{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T22:10:14Z","timestamp":1777932614991,"version":"3.51.4"},"reference-count":18,"publisher":"SAGE Publications","issue":"9-10","license":[{"start":{"date-parts":[[2008,9,1]],"date-time":"2008-09-01T00:00:00Z","timestamp":1220227200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Vibration and Control"],"published-print":{"date-parts":[[2008,9]]},"abstract":"<jats:p>This work advances our understanding of the drag force acting on a particle due to the oscillatory flow of a viscous fluid with finite Reynolds and Strouhal numbers. The drag force is is determined using the novel concept of variable order (VO) calculus, where the order of derivative can vary with the parameters and variables, according to the dynamics of the flow. Using the VO formulation we determine: (i) The region of validity of Tchen's equation for oscillatory flow, (ii) the region where the order of the derivative is fractional but constant, and (iii) the region where the strong non-linearity of the flow requires a variable order derivative to account for the increased complexity of the flow.<\/jats:p>","DOI":"10.1177\/1077546307087397","type":"journal-article","created":{"date-parts":[[2008,9,30]],"date-time":"2008-09-30T09:57:52Z","timestamp":1222768672000},"page":"1659-1672","source":"Crossref","is-referenced-by-count":102,"title":["Variable Order Modeling of Diffusive-convective Effects on the Oscillatory Flow Past a Sphere"],"prefix":"10.1177","volume":"14","author":[{"given":"H.T.C.","family":"Pedro","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Hawaii, 2540 Dole Street 302, Honolulu, HI 96822 USA"}]},{"given":"M.H.","family":"Kobayashi","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Hawaii, 2540 Dole Street 302, Honolulu, HI 96822 USA,"}]},{"given":"J.M.C.","family":"Pereira","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering\/SMA, IST, Av. Rovisco Pais, 1, 1049-001 Lisbon, Portugal"}]},{"given":"C.F.M.","family":"Coimbra","sequence":"additional","affiliation":[{"name":"School of Engineering, University of California, Merced, PO Box 2039, Merced, CA 95344 USA"}]}],"member":"179","published-online":{"date-parts":[[2008,9,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1888.0003"},{"key":"atypb2","first-page":"935","volume":"100","author":"Boussinesq, J.","year":"1885","journal-title":"Coptes Rendus Academie Sciences Paris"},{"key":"atypb3","volume-title":"Unsteady motion and heat transfer of small particles in suspension,\" Ph.D. Thesis","author":"Coimbra, C.F.M.","year":"1998"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1002\/andp.200310032"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112002001829"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112098001967"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.2514\/2.1524"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1017\/S002211200400789X"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1115\/1.1497364"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112098001657"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1063\/1.2128254"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1255"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016586905654"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1063\/1.864230"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112092003434"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1002\/andp.200410140"},{"key":"atypb17","first-page":"8","volume":"9","author":"Stokes, G.G.","year":"1850","journal-title":"Transactions of the Cambridge Philosophical Society"},{"key":"atypb18","volume-title":"Mean value and correlation problems connected with the motion of small particles suspended in a turbulent fluid","author":"Tchen, C.M.","year":"1947"}],"container-title":["Journal of Vibration and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546307087397","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546307087397","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T01:24:56Z","timestamp":1777685096000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1077546307087397"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9]]},"references-count":18,"journal-issue":{"issue":"9-10","published-print":{"date-parts":[[2008,9]]}},"alternative-id":["10.1177\/1077546307087397"],"URL":"https:\/\/doi.org\/10.1177\/1077546307087397","relation":{},"ISSN":["1077-5463","1741-2986"],"issn-type":[{"value":"1077-5463","type":"print"},{"value":"1741-2986","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,9]]}}}