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.

In this paper, we provide an analytical solution of the Navier–Stokes equations subject to second-order slip boundary conditions for gas flow in a long open-ended parallel-plate microchannel with variable working temperature. Comparisons with available experimental data show the limits of various slip laws in the experimental setups. It is found that the Maxwell (first-order) slip law can be valid for average Knudsen numbers up to 0.255 and that the Maxwell–Burnett slip law should be preferred and can be valid for values up to 1.60. The influences of working temperature on the appearance of the Knudsen paradox and the change in the centerline pressure curvature for different values of the pressure-drop parameter are further predicted. Results reveal that the value of the Knudsen number where the Knudsen paradox appears is always greater than the value where the pressure curvature changes. When the working temperature rises, both the critical values increase. However, both the corresponding values of the mass flow rate decrease. For low values of the pressure-drop parameter, this effect seems to be negligible on the critical Knudsen number and constant on the corresponding mass flow rate.