I have been reviewing the experimental literature on flows through (so called) microchannels. Flows in such channels exhibit heat and mass transfer rates (i.e. Sherwood and Nusselt numbers) that are much higher than those computed using laminar flow equations even at Reynolds as small as 50 to 400. In fact, the Sherwood number and Nusselt number show a Reynolds number dependence in this regime (Nusselt numbers and Sherwood numbers for laminar fully developed channels flows with Dirchlet-type wall BCs for scalars are independent of Re). Does any one have an explanation. I would also like to know of any simulations of microchannel flows.

In one of the experimental papers, it has been suggested that the transition (from laminar state) is not just a function of Re but also a function of so called Brinkman number (defined as mu*u*u/(k*DT), where mu = viscosity, u = bulk velocity, k = thermal conductivity, DT = temperature difference between the flow and the walls). This is appararently true for both gases and liquids. Thus, one can rule out equation of state (i.e., density change due to temperature) as a factor contributing to the dependence of transition on the Brinkman number. If density is held constant, the only way the temperature can affect the momentum equation is through its effect on viscosity. The temperature dependence of viscosity also can not explain the transition depedence on Brinkman number since the viscosity increases with temperature in gases while it reduces with temperature in liquids. So, how (or why) does transition depend on the Brinkman number.

The only explanation I can think of (which is yet to be confirmed) is that the flow transition depends on the Reynolds number only. It is likely that the temperature (or the scalar) fields can exhibit some sort of turbulent-like behavior (which depends on Re and Br) even if the velocity field were laminar. Does any one know if this is possible. Any and all explanations are welcome.

(1). How was the heat transfer rate measured? (2). Was the micro-channel 2-D or 3-D? (3). Was the micro-channel surface smooth? (relative to the channel width)(4). If you are getting fully-developed velocity profile (2-D or 3-D?), then the flow is laminar. (5). I am just guessing that the measurement is probably not very accurate.

I am sure the measurements are accurate because a number of papers report this. The wall roughness could be a factor but none of papers talk about the roughness effects. Since similar heat/mass transfer correlations have been reported in channels made of different materials, I suppose the roughness is not a factor. All experimental channels are 3D.

I have not seen velocity profiles in any of the papers. The problem with microchannels is that the hydraulic diameter being very small (< 1mm usually), it may be difficult to measure the profiles.

My question was simple : How can you explain the dependence of transition on the Brinkman number when no terms/quantity in the momentum equation (in the constant density case) have a temperature dependence other than the viscosity. With increasing temperature, viscosity increases in gases and decreases in liquids. But they do not show the opposite behavior. So it has to be something else.

If the increases heat/mass transfer (and their dependence on Re) is not due to transition (i.e., the flow is laminar), then what is the actual reason.

(1). One thing at a time, please. (2).We know that the wall roughness can affect the skin friction coefficient.(please, it is not my idea.) (3). So, the logical step is: is the geometry used in the cfd simulation identical to the experimental geometry? (4). Was the actual geometry "measured"? or it was assumed? Even under the electron microscope, the lines of semiconductor are not smooth. (4). If the channel is 3-D, then how was this 1mm size channel created? And if the roughness is 0.05mm, do you think that the flow will be relatively smooth? (5). Well, I guess, you can easily run a few cfd cases with simulated roughness to see if the results will be different from the perfectly smooth result. For example, take a long channel with some wall roughness elements on the wall, and run a few cases at Re=10,50,100,200. And compare the results with the one with smooth wall. (6). If you have been in the turbine cooling business, you know that internal roughness elements in the blade cooling channel are designed to improve the heat transfer coefficient. (7). Anyway, it is just something one should study first. (I am not here to invent the new physics. It is for someone else with creative thinking.)

Sounds like this needs some detective work. Can you cite (or even better, provide a link to) one of these papers; then we can all see the full story. I doubt if any simulations will show this effect since it seems to arise either from an incomplete/incorrect description of the boundary conditions or physical properties, or some new physical phenomena.

These are the most useful papers I could find on the subject.

"Developing convective heat transfer in deep rectangular micro-channels", Harms, T., Kazmierczak, M. J. and Gerner, F. M., International Journal of Heat and Fluid Flow, 20 (149-157), 1999.

"The role of Brinkman number in analyzing flow transitions in microchannels", International Journal of Heat and Mass Transfer, 42 (1813-1833), 1999.

"Experimental verification of the role of Brinkman number in microchannels using local parameters", Tso, C. P. and Mahulikar, S. P., International Journal of Heat and Mass Transfer, 43 (1837-1849), 2000.

"Heat transfer studies of a porous heat sink characterized by straight circular ducts", Zhang, H. Y. and Huang, X. Y., International Journal of Heat and Mass Transfer, 44 (1593-1603), 2001.

"Mass transfer in monolith catalysts - CO oxidation experiments and simulations", Homlgren, A and Andersson, B., Chemical Engineering Science, 53 (2285-2298), 1998.

"Measurement and correlation of volumetric heat transfer coefficients of cellular ceramics", Fu, X., Viskanta, R. and Gore, J. P., Experimental Thermal and Fluid Science, 17 (285-293), 1998.

"Measurements of heat transfer in microchannel heat sinks", International Communications in Heat and Mass Transfer, 27 (495-506), 2000.

Some claim that the transition depends on the Brinkman number (which depends on the difference in the wall and gas temperatures) while others say it is affected by wall roughness.

In the most general sense, the Nusselt (Nu) and Sherwood numbers (Sh) seem to depend on Reynolds number (Br), Brinkman number (Br) and wall roughness. For larger channels the dependence on the latter two seems to be weak and hence the coefficients depend on Re only.

If any one knows of correlations for Nu and Sh in terms of Re, Br and wall roughness (relative to channel hydraulic diameter), that cover the whole range (from macro to micro-channels and those with and without heat transfer), I would like to know them. I would be happy if you have something even close to what I need.