Mixed convection in a vertical flat microchannel

The paper presents results of an investigation into mixed convection in a vertically oriented microchannel with slip boundary conditions. Solutions of the problem were obtained analytically and using a numerical approach based on the Lattice Boltzmann method (LBM). The solution yields relations, which enable estimating velocity and temperature profiles and the Nusselt number as functions of the Knudsen, Rayleigh and Prandtl numbers. It was shown that Knudsen number effects are prevailing in the vicinity of the wall, whereas near the centerline of the channel effects of the Rayleigh number are stronger. If the Rayleigh numbers are high, velocity profiles demonstrate M-shapes with a point of minimum at the channel centerline, whereas temperature profiles flatten so that the fluid temperature in the channel cross-section tends to the wall temperature. The temperature jump magnitude on the wall is dependent on the Prandtl number value and decreases with the increasing Prandtl numbers. For almost all combinations of the parameters considered in this paper, higher Knudsen numbers entail heat transfer deterioration except for the case of Pr = 10 and Ra = 100. Increasing the Knudsen number diminishes hydraulic resistance for low Rayleigh numbers, but for high values of the Rayleigh numbers the trend is reversed. It was shown that mixed convection in microchannels can be successfully simulated using the LBM methodology, whose deviation from the analytical solution and is less than 1%.