HEAT TRANSFER AT NATURAL CONVECTION IN A FLAT POROUS MICRO-CHANNEL WITH UNSYMMETRICAL HEATING
Abstract
This work is dedicated to studying natural convection in a flat porous microchannel with asymmetric heating. Analytical solutions for velocity and temperature profiles have been obtained based on symmetry analysis, considering boundary conditions such as slip and temperature jump at the channel walls. The study demonstrates the effect of Grashof, Knudsen, Darcy, and Prandtl numbers on the flow characteristics in the microchannel and on the heat transfer coefficients.
At high Grashof numbers, an ascending flow near the hot wall and a descending flow near the cold wall are formed. With an increase in Gr number, the heat transfer coefficient near the hot wall increases, while it decreases near the cold wall. This is attributed to the asymmetry in the change of velocity profiles of ascending and descending flows.
The study also shows the effect of the Knudsen number on flow parameters. As Kn number increases the thermal interaction of the heat carrier with the walls decreases, the temperature jumps at the walls increase, and the heat transfer coefficients decrease.
With an increase in the Darcy number velocities increase, and velocity jumps at the walls rise due to decreased hydraulic resistance. The heat transfer coefficient near the hot wall increases with Da, while the opposite trend is observed at the cold wall – the heat transfer coefficient decreases with increasing Da number. This is linked to the decrease in temperature gradient near the cold wall due to the increase in the nonlinearity of the temperature profile.
As the Pr number increases the temperature jump at the walls decreases, and the temperature profile becomes close to linear. The thermal interaction of the heat carrier with the walls increases, and the heat transfer coefficient also increases. At higher Pr values (Pr = 100) the heat transfer coefficient near the hot wall sharply increases, while near the cold wall it decreases. This is linked to the decrease in temperature gradient near the cold wall. Such deformation of the temperature profile is caused by the growth of hydraulic resistance due to the increase in the medium's viscosity.
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