Application of discrete symmetry to natural convection in vertical porous microchannels

Abstract This work focuses on the study of natural convection in a flat porous microchannel with asymmetric heating. The novelty of the work lies in the fact that for the first time the method of discrete symmetries was used to analyze the complete system of Navier–Stokes and energy equations in a two-dimensional approximation. Analytical solutions for velocity and temperature profiles have been derived based on symmetry analysis, taking into account boundary conditions such as slip and temperature jump at the channel walls. The effect of Grashof, Knudsen, Darcy, and Prandtl numbers on the flow characteristics in the microchannel and heat transfer coefficients was elucidated. At high Grashof numbers, an ascending flow near the hot wall and a descending flow near the cold wall arise. Increasing the Knudsen number leads to an increase in the velocity, temperature jump at the walls and a decrease in heat transfer coefficients. As the Darcy number increases, velocities amplify in both ascending and descending flows. The temperature jump at the hot wall grows up, while it remains unchanged at the cold wall. In the same time, the heat transfer coefficient at the hot wall decreases.