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Home Archive Thermal Letter Beauftragte Zukünftige Meetings Assembly for International Heat Transfer Conferences
International Heat Transfer Conference 3
1966, 7-12 August, Chicago, USA

VARIATIONAL ANALYSES OF FORCED HEAT CONVECTION IN A DUCT OF ARBITRARY CROSS SECTION

Get access DOI: 10.1615/IHTC3.1580
pages 56-63

Abstrakt

A variational principle for the Graetz problem with the inclusion of viscous dissipation and heat generation is presented for prescribed wall temperature and prescribed wall temperature gradient. Two variational formulations are developed, completely equivalent to the differential formulation with appropriate boundary conditions. As illustrated, the variational procedure is applied to three problems; a circular tube with uniform velocity, a circular tube with velocity of parabolic profile, and an elliptical tube. In the latter two examples the fluid is taken as viscous. In the first example the exact solution is derived, while in the other two examples only approximate solutions are found. The approximate result for the circular tube with viscous flow agrees extremely well with the known solution of the problem.
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