Composite relation for laminar free convection in inclined channels with uniform heat flux boundaries

Gur Mittelman; Aiman Alshare; Jane H. Davidson

doi:10.1016/j.ijheatmasstransfer.2009.06.003

Composite relation for laminar free convection in inclined channels with uniform heat flux boundaries

Gur Mittelman, Aiman Alshare, Jane H. Davidson

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

A composite correlation of the average Nusselt number and the channel Rayleigh number for buoyant air flow through inclined channels with uniform heat flux boundaries is presented. The form of the correlation is based on dimensional analysis and is a superposition of the developing and fully developed flow limits. In the limit of fully developed flow, an analytical solution for the Nusselt number is derived. The developing flow limit follows the format of the correlation for a single plate. The composite relationship based on the top wall temperature is over(Nu, -) = fenced(frac(6.25 (1 + r), Ra^″ sin φ{symbol}) + frac(1.64, (Ra^″ sin φ{symbol})^{2 / 5}))^{- 1 / 2}, where r is ratio of the heat flux at the top and bottom wall. At inclination angles of 30 ° ≤ φ{symbol} ≤ 90 °, this correlation predicts the available data base for 10 ≤ Ra^″ ≤ 10⁵ and agrees with the analytical solution for 1 ≤ Ra^″ ≤ 10².

Original language	English (US)
Pages (from-to)	4689-4694
Number of pages	6
Journal	International Journal of Heat and Mass Transfer
Volume	52
Issue number	21-22
DOIs	https://doi.org/10.1016/j.ijheatmasstransfer.2009.06.003
State	Published - Oct 2009

Bibliographical note

Funding Information:
The authors gratefully acknowledge the financial support of the National Renewable Energy Laboratory, the US Department of Energy, and the University of Minnesota through the Initiative for Renewable Energy and the Environment.

Keywords

Free convection
Inclined channels
Uniform heat flux

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10.1016/j.ijheatmasstransfer.2009.06.003

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@article{fe9e7074417e4d8a82c7f0e5f4aa2a64,

title = "Composite relation for laminar free convection in inclined channels with uniform heat flux boundaries",

abstract = "A composite correlation of the average Nusselt number and the channel Rayleigh number for buoyant air flow through inclined channels with uniform heat flux boundaries is presented. The form of the correlation is based on dimensional analysis and is a superposition of the developing and fully developed flow limits. In the limit of fully developed flow, an analytical solution for the Nusselt number is derived. The developing flow limit follows the format of the correlation for a single plate. The composite relationship based on the top wall temperature is over(Nu, -) = fenced(frac(6.25 (1 + r), Ra″ sin φ{symbol}) + frac(1.64, (Ra″ sin φ{symbol})2 / 5))- 1 / 2, where r is ratio of the heat flux at the top and bottom wall. At inclination angles of 30 ° ≤ φ{symbol} ≤ 90 °, this correlation predicts the available data base for 10 ≤ Ra″ ≤ 105 and agrees with the analytical solution for 1 ≤ Ra″ ≤ 102.",

keywords = "Free convection, Inclined channels, Uniform heat flux",

author = "Gur Mittelman and Aiman Alshare and Davidson, {Jane H.}",

note = "Funding Information: The authors gratefully acknowledge the financial support of the National Renewable Energy Laboratory, the US Department of Energy, and the University of Minnesota through the Initiative for Renewable Energy and the Environment.",

year = "2009",

month = oct,

doi = "10.1016/j.ijheatmasstransfer.2009.06.003",

language = "English (US)",

volume = "52",

pages = "4689--4694",

journal = "International Journal of Heat and Mass Transfer",

issn = "0017-9310",

publisher = "Elsevier Limited",

number = "21-22",

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TY - JOUR

T1 - Composite relation for laminar free convection in inclined channels with uniform heat flux boundaries

AU - Mittelman, Gur

AU - Alshare, Aiman

AU - Davidson, Jane H.

N1 - Funding Information: The authors gratefully acknowledge the financial support of the National Renewable Energy Laboratory, the US Department of Energy, and the University of Minnesota through the Initiative for Renewable Energy and the Environment.

PY - 2009/10

Y1 - 2009/10

N2 - A composite correlation of the average Nusselt number and the channel Rayleigh number for buoyant air flow through inclined channels with uniform heat flux boundaries is presented. The form of the correlation is based on dimensional analysis and is a superposition of the developing and fully developed flow limits. In the limit of fully developed flow, an analytical solution for the Nusselt number is derived. The developing flow limit follows the format of the correlation for a single plate. The composite relationship based on the top wall temperature is over(Nu, -) = fenced(frac(6.25 (1 + r), Ra″ sin φ{symbol}) + frac(1.64, (Ra″ sin φ{symbol})2 / 5))- 1 / 2, where r is ratio of the heat flux at the top and bottom wall. At inclination angles of 30 ° ≤ φ{symbol} ≤ 90 °, this correlation predicts the available data base for 10 ≤ Ra″ ≤ 105 and agrees with the analytical solution for 1 ≤ Ra″ ≤ 102.

AB - A composite correlation of the average Nusselt number and the channel Rayleigh number for buoyant air flow through inclined channels with uniform heat flux boundaries is presented. The form of the correlation is based on dimensional analysis and is a superposition of the developing and fully developed flow limits. In the limit of fully developed flow, an analytical solution for the Nusselt number is derived. The developing flow limit follows the format of the correlation for a single plate. The composite relationship based on the top wall temperature is over(Nu, -) = fenced(frac(6.25 (1 + r), Ra″ sin φ{symbol}) + frac(1.64, (Ra″ sin φ{symbol})2 / 5))- 1 / 2, where r is ratio of the heat flux at the top and bottom wall. At inclination angles of 30 ° ≤ φ{symbol} ≤ 90 °, this correlation predicts the available data base for 10 ≤ Ra″ ≤ 105 and agrees with the analytical solution for 1 ≤ Ra″ ≤ 102.

KW - Free convection

KW - Inclined channels

KW - Uniform heat flux

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U2 - 10.1016/j.ijheatmasstransfer.2009.06.003

DO - 10.1016/j.ijheatmasstransfer.2009.06.003

M3 - Article

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VL - 52

SP - 4689

EP - 4694

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

SN - 0017-9310

IS - 21-22

ER -

Composite relation for laminar free convection in inclined channels with uniform heat flux boundaries

Abstract

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Keywords

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