{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T07:55:01Z","timestamp":1790668501671,"version":"4.1.0"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discover Nano"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>This study introduces a novel analysis of Maxwell nanofluid flow over a stretching surface, integrating multiple coupled physical mechanisms previously overlooked in the literature. The comprehensive model incorporates boundary convection, internal heat generation, Ohmic heating, temperature-dependent transport properties (viscosity, density, and diffusivity), and viscous dissipation effects. This holistic approach distinguishes the current work from earlier studies, which have not simultaneously examined the coupled effects of these interacting mechanisms within a unified Maxwell nanofluid model. A mathematical model is developed and solved numerically using similarity transformations, the shooting method, and the fourth-order Runge-Kutta scheme. Validation against established benchmarks confirms the method\u2019s reliability. Further, the results demonstrate the coupled influence of key parameters on flow, thermal, and concentration profiles, along with their effects on skin friction, heat transfer (Nusselt number), and mass transfer (Sherwood number) rates. This study addresses a significant research void while providing useful theoretical guidance for the design and optimization of polymer processing, heat exchanger systems, and nanofluid-based thermal management technologies. A central revelation of this research is the dual role of temperature-sensitive density: it simultaneously amplifies thermal distribution while attenuating both nanoparticle concentration and fluid velocity. This parameter further enhances thermal and mass transfer rates while increasing the surface drag, indicating its important role in the coupled transport behavior of Maxwell nanofluids. Additionally, heat generation and convective mechanisms, as anticipated, elevate temperature profiles but inhibit flow momentum, resulting in suppressed velocity and refined control over transport behavior. Quantitatively, increasing the porous parameter enhances the skin-friction coefficient, local Nusselt number, and local Sherwood number by approximately 20.8%, 45.6%, and 3.0%, respectively, while increasing the density parameter raises these quantities by about 75.1%, 79.8%, and 69.2%, respectively. These quantitative improvements highlight the theoretical potential of the proposed model to support the design and optimization of heat exchangers, polymer processing, and nanofluid-based thermal management systems, while accounting for the associated increase in surface drag.<\/jats:p>","DOI":"10.1186\/s11671-026-04947-2","type":"journal-article","created":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T07:00:18Z","timestamp":1790665218000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analysis of Maxwell nanofluid model with convective variations, variable-density and heat generation in a porous medium"],"prefix":"10.1186","volume":"21","author":[{"given":"Mohammed","family":"Alrehili","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,9,29]]},"reference":[{"key":"4947_CR1","doi-asserted-by":"publisher","first-page":"e22740","DOI":"10.1016\/j.heliyon.2023.e22740","volume":"9","author":"SI Abdelsalam","year":"2023","unstructured":"Abdelsalam SI, Abbas WW, Megahed AM, Said AAM. A comparative study on the rheological properties of upper convected Maxwell fluid along a permeable stretched sheet. Heliyon. 2023;9:e22740.","journal-title":"Heliyon"},{"key":"4947_CR2","first-page":"1200","volume":"45","author":"N Venkatesh","year":"2023","unstructured":"Venkatesh N, Raju RS, Kumar MA, Vijayabhaskar C. Heat and mass transfer in Maxwell fluid with nanoparticles past a stretching sheet in the existence of thermal radiation and chemical reaction. Int J Model Simul. 2023;45:1200\u201313.","journal-title":"Int J Model Simul"},{"key":"4947_CR3","doi-asserted-by":"publisher","first-page":"100644","DOI":"10.1016\/j.padiff.2024.100644","volume":"9","author":"IC Mandal","year":"2024","unstructured":"Mandal IC, Mukhopadhyay S, Mandal MS. MHD mixed convective Maxwell liquid flow passing an unsteady stretched sheet. Partial Differ Equ Appl Math. 2024;9:100644.","journal-title":"Partial Differ Equ Appl Math"},{"key":"4947_CR4","doi-asserted-by":"publisher","first-page":"100832","DOI":"10.1016\/j.ijft.2024.100832","volume":"24","author":"JR Gurejala","year":"2024","unstructured":"Gurejala JR, Pampera M, Pemmaraju RS, Rallabandi SR. Impact of viscous dissipation on MHD flow of Maxwell nanofluid across a linear stretching sheet. Int J Thermofluids. 