solutions are very relevant to check the accuracy of numerical solutions in the limiting case of fully developed flows.

In this study, fully developed steady state forced convection, in parallel plates micro-channels, filled with a porous medium saturated with rarefied gases at high temperatures, in local thermal non-equilibrium (NTLE) condition, is investigated for the first-order slip flow regime (0≤Kn≤0.1). Both velocity and temperature jumps at the walls are accounted for. An analytic solution is proposed for the Darcy-extended Brinkman flow model with assigned uniform heat flux at micro-channel walls and without and with viscous heat dissipation in the fluid phase. This analytical solution for NTLE includes the shear work done by the slipping effects. A closed-form expression of the Nusselt number is derived. It involves six of the dimensionless parameters.

The effects of the main dimensionless parameters on the Nusselt number, dimensionless temperatures and total entropy generation number are reported in the Results section. The focus is on the effects of the Darcy number, Knudsen number, accommodation coefficients, internal Biot number and thermal conductivity ratio. It is shown that the Nusselt number as a function of the Biot number increases and reaches constant asymptotic values. The asymptotic values depend on different dimensionless parameters such as the Knudsen number, velocity and thermal accommodation coefficients, Darcy number and effective conductivity ratio. It is also observed that Nu presents different trends with respect to the tangential momentum accommodation coefficient for an assigned thermal accommodation coefficient. In fact, thermal accommodation coefficient or Kn small values determine the increase in Nu value when increasing the velocity accommodation value. In any case, Nu is shown to be a decreasing function of thermal accommodation coefficient. The entropy generation analysis shows that minimum entropy generation values are attained with respect to the Da-1/2 values for assigned Biot number, accommodation coefficients, effective conductivity ratio and Brinkman number.

In conclusion, a new analytical solution of an improved heat transfer model for forced convection in parallel-plate channels is derived. This solution overlaps with recently published analytical solutions when the Knudsen or Biot numbers reach asymptotic values. The viscous dissipation effects on the Nusselt number are discussed in detail according to the values of the main important dimensionless parameters. < back >