Graetz problem for slip flow in a channel in the presence of axial conduction, viscous dissipation and flow work

This thesis investigates developing heat transfer in laminar, hydrodynamically fully developed slip flow in a channel with a constant wall temperature. Slip flow is a good approximation when the Knudsen number, the ratio of the molecular mean free path to the channel width, is less than approximately 0.1. Our analysis includes the effects of viscous dissipation, flow work, and axial heat conduction. A series solution is used to solve for the temperature distribution and provide predictions for the Nusselt number. It is found that inclusion of axial conduction increases both the non-dimensional temperature and the Nusselt number at a given location. The effect of slip flow is to increase the non-dimensional temperature and decrease the Nusselt number at a given location. The effects of viscous dissipation and flow work are more complex, and can either increase or decrease the non-dimensional temperature and the Nusselt number at various points along the length of the channel. It is found that a non-zero Eckert number will result in an asymptotic N usselt number (based on energy transfer to the wall) of zero. The joint effects of slip flow, axial heat conduction, and viscous dissipation and flow work, are also illustrated through exploration of the relevant parameter space.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2002

Author dc:creator

• Baker, Lowell L. (Lowell Lane), 1980-

Advisor dc:contributor.advisor

• Nicolas Hadjiconstantinou.

• Mechanical Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/29586

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/29586