Noncontinuum Gas-Phase Heat Transfer From a Heated Microbeam to the Adjacent Substrate

Abstract

Noncontinuum gas-phase heat transfer in two microscale geometries is investigated using two computational methods. The motivation is microscale thermal actuation produced by heating-induced expansion of a near-substrate microbeam in air. The first geometry involves a 1-μm microgap filled with gas and bounded by parallel solid slabs. The second geometry involves a heated I-shaped microbeam 2 μm from the adjacent substrate, with gas in between. Two computational methods are applied. The Navier-Stokes slip-jump (NSSJ) method uses continuum heat transfer in the gas, with temperature jumps at boundaries to treat noncontinuum effects. The Direct Simulation Monte Carlo (DSMC) method uses computational molecules to simulate noncontinuum gas behavior accurately. For the microgap, the heat-flux values from both methods are in good agreement for all pressures and accommodation coefficients. For the microbeam, there is comparably good agreement except for cases with low pressures and near-unity accommodation coefficients. The causes of this discrepancy are discussed.

Modeling microscale heat transfer using Calore.

“…At atmospheric conditions, the mean free path , the distance that molecules travel on average between pairwise collisions, is extremely small. For example, the mean free path of nitrogen at STP is 0.0583 µm (Gallis et al, 2005). When the mean free path is much smaller than a representative geometric length scale, noncontinuum effects on heat transfer in the gas are small and can be neglected.…”

“…For a given composition, the mean free path increases at least linearly with temperature and is inversely proportional to the pressure. The temperature dependence is of some importance since temperature differences in microsystems can vary by up to a factor of three (Wong and Graham, 2003;Gallis et al, 2005), but the pressure dependence is particularly significant since microsystems can be packaged at pressures that are one to several orders of magnitude smaller than atmospheric pressure.…”

“…Here, the heat transfer coefficient can in principle be a function of the temperatures and other properties of the two materials, of interface-specific quantities such as accommodation coefficients (Karniadakis and Beskok, 2002), and of position and time. This model belongs to the general class of models known as Navier-Stokes Slip-Jump (NSSJ) models (Gallis et al 2005).…”

“…If desired, another functional form such as the well-known Sutherland formula can be implemented (Karniadakis and Beskok, 2002). The accuracy of using the continuum thermal conductivity has been demonstrated under two types of conditions known to produce noncontinuum behavior in a gas: large mean free paths (Gallis et al, 2005) and large heat fluxes (Gallis et al, 2004). Both of these situations are illustrated in subsequent sections.…”

“…Although it nowhere appears in any of the relations above, the mean free path is often a convenient quantity to calculate. Two forms are particularly convenient (Gallis et al, 2005):…”