2024;24:100832.","journal-title":"Int J Thermofluids"},{"key":"4947_CR5","doi-asserted-by":"publisher","first-page":"109322","DOI":"10.1016\/j.ijheatfluidflow.2024.109322","volume":"106","author":"MA Basit","year":"2024","unstructured":"Basit MA, Imran M, Tahir M, Eladeb A, Kolsi L. Numerical analysis of mathematical model for heat and mass transfer through Bioconvective Maxwell nanofluid flow subject to Darcy-Forcheimer and Lorentz forces. Int J Heat Fluid Flow. 2024;106:109322.","journal-title":"Int J Heat Fluid Flow"},{"key":"4947_CR6","doi-asserted-by":"publisher","first-page":"e70204","DOI":"10.1002\/zamm.70204","volume":"105","author":"KW Zeeshan","year":"2025","unstructured":"Zeeshan KW, Elmasry Y, Thaljaoui A, Kallel M, AL Garalleh H. Mathematical model and stability analysis of thermally magnetized Maxwell fluid flow over an unsteady stretching sheet. ZAMM. 2025;105:e70204.","journal-title":"ZAMM"},{"key":"4947_CR7","doi-asserted-by":"publisher","first-page":"035211","DOI":"10.1088\/1402-4896\/ab4ba9","volume":"95","author":"MS Anwar","year":"2020","unstructured":"Anwar MS. Numerical study of transport phenomena in a nanofluid using fractional relaxation times in Buongiorno model. Phys Scr. 2020;95:035211.","journal-title":"Phys Scr"},{"key":"4947_CR8","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s12043-021-02217-7","volume":"95","author":"M Irfan","year":"2021","unstructured":"Irfan M, Rafiq K, Anwar MS, Khan M, Khan WA, Iqbal K. Evaluating the performance of new mass flux theory on Carreau nanofluid using the thermal aspects of convective heat transport. Pramana-J Phys. 2021;95:203.","journal-title":"Pramana-J Phys"},{"key":"4947_CR9","doi-asserted-by":"publisher","first-page":"025205","DOI":"10.1088\/1402-4896\/acab92","volume":"98","author":"M Sarfraz","year":"2023","unstructured":"Sarfraz M, Khan M. Thermodynamic irreversibility analysis of water conveying argentum and titania nanoparticles subject to inclined stretching surface. Phys Scr. 2023;98:025205.","journal-title":"Phys Scr"},{"key":"4947_CR10","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.aej.2024.05.010","volume":"100","author":"M Muhammad, Sarfraz","year":"2024","unstructured":"Muhammad, Sarfraz M, Khan M, Alqahtani AS, Malik MY. Simulation of gyrotactic microorganisms in Jeffrey nanofluid using Buongiorno model and Ohmic heating. Alexandria Eng J. 2024;100:32\u201341.","journal-title":"Alexandria Eng J"},{"key":"4947_CR11","doi-asserted-by":"publisher","first-page":"36506","DOI":"10.1038\/s41598-025-20648-9","volume":"15","author":"W Rajhi","year":"2025","unstructured":"Rajhi W, Ben Hamida MB, Adnan Walelign T, Ahmad H, Khan SU, Alrasheedi N. Comparative study of thermal response for tetra nanofluid through a vertically oriented needle device inspired by combined convection and porous media. Sci Rep. 2025;15:36506.","journal-title":"Sci Rep"},{"key":"4947_CR12","doi-asserted-by":"publisher","first-page":"100349","DOI":"10.1016\/j.physo.2025.100349","volume":"25","author":"B Gizachew","year":"2025","unstructured":"Gizachew B, Dessie H, Haile E, Walelign T. Investigation of time-dependent MHD flow characteristics of Williamson nanofluid across a heated, permeable and inclined stretching sheet within a porous medium. Phys Open. 2025;25:100349.","journal-title":"Phys Open"},{"key":"4947_CR13","doi-asserted-by":"publisher","first-page":"707","DOI":"10.1080\/17455030.2022.2157507","volume":"36","author":"V Puneeth","year":"2026","unstructured":"Puneeth V, Anwar MS, Khan MR. Bioconvective Darcy-Frochherimer flow of the Ree-Eyring nanofluid through a stretching sheet with velocity and thermal slips. Waves Random Complex Media. 2026;36:707\u201328.","journal-title":"Waves Random Complex Media"},{"key":"4947_CR14","doi-asserted-by":"publisher","first-page":"100857","DOI":"10.1016\/j.rsurfi.2026.100857","volume":"24","author":"SU Khan","year":"2026","unstructured":"Khan SU, Abdalrahem MK, Pasha AA, Djouider F, Waqas M, Bourchak M, Walelign T. Triple diffusion flow of radiated Prandtl nanofluid with diverse thermal features: A mathematical analysis. Res Surf Interfaces. 