Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters
We provide an analytical solution of the heat equation in the half-space subject to a moving Gaussian heat flux with piecewise constant parameters. The solution is of interest in powder bed fusion applications where these parameters can be used to control the conduction of heat due to a scanning bea...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2018-03 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | slund, Robert Snis, Anders Larsson, Stig |
| description | We provide an analytical solution of the heat equation in the half-space subject to a moving Gaussian heat flux with piecewise constant parameters. The solution is of interest in powder bed fusion applications where these parameters can be used to control the conduction of heat due to a scanning beam of concentrated energy. The analytical solution is written in a dimensionless form as a sum of integrals over (dimensionless) time. For the numerical computation of these integrals we suggest a quadrature scheme that utilizes pre-calculated look-up tables for the required quadrature orders. Such a scheme is efficient because the required quadrature orders are strongly dependent on the parameters in the heat flux. The possibilities of using the obtained computational technique for the control and optimization of powder bed fusion processes are discussed. |
| doi_str_mv | 10.48550/arxiv.1803.10668 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_1803_10668</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2071936175</sourcerecordid><originalsourceid>FETCH-LOGICAL-a525-9e2e4570bd5f1bd8de66b72fcba5d7a9617f4b7fb74be707e9be58c0a316b9513</originalsourceid><addsrcrecordid>eNotkMtqwzAQRUWh0JDmA7qqoGuneliWvQyhTQOBbrI3I3vcKNiWK8l5_H3z6Grgcu4dOIS8cDZPc6XYO_iTPcx5zuScsyzLH8hESMmTPBXiicxC2DPGRKaFUnJCukUP7TnaCloaXDtG63raOE93CJFWrq_H6pbVI9LoKNDOHWz_Q1cwhmChv4NNO57o0cYdHSxWeLQBr-UQoY90AA8dRvThmTw20Aac_d8p2X5-bJdfyeZ7tV4uNgkooZICBaZKM1Orhps6rzHLjBZNZUDVGoqM6yY1ujE6NaiZxsKgyisGkmemUFxOyet99uaiHLztwJ_Lq5Py5uRCvN2JwbvfEUMs9270FxWhFEzzQl5-KPkHHnpm7A</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2071936175</pqid></control><display><type>article</type><title>Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters</title><source>arXiv.org</source><source>Free E- Journals</source><creator>slund, Robert ; Snis, Anders ; Larsson, Stig</creator><creatorcontrib>slund, Robert ; Snis, Anders ; Larsson, Stig</creatorcontrib><description>We provide an analytical solution of the heat equation in the half-space subject to a moving Gaussian heat flux with piecewise constant parameters. The solution is of interest in powder bed fusion applications where these parameters can be used to control the conduction of heat due to a scanning beam of concentrated energy. The analytical solution is written in a dimensionless form as a sum of integrals over (dimensionless) time. For the numerical computation of these integrals we suggest a quadrature scheme that utilizes pre-calculated look-up tables for the required quadrature orders. Such a scheme is efficient because the required quadrature orders are strongly dependent on the parameters in the heat flux. The possibilities of using the obtained computational technique for the control and optimization of powder bed fusion processes are discussed.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1803.10668</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Conduction heating ; Conductive heat transfer ; Dimensionless analysis ; Dimensionless numbers ; Half spaces ; Heat flux ; Integrals ; Lookup tables ; Mathematics - Numerical Analysis ; Numerical analysis ; Parameters ; Powder beds ; Temperature ; Thermodynamics</subject><ispartof>arXiv.org, 2018-03</ispartof><rights>2018. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,780,881,27904</link.rule.ids><backlink>$$Uhttps://doi.org/10.48550/arXiv.1803.10668$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.1016/j.apm.2018.09.018$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>slund, Robert</creatorcontrib><creatorcontrib>Snis, Anders</creatorcontrib><creatorcontrib>Larsson, Stig</creatorcontrib><title>Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters</title><title>arXiv.org</title><description>We provide an analytical solution of the heat equation in the half-space subject to a moving Gaussian heat flux with piecewise constant parameters. The solution is of interest in powder bed fusion applications where these parameters can be used to control the conduction of heat due to a scanning beam of concentrated energy. The analytical solution is written in a dimensionless form as a sum of integrals over (dimensionless) time. For the numerical computation of these integrals we suggest a quadrature scheme that utilizes pre-calculated look-up tables for the required quadrature orders. Such a scheme is efficient because the required quadrature orders are strongly dependent on the parameters in the heat flux. The possibilities of using the obtained computational technique for the control and optimization of powder bed fusion processes are discussed.