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Technical Brief

Analytical Solution of the Thermal Entrance Heat Transfer Problem for Viscous Flow in Annulus

[+] Author and Article Information
E. K. Vachagina, A. I. Kadyirov

Kazan Scientific Center of the Russian
Academy of Sciences,
Lobachevsky Street,
2/31, P.O. Box 190,
Kazan 420111, Russia

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 10, 2015; final manuscript received March 15, 2016; published online April 19, 2016. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 138(7), 074504 (Apr 19, 2016) (4 pages) Paper No: HT-15-1108; doi: 10.1115/1.4033093 History: Received February 10, 2015; Revised March 15, 2016

The Graetz–Nusselt problem with Brinkman extension is considered for steady-state laminar Newtonian flow in annuli. To solve the problem, a separation of variables method is used. In the limiting cases, the eigenvalues are in full agreement with the eigenvalues corresponding to flat channel and circular pipe. Useful formulas are represented to calculate the length of the thermal entrance region and Nusselt numbers in annuli.

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Grahic Jump Location
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Geometry and coordinate system of the problem

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