Problem 2831. Radiation Heat Transfer — View Factors (4)

Created by goc3

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In particular, the thermal energy leaving a given surface is applied to other surfaces, as appropriate, based on how much the hot surface \"sees\" the other surfaces. As such, view factors are purely geometrical in nature. A range of view factor formulae are available</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.thermalradiation.net/tablecon.html\"><w:r><w:t>here</w:t></w:r></w:hyperlink><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For this problem, calculate the view factor from surface 1 (an infinitely long plate) to surfaces 2 (n rows of in-line pipes):</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"-1\"/><w:attr w:name=\"width\" w:val=\"-1\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The view factor for one row of pipes is F_1-2 (the first equation):</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"-1\"/><w:attr w:name=\"width\" w:val=\"-1\"/><w:attr w:name=\"relationshipId\" w:val=\"rId2\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The second equation is utilized for more than one row of pipes. Any of the variables can be a vector. Also, note that D = d/b, where d is the pipe diameter and b is the center-to-center spacing between pipes.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray 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View factors (aka configuration factors) are utilized in some radiation heat transfer models to estimate heat transfer rates between surfaces. In particular, the thermal energy leaving a given surface is applied to other surfaces, as appropriate, based on how much the hot surface "sees" the other surfaces. As such, view factors are purely geometrical in nature. A range of view factor formulae are available <a href = "http://www.thermalradiation.net/tablecon.html">here</a>.For this problem, calculate the view factor from surface 1 (an infinitely long plate) to surfaces 2 (n rows of in-line pipes):<img src = "http://www.thermalradiation.net/images/C-7fig.gif">The view factor for one row of pipes is F_1-2 (the first equation):<img src = "http://www.thermalradiation.net/images/C-7eq.gif">The second equation is utilized for more than one row of pipes. Any of the variables can be a vector. Also, note that D = d/b, where d is the pipe diameter and b is the center-to-center spacing between pipes.

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57 Solutions
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Last Solution submitted on Jan 13, 2021

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Problem Comments

3 Comments

3 Comments

Tim on 15 Jan 2015

Test case 3 appears to be incorrect.

goc3 on 16 Jan 2015

You were correct. It has been fixed.

Martin C. on 19 Dec 2018

hmm, interesting problem.

Solution Comments

Solution 557733

2 Comments

2 Comments

Tim on 15 Jan 2015

I think D*atan(sqrt((1-D.^2)/D.^2)) should actually be D.*atan(sqrt((1-D.^2)./D.^2))

goc3 on 16 Jan 2015

Thanks for the catch.

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