{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T20:27:24Z","timestamp":1775161644934,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,21]],"date-time":"2022-01-21T00:00:00Z","timestamp":1642723200000},"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 purpose of this research is to analyze the general equations of double diffusive magneto-free convection in an Oldroyd-B fluid flow based on the fundamental symmetry that are presented in non-dimensional form and are applied to a moving heated vertical plate as the boundary layer flow up, with the existence of an external magnetic field that is either moving or fixed consistent with the plate. The thermal transport phenomenon in the presence of constant concentration, coupled with a first order chemical reaction under the exponential heating of the symmetry of fluid flow, is analyzed. The Laplace transform method is applied symmetrically to tackle the non-dimensional partial differential equations for velocity, mass and energy. The contribution of mass, thermal and mechanical components on the dynamics of fluid are presented and discussed independently. An interesting property regarding the behavior of the fluid velocity is found when the movement is observed in the magnetic intensity along with the plate. In that situation, the fluid velocity is not zero when it is far and away from the plate. Moreover, the heat transfer aspects, flow dynamics and their credence on the parameters are drawn out by graphical illustrations. Furthermore, some special cases for the movement of the plate are also studied.<\/jats:p>","DOI":"10.3390\/sym14020209","type":"journal-article","created":{"date-parts":[[2022,1,23]],"date-time":"2022-01-23T20:36:27Z","timestamp":1642970187000},"page":"209","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Double Diffusive Magneto-Free-Convection Flow of Oldroyd-B Fluid over a Vertical Plate with Heat and Mass Flux"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5153-297X","authenticated-orcid":false,"given":"Muhammad Bilal","family":"Riaz","sequence":"first","affiliation":[{"name":"Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1\/15 Stefanowskiego St., 90-924 Lodz, Poland"},{"name":"Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan"}]},{"given":"Aziz Ur","family":"Rehman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0387-921X","authenticated-orcid":false,"given":"Jan","family":"Awrejcewicz","sequence":"additional","affiliation":[{"name":"Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1\/15 Stefanowskiego St., 90-924 Lodz, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3303-0623","authenticated-orcid":false,"given":"Fahd","family":"Jarad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Cankaya University, 06790 Ankara, Turkey"},{"name":"King Abdulaziz University, P. O. Box 80257, Jeddah 21589, Saudi Arabia"},{"name":"Department of Medical Research, China Medical University, Taichung 40402, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Radko, T. (2013). Double-Diffusive Convection, Cambridge University Press.","DOI":"10.1017\/CBO9781139034173"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1146\/annurev.ea.12.050184.000303","article-title":"Double-Diffusive Convection Due to Crystallization in Magmas","volume":"12","author":"Huppert","year":"1984","journal-title":"Ann. Rev. Earth Planet Sci."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Sahoo, S.K., Ahmad, H., Tariq, M., Kodamasingh, B., Aydi, H., and De la Sen, M. (2021). Hermite\u2013Hadamard Type Inequalities Involving k-Fractional Operator for (h\u2014,m)-Convex Functions. Symmetry, 13.","DOI":"10.3390\/sym13091686"},{"key":"ref_4","first-page":"10883","article-title":"Enhanced sedimentation beneath particle-laden flows in lakes and the ocean due to double-diffusive convection","volume":"43","author":"Davarpanah","year":"2016","journal-title":"Geophys. Res. Lett."},{"key":"ref_5","first-page":"376","article-title":"Effect of radiation on MHD free convection flow past an impulsively moving vertical plate with ramped wall temperature","volume":"3","author":"Ghara","year":"2012","journal-title":"Am. J. Sci Ind. Res."},{"key":"ref_6","first-page":"1","article-title":"Exact solutions of unsteady MHD free convection in a heat absorbing fluid flow past flat plate with ramped wall temperature","volume":"247","author":"Nandkeolyar","year":"2013","journal-title":"Bound. Value Probl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"714","DOI":"10.5560\/zna.2014-0068","article-title":"Magnetohydrodynamic natural convection flow with Newtonian heating and mass diffusion over an infinite plate that applies shear stress to a viscous fluid","volume":"69","author":"Vieru","year":"2014","journal-title":"Z. Naturforsch."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/j.jksus.2014.12.002","article-title":"Fully developed MHD natural convection flow in a vertical annular microchannel: An exact solution","volume":"27","author":"Jha","year":"2015","journal-title":"J. King Saud Univ. