Transient natural convection in a vertical microchannel, heated at uniform heat flux

Miniaturization of devices has received a rapid expansion in the recent years and a great volume of research activities have been dedicated to micro-flow due to its new applications of micro-fluidic systems and components. In the present paper, an investigation of transient natural convection in parallel-plate vertical microchannels is carried out numerically. The vertical microchannel is considered asymmetrically or symmetrically heated at uniform heat flux. The first-order model for slip velocity and jump temperature is assumed in micro-scale conditions. The analysis is performed under laminar boundary layer assumption for different values of Knudsen number, Rayleigh number and the ratio of wall heat flux in order to evaluate their effects on wall temperatures, mass flow rate, velocity profiles and Nusselt number. Wall temperature overshoots are detected for the different conditions. These values increase with the increasing Knudsen number, Kn, at high Rayleigh number, Ra, whereas for lower Ra the lowest wall temperature are obtained at Kn=0.05. Mass flow rate increases with increasing Kn whereas Nusselt number decreases with increasing Kn. A composite correlation to evaluate the average Nusselt number in terms of Rayleigh and Knudsen numbers is proposed in the ranges 0 ≤ Kn ≤0.1 and 10^-3< Ra <10^8.