Problem 2833. Radiation Heat Transfer — View Factors (5)

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:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Note: This problem is identical to the previous problem (4) except that the variables will be provided in vectors of varying sizes.</w:t></w:r><w:r><w:t> The variables will need to be combined to produce all the applicable combinations. For example, if the sizes of d, b, and n are 2, 5, and 1, respectively, there will be ten total variable combinations (and answers). As another example, if the sizes of d, b, and n are 4, 3, and 2, respectively, there will be 24 total variable combinations. This simulates a parametric design study. Also, because all possible combinations can be generated in various orders, the answers will be sorted; the order that you output answers does not matter.</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.Note: This problem is identical to the previous problem (4) except that the variables will be provided in vectors of varying sizes. The variables will need to be combined to produce all the applicable combinations. For example, if the sizes of d, b, and n are 2, 5, and 1, respectively, there will be ten total variable combinations (and answers). As another example, if the sizes of d, b, and n are 4, 3, and 2, respectively, there will be 24 total variable combinations. This simulates a parametric design study. Also, because all possible combinations can be generated in various orders, the answers will be sorted; the order that you output answers does not matter.

Solve

Solution Stats

29 Solutions
17 Solvers

Last Solution submitted on Jun 29, 2020

Last 200 Solutions

Problem Comments

Problem Recent Solvers17

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 2833. Radiation Heat Transfer — View Factors (5)

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers17

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Problem 2833. Radiation Heat Transfer — View Factors (5)

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers17

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Players