{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T14:06:09Z","timestamp":1777385169975,"version":"3.51.4"},"reference-count":24,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,4,3]],"date-time":"2024-04-03T00:00:00Z","timestamp":1712102400000},"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>The time-periodic plane Poiseuille flow of electrically conducting incompressible generalized Burgers fluids through a porous medium is analytically and numerically investigated in the presence of a transverse uniform magnetic field. The main purpose is to provide analytical expressions for the dimensionless steady-state fluid velocity, non-trivial shear stress and Darcy\u2019s resistance, which can be used to bring to light important characteristics concerning fluid behavior. Similar solutions corresponding to the Poiseuille flow of the same fluids induced by a constant pressure gradient are obtained as limiting cases of previous results. The present results reduce to known solutions from the literature when magnetic and porous effects are neglected, and their validation is graphically proved. The needed time to reach a steady state has been graphically determined. It was found that the steady state is later obtained in the absence of a magnetic field and porous medium. The impact of a magnetic field and porous medium on the fluid velocity, shear stress and flow resistance has been systematically examined and elucidated through graphical representations. The findings reveal that the presence of a magnetic field or porous medium results in a reduction in the fluid velocity, accompanied by an increase in the flow resistance.<\/jats:p>","DOI":"10.3390\/sym16040425","type":"journal-article","created":{"date-parts":[[2024,4,3]],"date-time":"2024-04-03T11:01:41Z","timestamp":1712142101000},"page":"425","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["MHD Time-Periodic Plane Poiseuille Flow of Generalized Burgers Fluids through a Porous Medium"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9056-0911","authenticated-orcid":false,"given":"Constantin","family":"Fetecau","sequence":"first","affiliation":[{"name":"Section of Mathematics, Academy of Romanian Scientists, 3 Ilfov, 050044 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shehraz","family":"Akhtar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Rahim Yar Khan Campus, Rahim Yar Khan 64200, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7250-3131","authenticated-orcid":false,"given":"Costic\u0103","family":"Moro\u015fanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, \u201cAlexandru Ioan Cuza\u201d University, 700506 Iasi, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Coleman, B.D., Markovitz, H., and Noll, W. (1966). Viscometric Flows of Non-Newtonian Fluids. Theory and Experiment, Springer.","DOI":"10.1007\/978-3-642-88655-3"},{"key":"ref_2","unstructured":"Spurk, J.H., and Aksel, N. (2008). Fluid Mechanics, Springer. [2nd ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/0020-7462(82)90006-3","article-title":"A note on unsteady unidirectional flows of a non-Newtonian fluid","volume":"17","author":"Rajagopal","year":"1982","journal-title":"Int. J. Non-Linear Mech."},{"key":"ref_4","first-page":"92","article-title":"Analytical solution for transient one-dimensional Couette flow considering constant and time-dependent pressure gradients","volume":"8","author":"Mendiburu","year":"2009","journal-title":"Eng. Thermica (Therm. Eng.)"},{"key":"ref_5","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_6","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0020-7225(00)00026-4","article-title":"Some simple flows of an Oldroyd-B fluid","volume":"39","author":"Hayat","year":"2001","journal-title":"Int. J. Eng. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1016\/j.ijnonlinmec.2006.06.004","article-title":"Steady-state solutions for some simple flows of generalized Burgers fluids","volume":"41","author":"Fetecau","year":"2006","journal-title":"Int. J. Non-Linear Mech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1089","DOI":"10.1016\/j.cnsns.2011.07.037","article-title":"Exact analytical solutions for the Poiseuille and Couette-Poiseuille flow of third grade fluid between parallel plates","volume":"17","author":"Danish","year":"2012","journal-title":"Commun. Nonlinear Sci. Numer. Simulat."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Baranovskii, E. (2024). Analytical solutions to the unsteady Poiseuille flow of a second grade fluid with slip boundary conditions. Polymers, 16.","DOI":"10.3390\/polym16020179"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"334","DOI":"10.2514\/8.8535","article-title":"Magneto hydrodynamic effects on the formation of Couette flow","volume":"27","author":"Tao","year":"1960","journal-title":"J. Aerospace Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1143\/JPSJ.17.393","article-title":"Flow formation in Couette motion in magneto hydrodynamics","volume":"17","author":"Katagiri","year":"1962","journal-title":"Phys. Soc. Jpn."},{"key":"ref_12","first-page":"1977","article-title":"Unsteady magneto-hydrodynamic fluid flow through a channel","volume":"28","author":"Singh","year":"1978","journal-title":"J. Sci. Res. Banaras Hindu Univ."},{"key":"ref_13","first-page":"87","article-title":"On the steady MHD Couette flow between two infinite parallel plates in an uniform transverse magnetic field","volume":"5","author":"Kiema","year":"2015","journal-title":"J. Appl. Math. Bioinform."},{"key":"ref_14","first-page":"73","article-title":"MHD flow of Burgers\u2019 fluid under the effect of pressure gradient through a porous material pipe","volume":"50","author":"Safdar","year":"2018","journal-title":"Punjab Univ. J. Math."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Fetecau, C., and Vieru, D. (2021). Symmetric and non-symmetric flows of Burgers\u2019 fluids through porous media between parallel plates. Symmetry, 13.","DOI":"10.3390\/sym13071109"},{"key":"ref_16","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 application","volume":"16","author":"Krishnan","year":"2004","journal-title":"J. Mater. Civil Eng."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Cramer, K.R., and Pai, S.I. (1973). Magnetofluid Dynamics for Engineers and Applied Physicists, McGraw-Hill.","DOI":"10.1002\/eej.4390930120"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1186\/s13661-014-0152-0","article-title":"Flow of generalized Burgers fluid between parallel walls induced by rectified sine pulses stress","volume":"2014","author":"Sultan","year":"2014","journal-title":"Bound. Value Probl."},{"key":"ref_19","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.\u2013Engl."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Fetecau, C., Akhtar, S., and Morosanu, C. (2023). Permanent solutions for MHD motions of generalized Burgers fluids adjacent to an unbounded plate subject to oscillatory shear stresses. Symmetry, 15.","DOI":"10.3390\/sym15091683"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0020-7462(99)00019-0","article-title":"A note on an unsteady flow of a viscous fluid due to an oscillating plane wall","volume":"35","author":"Erdogan","year":"2000","journal-title":"Int. J. Non-Linear Mech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2054","DOI":"10.1016\/j.ijengsci.2010.04.009","article-title":"Revisiting Stokes first and second problems for fluids with pressure-dependent viscosity","volume":"48","author":"Prusa","year":"2010","journal-title":"Int. J. Eng. Sci."},{"key":"ref_23","unstructured":"Sneddon, I.N. (1951). Fourier Transforms, McGraw-Hill."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"e2923","DOI":"10.1002\/apj.2923","article-title":"Mixed convective magnetized GO-MoS2\/H2O hybrid nanofluid flow about a permeable rotating disk","volume":"18","author":"Kulkarni","year":"2023","journal-title":"Asia-Pac. J. Chem. Eng."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/4\/425\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:23:05Z","timestamp":1760106185000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/4\/425"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,3]]},"references-count":24,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["sym16040425"],"URL":"https:\/\/doi.org\/10.3390\/sym16040425","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,3]]}}}