{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T06:48:48Z","timestamp":1774334928854,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T00:00:00Z","timestamp":1684972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006701","name":"Deanship of Scientific Research at Umm Al-Qura University","doi-asserted-by":"publisher","award":["23UQU4310392DSR002"],"award-info":[{"award-number":["23UQU4310392DSR002"]}],"id":[{"id":"10.13039\/501100006701","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Numerical and physical simulations of the magnetohydrodynamic mixed convective flow of electrically conducting fluid along avertical magnetized and symmetrically heated plate with slip velocity and thermal slip effects have been performed. The novelty of the present work is to evaluate heat transfer and magnetic flux along the symmetrically magnetized plate with thermal and velocity slip effects. For a smooth algorithm and integration, the linked partial differential equations of the existing fluid flow system are converted into coupled nonlinear ordinary differential equations with specified streaming features and similarity components. By employing the Keller Box strategy, the modified ordinary differential equations (ODEs) are again translated in a suitable format for numerical results. The MATLAB software is used to compute the numerical results, which are then displayed in graphical and tabular form. The influence of several governing parameters on velocity, temperature distribution and magnetic fields in addition to the friction quantity, magnetic flux and heat transfer quantity has been explored. Computational evaluation is performed along the symmetrically heated plate to evaluate the velocity, magnetic field, and temperature together with their gradients. The selection of the magnetic force element, the buoyancy factor 0&lt;\u03be&lt;\u221e , and the Prandtl parameter range 0.1\u2264Pr\u22647.0 were used to set the impacts of magnetic energy and diffusion, respectively. In the domains of magnetic resonance imaging (MRI), artificial heart wolves, interior heart cavities, and nanoburning systems, the present thermodynamic and magnetohydrodynamic issuesare significant.<\/jats:p>","DOI":"10.3390\/sym15061148","type":"journal-article","created":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T01:52:43Z","timestamp":1685065963000},"page":"1148","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Magnetohydrodynamic and Thermal Performance of Electrically Conducting Fluid along the Symmetrical and Vertical Magnetic Plate with Thermal Slip and Velocity Slip Effects"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7290-8398","authenticated-orcid":false,"given":"Khalid Abdulkhaliq M.","family":"Alharbi","sequence":"first","affiliation":[{"name":"Mechanical Engineering Department, College of Engineering, Umm Al-Qura University, Makkah 24382, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1163-6050","authenticated-orcid":false,"given":"Zia","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, The University of Lahore, Sargodha-Campus, Sargodha 40100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2229-2572","authenticated-orcid":false,"given":"Nawishta","family":"Jabeen","sequence":"additional","affiliation":[{"name":"Department of Physics, Fatima Jinnah Women University, Rawalpindi 46000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7016-9181","authenticated-orcid":false,"given":"Muhammad","family":"Ashraf","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10665-008-9248-9","article-title":"Mixed convection flow near an axisymmetric stagnation point on a vertical cylinder","volume":"64","author":"Revnic","year":"2009","journal-title":"J. Eng. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2509","DOI":"10.1016\/S0017-9310(01)00342-8","article-title":"On laminar hydromagnetic mixed convection flow in a vertical channel with symmetric and asymmetric wall heating conditions","volume":"45","author":"Chamkha","year":"2002","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Niazmand, H., and Rahimi, B. (2013). Mixed convective rarefied flows with symmetric and asymmetric heated walls. Comput. Therm. Sci. Int. J., 5.","DOI":"10.1615\/ComputThermalScien.2013004203"},{"key":"ref_4","first-page":"27","article-title":"Effect of Induced Magnetic Field on Mixed Convection Flow in a Vertical Channel with Symmetric and Asymmetric Wall Heating Conditions","volume":"15","author":"Zaidi","year":"2020","journal-title":"Appl. Appl. Math.Int. J. AAM"},{"key":"ref_5","first-page":"605","article-title":"Laminar mixed convection in a symmetrically or asymmetrically heated vertical channel","volume":"9","author":"Habchi","year":"1986","journal-title":"Numer. Heat Transf. Part A Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1162","DOI":"10.1108\/HFF-03-2014-0077","article-title":"Unsteady mixed convection boundary layer flow along a symmetric wedge with variable surface temperature embedded in a saturated porous medium","volume":"25","author":"Ibrahim","year":"2015","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"119","DOI":"10.2298\/TSCI120718110S","article-title":"Mixed convection slip flow with temperature jump along a moving plate in presence of free stream","volume":"19","author":"Singh","year":"2015","journal-title":"Therm. