{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T11:09:31Z","timestamp":1761217771088,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2015,2,16]],"date-time":"2015-02-16T00:00:00Z","timestamp":1424044800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The article aimed to analytically investigate the thermophysical behaviors of a ferrofluid in a vertical rectangle with the variation of intensity of the magnetic field, viscosity of the ferrofluid and boundary conditions. The governing equations of the ferrofluid include the continuity, momentum and energy equations for describing the thermal-fluidic behaviors of the ferrofluid and the Maxwell equation and magnetization equation are also added to consider rotating effect of the nano-sized particles. The flow behavior and heat transfer characteristics of the ferrofluid with the intensity of the magnetic field, viscosities of the ferrofluid and boundary conditions were analyzed through isotherms, velocity profiles and both mean and local Nusselt numbers. As a result, the isotherms of the ferrofluid in the vertical rectangle increased with the increase of the magnetic volume fractions and magnetic field intensities. In addition, the mean Nusselt numbers increased with the increase of magnetite volume fractions at all magnetic field intensities because of the combined effects of both heat conduction by magnetite and the magnetic volume force.<\/jats:p>","DOI":"10.3390\/e17020903","type":"journal-article","created":{"date-parts":[[2015,2,16]],"date-time":"2015-02-16T10:30:38Z","timestamp":1424082638000},"page":"903-913","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Thermophysical Characteristics of the Ferrofluid in  a Vertical Rectangle"],"prefix":"10.3390","volume":"17","author":[{"given":"Jae-Hyeong","family":"Seo","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Dong-A University, Busan 604-714, Korea"}]},{"given":"Byoung-Hee","family":"You","sequence":"additional","affiliation":[{"name":"Department of Engineering Technology, College of Science and Engineering, Texas State University, 601 University Drive, San Marcos, TX 78666, USA"}]},{"given":"Sang-Seuk","family":"Kwen","sequence":"additional","affiliation":[{"name":"Daegyeong Regional Division, Korea Institute of Industrial Technology, 13-13 Hayang-ro, Gyeongsan-si, Gyeongsangbuk-do 712-702, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8857-4444","authenticated-orcid":false,"given":"Dong-Yeon","family":"Lee","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749, Korea"}]},{"given":"Moo-Yeon","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Dong-A University, Busan 604-714, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2015,2,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1016\/S0022-3697(01)00108-1","article-title":"Novel properties and applications in magnetic fluids","volume":"62","author":"Horng","year":"2001","journal-title":"J. Phys. Chem. Solids"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.jmmm.2011.07.033","article-title":"Lattice Boltzmann simulation for temperature-sensitive magnetic fluids in a porous square cavity","volume":"324","author":"Jin","year":"2012","journal-title":"J. Magn. Magn. Mater"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2987","DOI":"10.1016\/j.jmmm.2011.06.025","article-title":"Novel optical devices based on the tunable refractive index of magnetic fluid and their characteristics","volume":"323","author":"Zhao","year":"2011","journal-title":"J. Magn. Magn. Mater"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1450005","DOI":"10.1142\/S2010132514500059","article-title":"Experimental study on thermal transport phenomenon of nanofluids as working fluid in heat exchanger","volume":"22","author":"Torii","year":"2014","journal-title":"Int. J. Air Cond. Refrig"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1450011","DOI":"10.1142\/S2010132514500096","article-title":"Inflow condensation heat transfer characteristics of CO2 in microchannel","volume":"22","author":"Yun","year":"2014","journal-title":"Int. J. Air Cond. Refrig"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1450025","DOI":"10.1142\/S2010132514500254","article-title":"Thermal Performance of Flat Plate Pulsating Heat Pipes with Mini- and Micro-Channels","volume":"22","author":"Jang","year":"2014","journal-title":"Int. J. Air