{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:08:19Z","timestamp":1760234899303,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,22]],"date-time":"2021-06-22T00:00:00Z","timestamp":1624320000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Unidirectional unsteady flows of the incompressible Burgers\u2019 fluids between two infinite horizontal parallel plates are analytically studied when the magnetic and porous effects are taken into consideration. The fluid motion is induced by the two plates, which move in their planes with time-dependent velocities. Exact general expressions are established both for the dimensionless velocity and shear stress fields as well as the corresponding Darcy\u2019s resistance in the channel using the Laplace transform. If both plates move with equal velocities in the same direction, the fluid motion becomes symmetric with respect to the mid-plane between them. Otherwise, its motion is non-symmetric. To bring to light the behavior of the fluid, the dimensionless velocity profiles versus the spatial variable as well as its time evolution are presented both for the symmetric and asymmetric case. Finally, for comparison, similar graphical representations are presented together for the velocities of the incompressible Oldroyd-B and Burgers\u2019 fluids. For large values of the time t, as expected, the behavior of the two different fluids is almost identical. The Darcy\u2019s resistance against y is also graphically represented for the symmetric flow at different values of the time t. The influence of the magnetic field on the fluid motion is graphically revealed and discussed.<\/jats:p>","DOI":"10.3390\/sym13071109","type":"journal-article","created":{"date-parts":[[2021,6,22]],"date-time":"2021-06-22T22:10:59Z","timestamp":1624399859000},"page":"1109","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Symmetric and Non-Symmetric Flows of Burgers\u2019 Fluids through Porous Media between Parallel Plates"],"prefix":"10.3390","volume":"13","author":[{"given":"Constantin","family":"Fetecau","sequence":"first","affiliation":[{"name":"Section of Mathematics, Academy of Romanian Scientists, 050094 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9989-8452","authenticated-orcid":false,"given":"Dumitru","family":"Vieru","sequence":"additional","affiliation":[{"name":"Department of Theoretical Mechanics, Technical University of Ia\u0219i, 700050 Ia\u0219i, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,22]]},"reference":[{"key":"ref_1","unstructured":"Burgers, J.M. (1935). Mechanical Considerations\u2014Model Systems\u2014Phenomenological Theories of Relaxation and of Viscosity, Nordemann Publishing Company. First Report on Viscosity and Plasticity."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1111\/j.1745-4603.2003.tb01370.x","article-title":"Viscoelastic behavior of Arzua-Ulloa cheese","volume":"34","author":"Tovar","year":"2003","journal-title":"J. Texture Stud."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1115\/1.1529658","article-title":"Review of the uses and modeling of bitumen from and ancient to modern times","volume":"56","author":"Krishnan","year":"2003","journal-title":"Appl. Mech. Rev."},{"key":"ref_4","first-page":"146","article-title":"The mechanical properties of bituminous surfacing materials under constant stress","volume":"56","author":"Lee","year":"1937","journal-title":"J. Indian Chem. Soc."},{"key":"ref_5","unstructured":"Eirich, F.R. (1958). Rheological Properties of Asphalts, Academic Press. Chapter 9."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1111\/j.1365-246X.1982.tb04962.x","article-title":"Normal modes of the viscoelastic earth","volume":"69","author":"Yuen","year":"1982","journal-title":"Geophys. J. Int."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1111\/j.1365-246X.1996.tb07036.x","article-title":"Viscoelastic relaxation of a Burgers half-space; implications for the interpretation of the Fennoscandian uplift","volume":"124","author":"Rumpker","year":"1996","journal-title":"Geophys. J. Int."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1007\/s002690100189","article-title":"High-temperature viscoelasticity of fine-grained polycrystalline olivine","volume":"28","author":"Tan","year":"2001","journal-title":"Phys. Chem. Miner."