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"027134","DOI":"10.1063\/1.4913719","article-title":"Mixed convection radiative flow of three dimensional Maxwell fluid over an inclined stretching sheet in presence of thermophoresis and convective condition","volume":"5","author":"Ashraf","year":"2015","journal-title":"AIP Adv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"062001","DOI":"10.1088\/1757-899X\/263\/6\/062001","article-title":"Unsteady nonlinear convective Darcy flow of a non-Newtonian fluid over a rotating vertical cone","volume":"Volume 263","author":"Mallikarjuna","year":"2017","journal-title":"IOP Conference Series: Materials Science and Engineering"},{"key":"ref_10","first-page":"98","article-title":"Magnetohydrodynamic (MHD) mixed convection slip flow and heat transfer over a vertical porous plate","volume":"18","author":"Mukhopadhyay","year":"2015","journal-title":"Eng. Sci. Technol. Int. J."},{"key":"ref_11","first-page":"174","article-title":"Hydromagnetic flow of viscous incompressible fluid past a wedge with permeable surface","volume":"89","author":"Mahmood","year":"2009","journal-title":"J. Appl. Math. Mech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"8177","DOI":"10.1007\/s13369-021-06191-5","article-title":"Periodical analysis of convective heat transfer along electrical conducting cone embedded in porous medium","volume":"47","author":"Ilyas","year":"2022","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Maneengam, A., Bouzennada, T., Abderrahmane, A., Guedri, K., Weera, W., Younis, O., and Bouallegue, B. (2022). Numerical study of lid-driven hybrid nanofluid flow in a corrugated porous cavity in the presence of magnetic field. Nanomaterials, 12.","DOI":"10.3390\/nano12142390"},{"key":"ref_14","first-page":"71","article-title":"Simulation of laminar mixed convection recess flow combined with radiation heat transfer","volume":"37","author":"Atashafrooz","year":"2013","journal-title":"Iran. J. Sci. Technol. Trans. Mech. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"10120","DOI":"10.1038\/s41598-022-14259-x","article-title":"Numerical aspects of thermo migrated radiative nanofluid flow towards a moving wedge with combined magnetic force and porous medium","volume":"12","author":"Haq","year":"2022","journal-title":"Sci. Rep."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1685","DOI":"10.1007\/s10483-020-2680-8","article-title":"Darcy-Forchheimer flow with nonlinear mixed convection","volume":"41","author":"Hayat","year":"2020","journal-title":"Appl. Math. Mech."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3455","DOI":"10.2298\/TSCI171213112A","article-title":"Entropy generation analysis of mixed convection with considering magnetohydrodynamic effects in an open C-shaped cavity","volume":"23","author":"Armaghani","year":"2019","journal-title":"Therm. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Khan, U., Zaib, A., Sheikholeslami, M., Wakif, A., and Baleanu, D. (2020). Mixed convective radiative flow through a slender revolution bodies containing molybdenum-disulfide graphene oxide along with generalized hybrid nanoparticles in porous media. Crystals, 10.","DOI":"10.3390\/cryst10090771"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1016\/S1001-6058(15)60523-6","article-title":"Theoretical analysis of slip flow on a rotating cone with viscous dissipation effects","volume":"27","author":"Saleem","year":"2015","journal-title":"J. Hydrodyn. Ser. B"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"100612","DOI":"10.1016\/j.jics.2022.100612","article-title":"The convective heat transfer analysis of the casson nanofluid jet flow under the influence of the movement of gyrotactic microorganisms","volume":"99","author":"Puneeth","year":"2022","journal-title":"J. Indian Chem. Soc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1080\/10407780902864607","article-title":"Application of the finite-volume method to study the effects of baffles on radiative heat transfer in complex enclosures","volume":"55","author":"Guedri","year":"2009","journal-title":"Numer. Heat Transf. Part A Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1016\/j.aej.2016.04.021","article-title":"Finite element simulation of magnetohydrodynamic convective nanofluid slip flow in porous media with nonlinear radiation","volume":"55","author":"Uddin","year":"2016","journal-title":"Alex. Eng. J."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.aej.2015.03.003","article-title":"Magnetohydrodynamic mixed convective slip flow over an inclined porous plate with viscous dissipation and Joule heating","volume":"54","author":"Das","year":"2015","journal-title":"Alex. Eng. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1018","DOI":"10.29020\/nybg.ejpam.v12i3.3455","article-title":"Twice order slip on the flows of fractionalized MHD viscoelastic fluid","volume":"12","author":"Jamil","year":"2019","journal-title":"Eur. J. Pure Appl. Math."},{"key":"ref_25","first-page":"232","article-title":"Effects of second-order slip on the flow of a fractional Maxwell MHD fluid","volume":"24","author":"Liu","year":"2017","journal-title":"J. Assoc. Arab. Univ. Basic Appl. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1007\/s10973-020-09571-5","article-title":"Magneto-thermo analysis of oscillatory flow around a non-conducting horizontal circular cylinder","volume":"142","author":"Ullah","year":"2020","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"13","DOI":"10.2298\/TSCI20S1013U","article-title":"Surface temperature and free stream velocity oscillation effects on mixed convention slip flow from surface of a horizontal circular cylinder","volume":"24","author":"Ullah","year":"2020","journal-title":"Therm. Sci."