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

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 (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 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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"}]}

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.

Solve

Solution Stats

79 Solutions
26 Solvers

Last Solution submitted on Oct 11, 2021

Last 200 Solutions

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.

Problem Recent Solvers26

Problem Tags

Community Treasure Hunt

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

Start Hunting!

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

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers26

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

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

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers26

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Players