Fluid flow in microchannels has some characteristics, which one of them is rarefaction effect related with gas flow. In the present work, hydrodynamically and thermally fully developed laminar forced convection heat transfer of a rarefied gas flow in two microgeometries is studied, namely, microannulus and parallel plate microchannel. The rarefaction effects are taken into consideration using first-order slip velocity and temperature jump boundary conditions. Viscous heating is also included for either the wall heating or the wall cooling case. Closed form expressions are obtained for dimensionless temperature distribution and Nusselt number. The results demonstrate that for both geometries, as Brinkman number increases, the Nusselt number decreases. However, the effect of viscous heating on the Nusselt number at greater values of Knudsen number becomes insignificant. In the absence of viscous heating, increasing values of Knudsen number lead to smaller values of Nusselt number. Furthermore, it is observed that viscous heating causes singularities in Nusselt number values. Also, asymmetry causes singularities in Nusselt numbers of both microannulus walls and the parallel plate wall having lower heat flux, even in the absence of viscous heating. For parallel plate microchannel, in the absence of viscous heating, Nusselt number of the wall having larger heat flux is an increasing function of the wall heat fluxes ratio.

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# Viscous Dissipation and Rarefaction Effects on Laminar Forced Convection in Microchannels

Arman Sadeghi

,
Arman Sadeghi

Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering,

Sharif University of Technology

, P.O. Box 11155-9567, Tehran, Iran
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Mohammad Hassan Saidi

Mohammad Hassan Saidi

Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering,

saman@sharif.edu
Sharif University of Technology

, P.O. Box 11155-9567, Tehran, Iran
Search for other works by this author on:

Arman Sadeghi

Sharif University of Technology

, P.O. Box 11155-9567, Tehran, Iran
Mohammad Hassan Saidi

Sharif University of Technology

, P.O. Box 11155-9567, Tehran, Iransaman@sharif.edu

*J. Heat Transfer*. Jul 2010, 132(7): 072401 (12 pages)

**Published Online:**April 22, 2010

Article history

Received:

January 31, 2009

Revised:

January 12, 2010

Online:

April 22, 2010

Published:

April 22, 2010

Citation

Sadeghi, A., and Saidi, M. H. (April 22, 2010). "Viscous Dissipation and Rarefaction Effects on Laminar Forced Convection in Microchannels." ASME. *J. Heat Transfer*. July 2010; 132(7): 072401. https://doi.org/10.1115/1.4001100

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