ABSTRACT
The study of fluid flow and heat transfer at the microscale plays an important role in the development of micro-electromechanical systems (MEMS) [1,2] and their far reaching applications [3-6]. The challenge of reliable experimental measurements in microscale devices makes it difficult to discern how the various physical parameters affect the flow and thermal transport processes. Therefore, much insight can be gained from numerical simulations in the design and improvement of such devices. The reduction of channel dimensions in MEMS, however, can give rise to noncontinuum effects that cannot be appropriately modeled using the Navier-Stokes-Fourier (NSF) equations for fluid flow and heat transfer. Liquid flows in microchannels, for example, experience an increase in surface-to-volume ratio and interfacial phenomena becomes markedly important. In the presence of strong molecular interactions with the wall surface and an applied electric field, it can give rise to electrokinetic or electro-osmotic forces [7] sufficient to drive the flow. For microscale gas flows (referred to as microflows from this point onward), the mean free path (MFP) λ, which is the average distance a molecule travels between collisions, provides a good measure of the noncontinuum effects. In liquids, λ is close in size to the molecular diameter, whereas in gases λ can be comparable to the characteristic length of the flow geometry (H). Microflows, which are the focus of this chapter, are thus better categorized using the Knudsen number (Kn = λ/H). For low values (Kn ≤ 0.01) the gas is considered to follow the continuum hypothesis and the NSF equations are applicable throughout the flow domain [2]. When Kn ≥ 0(10), the gas enters the free molecular regime where the NSF equations are inapplicable, requiring the use of one of the other appropriate techniques such as the molecular dynamics (MD) simulation. Between those two Kn limits, the flow can be further divided into two regimes: (1) slip flow (0.01 < Kn < 0.1) and (2) transition flow (0.1 < Kn < 10). In the slip flow regime, the NSF equations are still applicable in the bulk flow region with the use of appropriate velocity slip and temperature jump boundary conditions. For the transition flow regime, which lies between the slip and free molecular regimes, the kinetic boundary (or Knudsen layer) between
15.1 Introduction .......................................................................................................................... 391 15.2 Thermal Lattice Boltzmann Method (TLBM) ..................................................................... 392 15.3 Application of TLBM to Thermal Microflows in the Continuum Limit (Kn ≤ 0.01) .......... 393 15.4 TLBM in the Slip Flow Regime (0.01 < Kn < 0.1) ............................................................... 395 15.5 TLBM in the Transition Flow Regime (0.1 < Kn < 10) ........................................................ 399 15.6 Conclusion ............................................................................................................................403 References ......................................................................................................................................404