Cond. Refrig"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1450026","DOI":"10.1142\/S2010132514500266","article-title":"Simulation Results for the Effect of Fin Geometry on the Performance of a Concentric Heat Exchanger","volume":"22","author":"Cho","year":"2014","journal-title":"Int. J. Air Cond. Refrig"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1906","DOI":"10.1108\/HFF-07-2013-0225","article-title":"A study of natural convection heat transfer in a nanofluid filled enclosure with elliptic inner cylinder","volume":"24","author":"Sheikholeslami","year":"2014","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjp\/i2014-14155-6","article-title":"Interaction of nano particles for the peristaltic flow in an asymmetric channel with the induced magnetic field","volume":"129","author":"Akbar","year":"2014","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1451","DOI":"10.1016\/j.apm.2012.04.004","article-title":"The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions","volume":"37","author":"Ellahi","year":"2013","journal-title":"Appl. Math. Model"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1007\/s12541-014-0479-6","article-title":"Thermodynamic behaviors of magnetic-fluid in a thin channel with magnetic field and aspect ratio","volume":"15","author":"Kim","year":"2014","journal-title":"Int. J. Precis. Eng. Manuf"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"240438","DOI":"10.1155\/2013\/240438","article-title":"Numerical investigation on heat and flow characteristics of temperature-sensitive ferrofluid in a square cavity","volume":"2013","author":"Lee","year":"2013","journal-title":"Adv. Mech. Eng"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3684","DOI":"10.1016\/j.ijheatmasstransfer.2007.01.045","article-title":"Numerical investigation of natural convection in an inclined enclosure filled with porous medium under magnetic field","volume":"50","author":"Wang","year":"2007","journal-title":"Int. J. Heat Mass Transfer"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1115\/1.3450517","article-title":"Free convective heat transfer across inclined air layers","volume":"98","author":"Hollands","year":"1976","journal-title":"J. Heat Transfer"},{"key":"ref_15","unstructured":"Ferrotec Corporation Available online: http:\/\/www.ferrotec.com\/."},{"key":"ref_16","first-page":"329","article-title":"Visualization of wall temperature distribution caused by natural convection of magnetic fluids in a cubic enclosure","volume":"4","author":"Sawada","year":"1994","journal-title":"Int. J. Appl. Electromagn. Mater"},{"key":"ref_17","unstructured":"Park, J.W. (2002). A Study on the Heat Transfer Characteristics and Fluid Flow of Magnetic Fluids in Concentric Double Pipe Annuli. [Ph.D. Thesis, Dong-A University]."},{"key":"ref_18","first-page":"997","article-title":"Numerical analysis on thermal-fluidic characteristics of the magnetic fluid in a cavity using GSMAC","volume":"14","author":"Seo","year":"2013","journal-title":"J. Korea Acad. Ind. Coop. Soc"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"637","DOI":"10.3795\/KSME-B.2013.37.7.637","article-title":"Study of natural convection of magnetic fluid in cubic cavity","volume":"37","author":"Seo","year":"2013","journal-title":"Trans. Korean Soc. Mech. Eng. B"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1103\/PhysRevLett.86.328","article-title":"Invalidation of the Kelvin force in ferrofluids","volume":"86","author":"Odenbach","year":"2001","journal-title":"Phys. Rev. Lett"},{"key":"ref_21","unstructured":"Seo, J.H., Kim, D.W., and Lee, M.Y. (2013, January 23\u201325). Heat transfer characteristics of the magnetic fluid in the inclined rectangular cavity using finite element method, Yeosu, Korea."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1525","DOI":"10.1016\/j.ijheatmasstransfer.2008.08.011","article-title":"Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium","volume":"52","author":"Grosan","year":"2009","journal-title":"Int. J. Heat Mass Transfer"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3508","DOI":"10.1016\/j.jmmm.2010.06.054","article-title":"Experimental investigation for enhanced ferrofluid heat transfer under magnetic field effect","volume":"322","author":"Lajvardi","year":"2010","journal-title":"J. Magn. Magn. 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