Heat transfer for laminar slip flow in a microchannel of arbitrary cross section with complex thermal boundary conditions

Laminar forced convective heat transfer for a gas flowing through a microchannel of arbitrary cross section with the axially-constant heat flux and circumferentially-varied wall temperature boundary condition in the slip-flow and temperature-jump regime is studied theoretically. The dimensionless temperature profile and the average Nusselt numbers are obtained by solving the fluid flow and energy equations for hydrodynamically and thermally fully developed incompressible slip flow by means of a computation-oriented method of the orthonormal function analysis. The work is then focused on studying the heat transfer characteristics of rectangular and triangular microchannels, which are more frequently encountered in real applications. The effects of Knudsen number, aspect ratio, and thermal boundary conditions on the heat transfer characteristics of these two types of microchannels are examined. The results show that the orthonormal function method is applicable to the fluid flow and heat transfer problems with the slip-velocity and temperature-jump boundary conditions for unsymmetrically heated microchannels with an arbitrary cross section. It is also shown that the increased thermal resistance caused by the temperature jump at the channel walls predominates in the overall heat transfer behavior in microchannels within a definite extension of Knudsen number, leading to a decrease in the heat transfer coefficient. Thus, the average Nusselt numbers in the slip flow are generally smaller than that in the no-slip-flow.