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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="elpub" pub-id-type="custom">najo-1281</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group></article-categories><title-group><article-title>Heat transport in Marangoni layer with nanoparticles</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Batischev</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="en"><p>Department of Theoretical and Computer Hydrodynamics </p><p>Rostov-on-Don</p><p> </p></bio><email xlink:type="simple">batishev-v@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Zaikin</surname><given-names>V. V.</given-names></name></name-alternatives><bio xml:lang="en"><p>Department of Theoretical and Computer Hydrodynamics </p><p>Rostov-on-Don</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Horoshunova</surname><given-names>E. V.</given-names></name></name-alternatives><bio xml:lang="en"><p>Department of Theoretical and Computer Hydrodynamics </p><p>Rostov-on-Don</p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>Southern Federal University</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2013</year></pub-date><pub-date pub-type="epub"><day>21</day><month>08</month><year>2025</year></pub-date><volume>4</volume><issue>3</issue><fpage>313</fpage><lpage>319</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Batischev V.A., Zaikin V.V., Horoshunova E.V., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Batischev V.A., Zaikin V.V., Horoshunova E.V.</copyright-holder><copyright-holder xml:lang="en">Batischev V.A., Zaikin V.V., Horoshunova E.V.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/1281">https://nanojournal.ifmo.ru/jour/article/view/1281</self-uri><abstract><p>This study investigates the influence of nanoparticle concentration on the Marangoni effect in the boundary layer near the free boundary of an incompressible fluid with small kinematic viscosity and thermal conductivity. The study was conducted on the basis of a single-phase model derived from the Navier-Stokes equations by replacing thermal parameters for their effective values. Two cases of stationary axisymmetric fluid flow are considered. In the first case, the fluid is cooled on the free surface near the symmetry axis, and in the second case, the fluid is heated. In the first case, a rotation of the fluid in a thin boundary layer appears near the free boundary, while there is no rotation outside the layer. In both cases, as the concentration of nanoparticles increases, the heat flux and the fluid velocity at the free boundary decrease.</p></abstract><kwd-group xml:lang="en"><kwd>nanoparticles</kwd><kwd>a free boundary</kwd><kwd>the Marangoni effect</kwd><kwd>the boundary layer</kwd><kwd>thermal conductivity</kwd></kwd-group><funding-group><funding-statement xml:lang="en">This work was supported by the RFBR grant No. 12-01-00582-a.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">J.C. Maxwell. A Treatise on Electricity and Magnetism. Clarendon Press, 2nd ed., 435 p. (1881).</mixed-citation><mixed-citation xml:lang="en">J.C. Maxwell. A Treatise on Electricity and Magnetism. Clarendon Press, 2nd ed., 435 p. (1881).</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">S.U.S. Choi. 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