Developing natural convection with thermal creep in a vertical microchannel

Abstract

Thermal creep occurs in anisothermal gas microflow. It is highly desirable to understand the creep effect on the flow and heat transfer characteristics for developing natural convective microflow. In this study, we investigate the steady developing natural convective flow in an open-ended vertical parallel-plate microchannel with asymmetric wall temperature distributions. The boundary-layer equations subject to the boundary conditions with respect to dynamic pressure at the channel entry as well as higher-order jump temperature and slip velocity with thermal creep along the channel surface are employed. The mathematical model and the numerical code are validated through available macroscale work. Numerical solutions of high-order slip coefficient, slip/jump, velocity, pressure, temperature, flow rate, flow drag and heat transfer rate are presented for air at the standard reference state with complete accommodation. It is found that thermal creep has significant effect on the high-order slip effect and the flow and thermal fields. The creep effect is to increase the flow rate; moreover, valuable reduced flow drag and enhanced heat transfer are obtained.

A boundary layer analysis for entrance region heat transfer in vertical microchannels within the slip flow regime

“…The remaining part of the calculation is same as before, and hence is not repeated here for the sake of brevity. However, an interesting comparison between our semianalytical solutions and the results presented by Chen and Weng [5], with regard to the Nusselt number predictions considering higher order slip/jump conditions, is presented in Fig. 5 to summarize our findings in this regard.…”

“…The first order wall-jump conditions are subsequently augmented to higher order effects by replacing the molecular mean free path with [5] l c k/(l c À bk), where l c is the characteristic length (defined as the hydraulic diameter of the channel) and b is a high order slip coefficient, defined as b ¼ 1 2 l c o 2 uns oy 2 ouns oy j j ; u ns being the corresponding no-slip velocity field. The remaining part of the calculation is same as before, and hence is not repeated here for the sake of brevity.…”

“…Variations in average Nusselt number with non-dimensional channel height for Kn = 0.09: comparison between the present solution and numerical solution[5].…”

“…Haddad et al [4] have reported implicit finite difference simulations of the developing natural convection in an isothermally heated microchannel filled with porous media. Chen and Weng [5], in a subsequent study, have emphasized the importance of thermal creep and high order slip/jump conditions for modeling developing natural convection problems, by employing a marching implicit procedure.…”

Compressible Gas Flow Inside a Two Dimensional Uniform Microchannel

“…Numerically, there were many simulations of compressible flows in a microchannel as well, for example, with the direct simulation Monte Carlo method [9][10][11], the Information Preservation method [12], the direct-solving Boltzmann method [13], the Boltzmann equations [14], and gas-kinetic BGK-Burnett method [15]. Discussions of thermal heating are reported as well [16,17].…”