Stochastic Model of Heat Transfer in the Atmospheric Surface Layer
A new stochastic model of heat transfer in the atmospheric surface layer is proposed. The model is based on the experimentally confirmed fact that the horizontal wind velocity can be treated as a random process. Accordingly, the model is formalized using a differential equation with random coefficie...
Gespeichert in:
| Veröffentlicht in: | Computational mathematics and mathematical physics 2020-03, Vol.60 (3), p.459-471 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 471 |
|---|---|
| container_issue | 3 |
| container_start_page | 459 |
| container_title | Computational mathematics and mathematical physics |
| container_volume | 60 |
| creator | Zadorozhniy, V. G. Nozhkin, V. S. Semenov, M. E. Ul’shin, I. I. |
| description | A new stochastic model of heat transfer in the atmospheric surface layer is proposed. The model is based on the experimentally confirmed fact that the horizontal wind velocity can be treated as a random process. Accordingly, the model is formalized using a differential equation with random coefficients. Explicit formulas for the expectation and the second moment function of the solution to the heat transfer equation with random coefficients are given. The error induced by replacing the random coefficient of the equation with its expectation is estimated. An example is given demonstrating the efficiency of the proposed approach in the case of a Gaussian distribution of the horizontal wind velocity, when the expectation and the second moment function can be determined within the framework of model representations. |
| doi_str_mv | 10.1134/S0965542520030173 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2401929572</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2401929572</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-c74505c9bb90e96a7c8a89fab4235530ac152723816c00ddeefea230f3fdef013</originalsourceid><addsrcrecordid>eNp1kEFPAjEQhRujiYj-AG9NPK_OtNvu9ohExQTjATxvSncqENhiWw78e5dg4sF4msP7vjfJY-wW4R5Rlg8zMFqpUigBIAErecYGqJQqtNbinA2OcXHML9lVSmsA1KaWA_Y4y8Etbcorx99CSxsePJ-QzXwebZc8Rb7qeF4SH-VtSLslxZ6c7aO3jvjUHiheswtvN4lufu6QfTw_zceTYvr-8joeTQsnUefCVaUC5cxiYYCMtpWrbW28XZRCKiXBOlSiErJG7QDalsiTFRK89C15QDlkd6feXQxfe0q5WYd97PqXjSgBjTCq14cMT5SLIaVIvtnF1dbGQ4PQHKdq_kzVO-LkpJ7tPin-Nv8vfQPnfGlx</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2401929572</pqid></control><display><type>article</type><title>Stochastic Model of Heat Transfer in the Atmospheric Surface Layer</title><source>SpringerNature Complete Journals</source><creator>Zadorozhniy, V. G. ; Nozhkin, V. S. ; Semenov, M. E. ; Ul’shin, I. I.</creator><creatorcontrib>Zadorozhniy, V. G. ; Nozhkin, V. S. ; Semenov, M. E. ; Ul’shin, I. I.</creatorcontrib><description>A new stochastic model of heat transfer in the atmospheric surface layer is proposed. The model is based on the experimentally confirmed fact that the horizontal wind velocity can be treated as a random process. Accordingly, the model is formalized using a differential equation with random coefficients. Explicit formulas for the expectation and the second moment function of the solution to the heat transfer equation with random coefficients are given. The error induced by replacing the random coefficient of the equation with its expectation is estimated. An example is given demonstrating the efficiency of the proposed approach in the case of a Gaussian distribution of the horizontal wind velocity, when the expectation and the second moment function can be determined within the framework of model representations.</description><identifier>ISSN: 0965-5425</identifier><identifier>EISSN: 1555-6662</identifier><identifier>DOI: 10.1134/S0965542520030173</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Coefficients ; Computational Mathematics and Numerical Analysis ; Differential equations ; Heat transfer ; Horizontal distribution ; Mathematics ; Mathematics and Statistics ; Normal distribution ; Random processes ; Stochastic models ; Surface layers ; Wind speed</subject><ispartof>Computational mathematics and mathematical physics, 2020-03, Vol.60 (3), p.459-471</ispartof><rights>Pleiades Publishing, Ltd. 2020</rights><rights>Pleiades Publishing, Ltd. 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-c74505c9bb90e96a7c8a89fab4235530ac152723816c00ddeefea230f3fdef013</citedby><cites>FETCH-LOGICAL-c316t-c74505c9bb90e96a7c8a89fab4235530ac152723816c00ddeefea230f3fdef013</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0965542520030173$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0965542520030173$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Zadorozhniy, V. G.</creatorcontrib><creatorcontrib>Nozhkin, V. S.</creatorcontrib><creatorcontrib>Semenov, M. E.</creatorcontrib><creatorcontrib>Ul’shin, I. I.</creatorcontrib><title>Stochastic Model of Heat Transfer in the Atmospheric Surface Layer</title><title>Computational mathematics and mathematical physics</title><addtitle>Comput. Math. and Math. Phys</addtitle><description>A new stochastic model of heat transfer in the atmospheric surface layer is proposed. The model is based on the experimentally confirmed fact that the horizontal wind velocity can be treated as a random process. Accordingly, the model is formalized using a differential equation with random coefficients. Explicit formulas for the expectation and the second moment function of the solution to the heat transfer equation with random coefficients are given. The error induced by replacing the random coefficient of the equation with its expectation is estimated. An example is given demonstrating the efficiency of the proposed approach in the case of a Gaussian distribution of the horizontal wind velocity, when the expectation and the second moment function can be determined within the framework of model representations.