Slip flow effect on laminar convection inside micro-tubes with permeable walls

In this study, a two-dimensional steady state simultaneously developing laminar flow along a permeable micro-tube is investigated numerically under slip flow conditions. The constant wall temperature boundary condition and the case of uniform suction at the entire tube wall were considered. The set of governing equations subjected to the appropriate boundary conditions for the hydrodynamic and thermal fields was solved by using the Finite Volume Method. The numerical model was validated using the available data for developing and fully developed continuum flow. The results show that increasing the Knudsen number reduces the axial velocity of the tube center and increases the streamwise fluid velocity at the wall, inducing a flattening of the velocity profiles. This leads to a reduced friction coefficient compared to the continuum case. Furthermore, the study reveals a significant effect on the rarefaction on the hydrodynamic and thermal fields especially for high values of the suction Reynolds number, Re-w. In fact, for values of Re-w close to zero, the impact on the apparent friction coefficient and Nusselt number was found to be negligible and the behavior of both parameters along the duct remains unchanged compared with the case of Re-w = 0 (impermeable tube). The variation of the fully developed Nusselt number with Prandtl number, Knudsen number, and suction Reynolds number is presented and analyzed.