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1007\/s10973-019-08943-w","article-title":"Magnetohydrodynamic flow and heat transfer of ferrofluid in a channel with non-symmetric cavities","volume":"140","author":"Hussain","year":"2020","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_10","first-page":"19","article-title":"Hall effects on unsteady MHD free convective flow past an accelerated moving vertical plate with viscous and Joule dissipations","volume":"70","author":"Sarkar","year":"2013","journal-title":"Int. J. Comput. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1007\/s00231-010-0740-1","article-title":"MHD natural convection flow with radiative heat transfer past an impulsively moving plate with ramped wall temperature","volume":"47","author":"Seth","year":"2011","journal-title":"Heat Mass Transf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1134\/S0021894415040069","article-title":"Non-Darcy natural convection from a vertical plate with a uniform wall temperature and concentration in a doubly stratified porous medium","volume":"56","author":"Srinivasacharya","year":"2015","journal-title":"J. Appl. Mech. Tech. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1002\/zamm.201200008","article-title":"Unsteady magnetohydrodynamic free convection flow past an accelerated vertical plate with constant heat flux and heat generation or absorptio","volume":"93","author":"Narahari","year":"2013","journal-title":"Z Angew Math Mech."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/s40065-017-0187-z","article-title":"General solution for MHD-free convection flow over a vertical plate with ramped wall temperature and chemical reaction","volume":"7","author":"Shah","year":"2018","journal-title":"Arab. J. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.cjph.2019.05.008","article-title":"Effects of Double Stratification and Heat Flux Damping on Convective Flows over a Vertical Cylinder","volume":"60","author":"Shah","year":"2019","journal-title":"Chin. J. Phys."},{"key":"ref_16","first-page":"49","article-title":"On the dynamical theory of gases. Philos","volume":"157","author":"Maxwell","year":"1867","journal-title":"Trans. R. Soc. Lond."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"104367","DOI":"10.1016\/j.rinp.2021.104367","article-title":"Exact solutions of thermomagetized unsteady non-singularized jeffery fluid: Effects of ramped velocity, concentration with Newtonian heating","volume":"26","author":"Rehman","year":"2021","journal-title":"Results Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"13272","DOI":"10.3934\/math.2021768","article-title":"Some Ostrowski type inequalities via n-polynomial exponentially s-convex functions and their applications","volume":"6","author":"Tariq","year":"2021","journal-title":"AIMS Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1016\/j.rinp.2018.01.036","article-title":"Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary","volume":"8","author":"Imran","year":"2018","journal-title":"Results Phys."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Rehman, A.U., Riaz, M.B., Akgul, A., Saeed, S.T., and Baleanu, D. (2021). Heat and mass transport impact on MHD second grade fluid: A comparative analysis of fractional operators. Heat Transf., 1\u201323.","DOI":"10.1002\/htj.22216"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Anwar, T., and Kumam, P. (2020). Watthayu and Asifa, Influence of Ramped Wall Temperature and Ramped Wall Velocity on Unsteady Magnetohydrodynamic Convective Maxwell Fluid Flow. Symmetry, 12.","DOI":"10.3390\/sym12030392"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1080\/00986445.2011.611058","article-title":"Effects of thermal radiation and mass diffusion on free convection flow near a vertical plate with Newtonian heating","volume":"199","author":"Narahari","year":"2012","journal-title":"Chem. Eng. Comm."},{"key":"ref_23","first-page":"130","article-title":"Radiative and porous effects on free convection flow near a vertical plate that applies shear stress to the fluid","volume":"68","author":"Fetecau","year":"2013","journal-title":"Z. Natur. For Sch."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1007\/BF00653524","article-title":"A class of exact solutions of the unsteady magneto hydrodynamic free-convection flows","volume":"112","author":"Tokis","year":"1985","journal-title":"Astrophys. Space Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/209\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:05:41Z","timestamp":1760133941000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,21]]},"references-count":24,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["sym14020209"],"URL":"https:\/\/doi.org\/10.3390\/sym14020209","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,21]]}}}