</description><subject>Coefficients</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Differential equations</subject><subject>Heat transfer</subject><subject>Horizontal distribution</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Normal distribution</subject><subject>Random processes</subject><subject>Stochastic models</subject><subject>Surface layers</subject><subject>Wind speed</subject><issn>0965-5425</issn><issn>1555-6662</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp1kEFPAjEQhRujiYj-AG9NPK_OtNvu9ohExQTjATxvSncqENhiWw78e5dg4sF4msP7vjfJY-wW4R5Rlg8zMFqpUigBIAErecYGqJQqtNbinA2OcXHML9lVSmsA1KaWA_Y4y8Etbcorx99CSxsePJ-QzXwebZc8Rb7qeF4SH-VtSLslxZ6c7aO3jvjUHiheswtvN4lufu6QfTw_zceTYvr-8joeTQsnUefCVaUC5cxiYYCMtpWrbW28XZRCKiXBOlSiErJG7QDalsiTFRK89C15QDlkd6feXQxfe0q5WYd97PqXjSgBjTCq14cMT5SLIaVIvtnF1dbGQ4PQHKdq_kzVO-LkpJ7tPin-Nv8vfQPnfGlx</recordid><startdate>20200301</startdate><enddate>20200301</enddate><creator>Zadorozhniy, V. G.</creator><creator>Nozhkin, V. S.</creator><creator>Semenov, M. E.</creator><creator>Ul’shin, I. I.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20200301</creationdate><title>Stochastic Model of Heat Transfer in the Atmospheric Surface Layer</title><author>Zadorozhniy, V. G. ; Nozhkin, V. S. ; Semenov, M. E. ; Ul’shin, I. I.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-c74505c9bb90e96a7c8a89fab4235530ac152723816c00ddeefea230f3fdef013</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Coefficients</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Differential equations</topic><topic>Heat transfer</topic><topic>Horizontal distribution</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Normal distribution</topic><topic>Random processes</topic><topic>Stochastic models</topic><topic>Surface layers</topic><topic>Wind speed</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zadorozhniy, V. G.</creatorcontrib><creatorcontrib>Nozhkin, V. S.</creatorcontrib><creatorcontrib>Semenov, M. E.</creatorcontrib><creatorcontrib>Ul’shin, I. I.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computational mathematics and mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zadorozhniy, V. G.</au><au>Nozhkin, V. S.</au><au>Semenov, M. E.</au><au>Ul’shin, I. I.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stochastic Model of Heat Transfer in the Atmospheric Surface Layer</atitle><jtitle>Computational mathematics and mathematical physics</jtitle><stitle>Comput. Math. and Math. Phys</stitle><date>2020-03-01</date><risdate>2020</risdate><volume>60</volume><issue>3</issue><spage>459</spage><epage>471</epage><pages>459-471</pages><issn>0965-5425</issn><eissn>1555-6662</eissn><abstract>A new stochastic model of heat transfer in the atmospheric surface layer is proposed. The model is based on the experimentally confirmed fact that the horizontal wind velocity can be treated as a random process. Accordingly, the model is formalized using a differential equation with random coefficients. Explicit formulas for the expectation and the second moment function of the solution to the heat transfer equation with random coefficients are given. The error induced by replacing the random coefficient of the equation with its expectation is estimated. An example is given demonstrating the efficiency of the proposed approach in the case of a Gaussian distribution of the horizontal wind velocity, when the expectation and the second moment function can be determined within the framework of model representations.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0965542520030173</doi><tpages>13</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0965-5425 |
| ispartof | Computational mathematics and mathematical physics, 2020-03, Vol.60 (3), p.459-471 |
| issn | 0965-5425 1555-6662 |
| language | eng |
| recordid | cdi_proquest_journals_2401929572 |
| source | SpringerNature Complete Journals |
| subjects | Coefficients Computational Mathematics and Numerical Analysis Differential equations Heat transfer Horizontal distribution Mathematics Mathematics and Statistics Normal distribution Random processes Stochastic models Surface layers Wind speed |
| title | Stochastic Model of Heat Transfer in the Atmospheric Surface Layer |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T12%3A52%3A49IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Stochastic%20Model%20of%20Heat%20Transfer%20in%20the%20Atmospheric%20Surface%20Layer&rft.jtitle=Computational%20mathematics%20and%20mathematical%20physics&rft.au=Zadorozhniy,%20V.%20G.&rft.date=2020-03-01&rft.volume=60&rft.issue=3&rft.spage=459&rft.epage=471&rft.pages=459-471&rft.issn=0965-5425&rft.eissn=1555-6662&rft_id=info:doi/10.1134/S0965542520030173&rft_dat=%3Cproquest_cross%3E2401929572%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2401929572&rft_id=info:pmid/&rfr_iscdi=true |