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1061\/(ASCE)0899-1561(2004)16:2(155)","article-title":"A thermodynamic framework for the constitutive modeling of asphalt concrete: Theory and applications","volume":"16","author":"Krishnan","year":"2004","journal-title":"J. Mater. Civ. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/S0377-0257(99)00023-3","article-title":"A thermodynamic frame work for rate type fluid models","volume":"88","author":"Rajagopal","year":"2000","journal-title":"J. Nonnewton. Fluid Mech."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1973","DOI":"10.1016\/j.ijengsci.2004.07.007","article-title":"A note on the flow of a Burgers\u2019 fluid in an orthogonal rheometer","volume":"42","author":"Ravindran","year":"2004","journal-title":"Int. J. Eng. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1367","DOI":"10.1080\/00986441003626078","article-title":"Exact solutions for the unsteady flow of a Burgers\u2019 fluid between two side wals perpendicular to a plate","volume":"197","author":"Khan","year":"2010","journal-title":"Chem. Eng. Commun."},{"key":"ref_13","unstructured":"Akram, S., Anjum, A., Khan, M., and Hussain, A. (2020). On Stokes\u2019 second problem for Burgers\u2019 fluid over a plane wall. J. Appl. Comput. Mech."},{"key":"ref_14","unstructured":"Schlichting, H. (1960). Boundary Layer Theory, McGraw-Hill."},{"key":"ref_15","first-page":"270","article-title":"Exact solutions of the unsteady Navier-Stokes equations","volume":"42","author":"Wang","year":"1969","journal-title":"Appl. Mech. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1146\/annurev.fl.23.010191.001111","article-title":"Exact solutions of the steady-state Navier-Stokes equations","volume":"23","author":"Wang","year":"1991","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1016\/S0020-7462(01)00035-X","article-title":"On the unsteady unidirectional flows generated by impulsive motion of a boundary or sudden application of a pressure gradient","volume":"37","author":"Erdogan","year":"2002","journal-title":"Int. J. Non Linear Mech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/0020-7462(82)90006-3","article-title":"A note on unsteady unidirectional flows of non-Newtonian fluid","volume":"17","author":"Rajagopal","year":"1992","journal-title":"Int. J. Non Linear Mech."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1016\/S0020-7462(98)00063-8","article-title":"Periodic flows of a non-Newtonian fluid between two parallel plates","volume":"34","author":"Siddiqui","year":"1999","journal-title":"Int. J. Non Linear Mech."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.1134\/S0965542516070058","article-title":"Mixed initial-boundary value problem for equations of motion of Kelvin-Voigt fluids","volume":"56","author":"Baranovskii","year":"2016","journal-title":"Comput. Math. Math. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Fetecau, C., Ellahi, R., and Sait, S.M. (2021). Mathematical analysis of Maxwell fluid flow through a porous plate channel induced by a constantly accelerating or oscillating wall. Mathematics, 9.","DOI":"10.3390\/math9010090"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5539007","DOI":"10.1155\/2021\/5539007","article-title":"Analytical Solutions for Two Mixed Initial-Boundary Value Problems Corresponding to Unsteady Motions of Maxwell Fluids through a Porous Plate Channel","volume":"2021","author":"Fetecau","year":"2021","journal-title":"Math. Probl. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s10483-015-1906-7","article-title":"Exact solutions of MHD second Stokes flow of generalized Burgers fluid","volume":"36","author":"Khan","year":"2015","journal-title":"Appl. Math. Mech. Engl."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Fetecau, C., Vieru, D., Abbas, T., and Ellahi, R. (2021). Analytical solutions of upper convected Maxwell fluid with exponential dependence of viscosity under the influence of pressure. Mathematics, 9.","DOI":"10.3390\/math9040334"},{"key":"ref_25","unstructured":"Robert, G.E., and Kaufman, H. (1966). Table of Laplace Transforms, W.B. Saunders Co."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/7\/1109\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:20:59Z","timestamp":1760163659000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/7\/1109"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,22]]},"references-count":25,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["sym13071109"],"URL":"https:\/\/doi.org\/10.3390\/sym13071109","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,6,22]]}}}