Problem 2806. Radiation Heat Transfer — View Factors (2)

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 directly opposed, infinitely long plates of different finite widths given the distance 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: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>Each variable may be a vector of values. Also, note that B = b/a and C = c/a.</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 Jan 11, 2023

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Solution 551077

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James on 31 Dec 2014

Same issue here as in your third problem. Please check the absolute value of the differences of the computed values with the correct ones. Otherwise, more silly answers (again, like this one :-) will slip through!

goc3 on 1 Jan 2015

Thanks for the catch. I've updated the test suite to check against upper and lower bounds of each answer.

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Problem 2806. Radiation Heat Transfer — View Factors (2)

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