Problem 2807. Radiation Heat Transfer — View Factors (3)

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 to surface 2 (F_1-2) for two infinitely long plates of different finite widths and having a common edge given the angle between the plates:</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>-</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>Any of the variables can be a vector. Also, note that A = a/b, and is different than A_1 or A_2. Finally, the angle is provided in degrees.</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 type=\"array\"/></embeddedOutputs>"},{"partUri":"/media/image1.gif","contentType":"image/gif","content":"data:image/gif;base64,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"},{"partUri":"/media/image2.gif","contentType":"image/gif","content":"data:image/gif;base64,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"}]}

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Last Solution submitted on Jun 25, 2020

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Solution 551071

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3 Comments

James on 31 Dec 2014

OK. I figured out the issue with the test suite. Please check the absolute value of the difference when comparing the computed answers to the correct ones. Otherwise, you'll get some really silly answers. (Like this one! :-)

goc3 on 1 Jan 2015

My, you are tricky, James, finding all those loopholes. I've fixed the test suite to check against upper and lower bounds of each answer.

James on 2 Jan 2015

I was just really curious why one of my answers worked when it didn't include a or b. Some experimentation and a lot of (now wrong) solutions narrowed it down. I had to use some of these equations in my senior project at college, so I knew that the dimensions were very important!

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Problem 2807. Radiation Heat Transfer — View Factors (3)

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Problem 2807. Radiation Heat Transfer — View Factors (3)

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