Perturbation solution of Poiseuille flow of a weakly compressible Oldroyd-B fluid |
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| Authors: | Kostas D Housiadas Georgios C Georgiou |
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| Institution: | 1. Department of Mathematics, University of the Aegean, Karlovassi, Samos 83200, Greece;2. Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, Nicosia, Cyprus;1. Université de Bordeaux, IPB-I2M UMR CNRS 5295, 33607 Pessac, France;2. Laboratoire de Mathématiques et de leurs Applications (U.M.R. 5142 CNRS), Batiment IPRA, Université de Pau et des Pays de l’Adour, France;1. Département de Physique Appliquée, Faculté des Sciences et Technique, Université Hassan I, B.P. 577, Settat, Morocco;2. Université de Bretagne-Sud, EA 4250, Laboratoire d’Ingénierie des Matériaux de Bretagne, F-56100 Lorient, France;1. Rubber Technology Centre, Indian Institute of Technology Kharagpur, Kharagpur 721302, WB, India;2. Civil Engineering Department, Indian Institute of Technology Kharagpur, Kharagpur 721302, WB, India;3. ALP Nishikawa Co. Pvt. Ltd. Lalru, Punjab 140501, India |
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| Abstract: | The isothermal, planar Poiseuille flow of a weakly compressible Oldroyd-B fluid is considered under the assumption that the density of the fluid obeys a linear equation of state. A perturbation analysis for all the primary flow variables is carried out with the isothermal compressibility serving as the perturbation parameter. The sequence of partial differential equations which results from the perturbation procedure is solved analytically up to second order. The effects of the compressibility parameter, the aspect ratio, and the Weissenberg number are discussed. In particular, it is demonstrated that compressibility has a significant effect on the transverse velocity and the first normal stress difference. |
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