Analytical Modeling of Fluid Flow and Heat Transfer in Micro/Nano-Channel Heat Sinks

Abstract

Laminar forced convection in two-dimensional rectangular micro and nano-channels under hydrodynamically and thermally fully developed conditions is investigated analytically in the slip flow regime (0.001 < Kn < 0.1). Closed form solutions for fluid friction and Nusselt numbers are obtained by solving the continuum momentum and energy equations with the first-order velocity slip and temperature jump boundary conditions at the channel walls. Isoflux thermal boundary condition is applied on the heat sink base. Results of the present analysis are presented in terms of channel aspect ratio, hydraulic diameter, momentum and thermal accommodation coefficients, Knudsen number, slip velocity, Reynolds number and Prandtl number. It is found that fluid friction decreases and heat transfer increases, compared to no-slip flow conditions, depending on aspect ratios and Knudsen numbers that include effects of the channel size or rarefaction and the fluid/wall interaction.

Transient response of thermocapillary pumping of a droplet in a micro heat engine

“…Past numerical analyses of heat transfer and fluid flow in microchannels showed that thermocouples embedded in the channels influenced the flow regime [9]. Friction was also shown to affect the thermal performance of the microchannels [10,11]. The frictional losses decreased upon heating of the channel at low Reynolds numbers, due to a change of viscosity of the fluid in the channel.…”

“…The frictional losses decreased upon heating of the channel at low Reynolds numbers, due to a change of viscosity of the fluid in the channel. Khan and Yovanovich [11] showed that lower fluid friction increases the heat transfer effectiveness in the channels. Past studies [12][13][14] showed that accurate predictions of the effects of surface roughness on the flow distribution are important for effective control of the droplet motion.…”

Slip-Flow Pressure Drop in Microchannels of General Cross Section

“…Assuming first order slip boundary condition, Morini and his coworkers [12,19] performed numerical studies for determination of pressure drop through microchannels of rectangular, circular, trapezoidal, and double trapezoidal cross-sections and reported their results in a tabular form for a range of crosssection aspect ratio for the slip-flow regime. Using similar boundary conditions Khan and Yovanovich [20] developed a solution for fluid flow and convective heat transfer in rectangular microchannels in slip-flow regime. Duan and Muzychka [21] proposed a model for the pressure drop of slip-flow through non-circular microchannels using the solution of the rectangular duct.…”