## Doctoral Dissertations

#### Title

Heat transfer in microchannels

Fall 1996

Dissertation

#### Degree Name

Doctor of Engineering (DEng)

#### Department

Micro and Nanoscale Systems

Randall Barron

#### Abstract

The objective of this research was to develop an analytical solution to the heat transfer problem in microchannels with slip-flow--a heat transfer problem for gases at low pressures or in extremely small geometries, and to verify this solution experimentally. In this investigation, an analytical expression for the velocity distribution with slip-flow was obtained which involved the Knudsen (Kn) number in an infinite series form. The result showed that the velocity always increased as the Knudsen number was increased. The Knudsen number for extremely small channels may become large enough to affect significantly the velocity distribution and consequently affect the heat transfer properties. A mathematical model of temperature distribution was established by combining the energy and momentum equations. A series solution was obtained. Also, expressions for the local and overall Nusselt numbers were derived in terms of the Knudsen number and Graetz number.

A new technique for evaluation of eigenvalues for the solution of the heat transfer problem in microchannels was developed. This method was based on the construction of a matrix. The computational results showed that the method was effective. The local values and average Nusselt number were found for Kn from 0.005 to 0.3 with aspect ratio $a=1,\ 2/3,\ 1/2,\ 1/4$ and 1/8. Experiments for helium through a microchannel with dimensions of 117 $\mu$m x 24 $\mu$m x 63.5 mm and a microtube with inside diameter of 52 $\mu$m were conducted.

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