Convective Heat Transfer in Micro and Nano Channels: Nusselt Number Beyond Slip Flow

Abstract We present calculations of the constant-wall-heat-flux Nusselt number for fully developed transition flow in two-dimensional microchannels. The Nusselt number cannot be obtained by a continuum analysis since the continuum description breaks down in the transition regime. We have used a molecular simulation technique known as the direct simulation Monte Carlo (DSMC). DSMC is a stochastic simulation technique previously shown to capture the hydrodynamic behavior of hard sphere gases. A wide range of Knudsen numbers is investigated: a channel height range of approximately 50 is analyzed starting from the micrometer scale that corresponds to slip flow. The channels have a length/height ratio of 20 to ensure fully developed flow, and care was taken to ensure that the Brinkman number is always small. The Nusselt number is found to decrease with increasing rarefaction (Knudsen number). The effects of thermal creep are discussed.