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

Created by goc3

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","targetMode":"","relationshipId":"rId1","target":"/media/image1.gif"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","targetMode":"","relationshipId":"rId2","target":"/media/image2.gif"}],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>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</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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"}]}

Solve

Solution Stats

93 Solutions
33 Solvers

Last Solution submitted on Dec 30, 2020

Last 200 Solutions

Problem Comments

Solution Comments

Solution 551077

2 Comments

2 Comments

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.

Problem Recent Solvers33

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

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

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers33

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

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

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers33

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Players