{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T13:25:27Z","timestamp":1773753927705,"version":"3.50.1"},"reference-count":27,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Higher Education Commission of Pakistan"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>The steady flow of an incompressible, third-grade fluid in helical screw rheometer (HSR) is studied by \u201cunwrapping or flattening\u201d the channel, lands, and the outside rotating barrel. The geometry is approximated as a shallow infinite channel, by assuming that the width of the channel is large as compared to the depth. The developed second-order nonlinear coupled differential equations are reduced to single differential equation by using a transformation. Using Adomian decomposition method, analytical expressions are calculated for the the velocity profiles and volume flow rates. The results have been discussed with the help of graphs as well. We observed that the velocity profiles are strongly dependant on non-Newtonian parameter (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>\u03b2<\/mml:mi><\/mml:mrow><mml:mo>~<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math>), and with the increase in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>\u03b2<\/mml:mi><\/mml:mrow><mml:mo>~<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math>, the velocity profiles increase progressively, which conclude that extrusion process increases with the increase in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>\u03b2<\/mml:mi><\/mml:mrow><mml:mo>~<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math>. We also observed that the increase in pressure gradients in<jats:italic>x<\/jats:italic>- and<jats:italic>z<\/jats:italic>-direction increases the net flow inside the helical screw rheometer, which increases the extrusion process. We noticed that the flow increases as the flight angle increase.<\/jats:p>","DOI":"10.1155\/2013\/620238","type":"journal-article","created":{"date-parts":[[2013,5,21]],"date-time":"2013-05-21T21:04:39Z","timestamp":1369170279000},"page":"1-11","source":"Crossref","is-referenced-by-count":6,"title":["Analysis of Third-Grade Fluid in Helical Screw Rheometer"],"prefix":"10.1155","volume":"2013","author":[{"given":"M.","family":"Zeb","sequence":"first","affiliation":[{"name":"Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan"}]},{"given":"S.","family":"Islam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan"}]},{"given":"A. M.","family":"Siddiqui","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Pennsylvania State University, York Campus, York, PA 17 403, USA"}]},{"given":"T.","family":"Haroon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan"}]}],"member":"98","reference":[{"key":"1","first-page":"323","volume":"4","year":"1955","journal-title":"Journal of Rational Mechanics and Analysis"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.icheatmasstransfer.2011.08.003"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.icheatmasstransfer.2012.07.026"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.icheatmasstransfer.2012.05.020"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jher.2012.04.002"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.powtec.2012.11.030"},{"key":"7","year":"2013","journal-title":"Advanced Poweder Tecnology"},{"key":"8","year":"1979"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(99)00018-3"},{"issue":"7","key":"10","first-page":"2739","volume":"3","year":"2011","journal-title":"International Journal on Computer Science and Engineering"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2003.08.011"},{"key":"12","year":"1983"},{"key":"13","year":"1986"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(97)10127-8"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.06.058"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2009.05.073"},{"key":"17","year":"2002"},{"issue":"2","key":"18","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1111\/j.1745-4530.1993.tb00164.x","volume":"16","year":"1993","journal-title":"Journal of Food Process Engineering"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.03.078"},{"issue":"3","key":"20","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1002\/pen.10422","volume":"36","year":"1996","journal-title":"Polymer Engineering and Science"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1111\/j.1745-4603.1977.tb01173.x"},{"issue":"4","key":"22","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1177\/002029408301600401","volume":"16","year":"1983","journal-title":"Measurement and Control"},{"key":"23","first-page":"184","volume-title":"Enhancement of axial annular flow by rottaing inner cylinder","volume":"1","year":"1987"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1021\/ie50594a034"},{"issue":"1","key":"26","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/0022-247X(85)90102-7","volume":"105","year":"1985","journal-title":"Journal of Mathematical Analysis and Applications"},{"issue":"2","key":"27","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/0377-0427(84)90022-0","volume":"11","year":"1984","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(88)90170-9"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/620238.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/620238.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/620238.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,8]],"date-time":"2020-05-08T16:08:56Z","timestamp":1588954136000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/620238\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":27,"alternative-id":["620238","620238"],"URL":"https:\/\/doi.org\/10.1155\/2013\/620238","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}