Mixed convection in a vertical circular microchannel

The paper focuses on a study of mixed convection in a vertically oriented circular microchannel with slip boundary conditions. Novelty of the work consists in analytical and numerical solutions of the problem using the Lattice Boltzmann method (LBM). The novel analytical solution enabled obtaining relations for velocity and temperature profiles and Nusselt numbers depending on the Knudsen, Rayleigh and Prandtl numbers. Knudsen number effects dominate in the vicinity of the channel wall, whereas close to the channel axis the Rayleigh number effects prevail. For high Rayleigh numbers, velocity profiles transform themselves to M-shapes with a minimum point at the channel axis, and temperature profiles flatten out and tend to the wall temperature. The magnitude of the temperature jump on the channel wall is a function of the Prandtl number and diminishes for high Prandtl numbers. For almost all computed cases, larger Knudsen numbers yield diminished heat transfer with an exception for the case of Pr = 10 and Ra = 200. Via comparing the quantitative results for circular and flat channels, it was demonstrated that the shape of channel cross-section makes significant influence on the average Nusselt numbers, so that the results for one channel cannot be extrapolated over the other one. It was also proved that mixed convection in circular vertical microchannels can be successfully modelled using the LBM methodology, whose deviation from the analytical solution is less than 1%.