</description><subject>Conduction heating</subject><subject>Conductive heat transfer</subject><subject>Dimensionless analysis</subject><subject>Dimensionless numbers</subject><subject>Half spaces</subject><subject>Heat flux</subject><subject>Integrals</subject><subject>Lookup tables</subject><subject>Mathematics - Numerical Analysis</subject><subject>Numerical analysis</subject><subject>Parameters</subject><subject>Powder beds</subject><subject>Temperature</subject><subject>Thermodynamics</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNotkMtqwzAQRUWh0JDmA7qqoGuneliWvQyhTQOBbrI3I3vcKNiWK8l5_H3z6Grgcu4dOIS8cDZPc6XYO_iTPcx5zuScsyzLH8hESMmTPBXiicxC2DPGRKaFUnJCukUP7TnaCloaXDtG63raOE93CJFWrq_H6pbVI9LoKNDOHWz_Q1cwhmChv4NNO57o0cYdHSxWeLQBr-UQoY90AA8dRvThmTw20Aac_d8p2X5-bJdfyeZ7tV4uNgkooZICBaZKM1Orhps6rzHLjBZNZUDVGoqM6yY1ujE6NaiZxsKgyisGkmemUFxOyet99uaiHLztwJ_Lq5Py5uRCvN2JwbvfEUMs9270FxWhFEzzQl5-KPkHHnpm7A</recordid><startdate>20180328</startdate><enddate>20180328</enddate><creator>slund, Robert</creator><creator>Snis, Anders</creator><creator>Larsson, Stig</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20180328</creationdate><title>Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters</title><author>slund, Robert ; Snis, Anders ; Larsson, Stig</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a525-9e2e4570bd5f1bd8de66b72fcba5d7a9617f4b7fb74be707e9be58c0a316b9513</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Conduction heating</topic><topic>Conductive heat transfer</topic><topic>Dimensionless analysis</topic><topic>Dimensionless numbers</topic><topic>Half spaces</topic><topic>Heat flux</topic><topic>Integrals</topic><topic>Lookup tables</topic><topic>Mathematics - Numerical Analysis</topic><topic>Numerical analysis</topic><topic>Parameters</topic><topic>Powder beds</topic><topic>Temperature</topic><topic>Thermodynamics</topic><toplevel>online_resources</toplevel><creatorcontrib>slund, Robert</creatorcontrib><creatorcontrib>Snis, Anders</creatorcontrib><creatorcontrib>Larsson, Stig</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection (ProQuest)</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>slund, Robert</au><au>Snis, Anders</au><au>Larsson, Stig</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters</atitle><jtitle>arXiv.org</jtitle><date>2018-03-28</date><risdate>2018</risdate><eissn>2331-8422</eissn><abstract>We provide an analytical solution of the heat equation in the half-space subject to a moving Gaussian heat flux with piecewise constant parameters. The solution is of interest in powder bed fusion applications where these parameters can be used to control the conduction of heat due to a scanning beam of concentrated energy. The analytical solution is written in a dimensionless form as a sum of integrals over (dimensionless) time. For the numerical computation of these integrals we suggest a quadrature scheme that utilizes pre-calculated look-up tables for the required quadrature orders. Such a scheme is efficient because the required quadrature orders are strongly dependent on the parameters in the heat flux. The possibilities of using the obtained computational technique for the control and optimization of powder bed fusion processes are discussed.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1803.10668</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2018-03 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_arxiv_primary_1803_10668 |
| source | arXiv.org; Free E- Journals |
| subjects | Conduction heating Conductive heat transfer Dimensionless analysis Dimensionless numbers Half spaces Heat flux Integrals Lookup tables Mathematics - Numerical Analysis Numerical analysis Parameters Powder beds Temperature Thermodynamics |
| title | Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-25T00%3A09%3A24IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Analytical%20solution%20for%20heat%20conduction%20due%20to%20a%20moving%20Gaussian%20heat%20flux%20with%20piecewise%20constant%20parameters&rft.jtitle=arXiv.org&rft.au=slund,%20Robert&rft.date=2018-03-28&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1803.10668&rft_dat=%3Cproquest_arxiv%3E2071936175%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2071936175&rft_id=info:pmid/&rfr_iscdi=true |