},{"key":"ref_28","first-page":"109","article-title":"Computational analysis of the oscillatory mixed convection flow along a horizontal circular cylinder in thermally stratified medium","volume":"65","author":"Ullah","year":"2020","journal-title":"CMC Comput. Mater. Contin."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Ullah, Z., Ashraf, M., Sarris, I.E., and Karakasidis, T.E. (2022). The Impact of Reduced Gravity on Oscillatory Mixed Convective Heat Transfer around a Non-Conducting Heated Circular Cylinder. Appl. Sci., 12.","DOI":"10.3390\/app12105081"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"10865","DOI":"10.1007\/s10973-022-11248-0","article-title":"Cattaneo\u2013Christov heat flux model in Darcy\u2013Forchheimer radiative flow of MoS2\u2013SiO2\/kerosene oil between two parallel rotating disks","volume":"147","author":"Yaseen","year":"2022","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"100669","DOI":"10.1016\/j.tsep.2020.100669","article-title":"A multiresolution wavelet optimised finite-difference method for simulation of thermal regenerator","volume":"19","author":"Kumar","year":"2020","journal-title":"Therm. Sci. Eng. Progress"},{"key":"ref_32","unstructured":"Kumar, S., Kumar, G., and Murthy, D.S. (2022). Experimental investigation on thermal performance characteristics of rotating packed bed. Exp. Heat Transf., 1\u201313."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"102341","DOI":"10.1016\/j.csite.2022.102341","article-title":"Combined effects of MHD and slip velocity on oscillatory mixed convective flow around a non-conducting circular cylinder embedded in a porous medium","volume":"38","author":"Ullah","year":"2022","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"124630","DOI":"10.1016\/j.energy.2022.124630","article-title":"Energy loss mechanisms of transition from pump mode to turbine mode of an axial-flow pump under bidirectional conditions","volume":"257","author":"Kan","year":"2022","journal-title":"Energy"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"124532","DOI":"10.1016\/j.energy.2022.124532","article-title":"Energy loss mechanism due to tip leakage flow of axial flow pump as turbine under various operating conditions","volume":"255","author":"Kan","year":"2022","journal-title":"Energy"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Kumar, P., Poonia, H., Ali, L., Shah, N.A., and Chung, J.D. (2023). Significance of Weissenberg Number, Soret Effect and Multiple Slips on the Dynamic of Biconvective Magnetohydrodynamic CarreauNanofuid Flow. Mathematics, 11.","DOI":"10.3390\/math11071685"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Ullah, Z., Bilal, M., Sarris, I.E., and Hussanan, A. (2022). MHD and Thermal Slip Effects on Viscous Fluid over Symmetrically Vertical Heated Plate in Porous Medium: Keller Box Analysis. Symmetry, 14.","DOI":"10.3390\/sym14112421"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.camwa.2022.01.009","article-title":"Melting effect on Cattaneo\u2013Christov and thermal radiation features for aligned MHD nanofluid flow comprising microorganisms to leading edge: FEM approach","volume":"109","author":"Ali","year":"2022","journal-title":"Comput. Math. Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"102247","DOI":"10.1016\/j.csite.2022.102247","article-title":"The numerical simulation of nanoparticle size and thermal radiation with the magnetic field effect based on tangent hyperbolic nanofluid flow","volume":"37","author":"Kumar","year":"2022","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Rehman, S.U., Fatima, N., Ali, B., Imran, M., Ali, L., Shah, N.A., and Chung, J.D. (2022). The Casson dusty nanofluid: Significance of Darcy\u2013forchheimer law, magnetic field, and non-Fourier heat flux model subject to stretch surface. Mathematics, 10.","DOI":"10.3390\/math10162877"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Muthukumaran, C., and Bathrinathan, K. (2020). Mathematical modeling of mixed convection boundary layer flows over a stretching sheet with viscous dissipation in presence of suction and injection. Symmetry, 12.","DOI":"10.3390\/sym12111754"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Tlili, I. (2019). Effects MHD and heat generation on mixed convection flow of Jeffrey fluid in microgravity environment over an inclined stretching sheet. Symmetry, 11.","DOI":"10.3390\/sym11030438"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Ullah, Z., Akkurt, N., Alrihieli, H.F., Eldin, S.M., Alqahtani, A.M., Hussanan, A., and Jabeen, M. (2022). Temperature-Dependent Density and Magnetohydrodynamic Effects on Mixed Convective Heat Transfer along Magnetized Heated Plate in Thermally Stratified Medium Using Keller Box Simulation. Appl. Sci., 12.","DOI":"10.3390\/app122211461"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"4021","DOI":"10.1038\/s41598-023-28379-5","article-title":"Numerical analysis of magnetohydrodynamics Casson nanofluid flow with activation energy, Hall current and thermal radiation","volume":"13","author":"Hussain","year":"2023","journal-title":"Sci. Rep."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/6\/1148\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:41:51Z","timestamp":1760125311000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/6\/1148"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,25]]},"references-count":44,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["sym15061148"],"URL":"https:\/\/doi.org\/10.3390\/sym15061148","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,25]]}}}