2026;24:100857.","journal-title":"Res Surf Interfaces"},{"key":"4947_CR15","doi-asserted-by":"publisher","first-page":"2748","DOI":"10.1080\/17455030.2023.2172626","volume":"36","author":"M Yasir","year":"2026","unstructured":"Yasir M, Khan M, Ahmed A, Sarfraz M. Flow of Oldroyd-B nanofluid in non-inertial frame inspired by Cattaneo-Christov theory. Waves Random Complex Media. 2026;36:2748\u201359.","journal-title":"Waves Random Complex Media"},{"key":"4947_CR16","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1007\/s42452-026-08850-4","volume":"8","author":"A Majeed","year":"2026","unstructured":"Majeed A, Ali MM, Alkhafaji A, Singh NSS, Jawad M, Walelign T. Advanced bioconvective hydromagnetic Ree-Eyring nanofluid transport with Cattaneo-Christov heat flux and gyrotactic microorganisms in a Darcy-Forchheimer medium. Discov Appl Sci. 2026;8:638.","journal-title":"Discov Appl Sci"},{"key":"4947_CR17","doi-asserted-by":"publisher","first-page":"880","DOI":"10.1080\/01430750.2022.2156607","volume":"44","author":"S Baag","year":"2022","unstructured":"Baag S, Panda S, Pattnaik PK, Mishra SR. Free convection of conducting nanofluid past an expanding surface with heat source with convective heating boundary conditions. Int J Ambient Energy. 2022;44:880\u201391.","journal-title":"Int J Ambient Energy"},{"key":"4947_CR18","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-023-42609-w","volume":"13","author":"W Abbas","year":"2023","unstructured":"Abbas W, Megahed AM, Emam MS, Sadek HMH. MHD dissipative Powell-Eyring fluid flow due to a stretching sheet with convective boundary conditions and slip velocity. Sci Rep. 2023;13:15674.","journal-title":"Sci Rep"},{"key":"4947_CR19","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/s12043-023-02676-0","volume":"97","author":"M Dhlamini","year":"2023","unstructured":"Dhlamini M, Zondo K, Mondal H, Sibanda P, Shaw S, Motsa SS, Mkhatshwa MP, Magodora M. Second-grade bioconvection flow of a nanofluid with slip convective boundary conditions. Pramana-J Phys. 2023;97:197.","journal-title":"Pramana-J Phys"},{"key":"4947_CR20","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/s43995-024-00056-2","volume":"15","author":"M Gundagani","year":"2024","unstructured":"Gundagani M, Babu NVN, Gadially D, Bhati SM, Sanjay Ch, Kasturi VN. Study of Nano-Powell-Erying fluid flow past a porous stretching sheet by the effects of MHD, thermal and mass convective boundary conditions. J Umm Al-Qura Univ Eng Archit. 2024;15:271\u201381.","journal-title":"J Umm Al-Qura Univ Eng Archit"},{"key":"4947_CR21","doi-asserted-by":"publisher","first-page":"e25088","DOI":"10.1016\/j.heliyon.2024.e25088","volume":"10","author":"P Francis","year":"2024","unstructured":"Francis P, Sambath P, Gamiz UF, Noeiaghdam S, Dinarvand S. Computational analysis of bio-convective eyring-powell nanofluid flow with magneto-hydrodynamic effects over an isothermal cone surface with convective boundary condition. Heliyon. 2024;10:e25088.","journal-title":"Heliyon"},{"key":"4947_CR22","doi-asserted-by":"publisher","first-page":"2165","DOI":"10.1007\/s10973-024-13804-2","volume":"150","author":"S Panda","year":"2025","unstructured":"Panda S, Pattnaik PK, Mishra SR, Baithalu R. Bi-directional tangent hyperbolic MHD hybrid nanofluid flow over an expanding surface with Darcy dissipation connecting to velocity slip and convective boundary condition. J Therm Anal Calorim. 2025;150:2165\u201379.","journal-title":"J Therm Anal Calorim"},{"key":"4947_CR23","first-page":"6576","volume":"46","author":"D Yadav","year":"2021","unstructured":"Yadav D, Nirala A, Kumar R, Singh PK. Density variation in nanofluids as a function of concentration and temperature. Mater Today: Proc. 2021;46:6576\u201380.","journal-title":"Mater Today: Proc"},{"key":"4947_CR24","doi-asserted-by":"publisher","first-page":"101640","DOI":"10.1016\/j.csite.2021.101640","volume":"28","author":"A Abbas","year":"2021","unstructured":"Abbas A, Ijaz I, Ashraf M, Ahmad H. Combined effects of variable density and thermal radiation on MHD Sakiadis flow. Case Stud Therm Eng. 2021;28:101640.","journal-title":"Case Stud Therm Eng"},{"key":"4947_CR25","doi-asserted-by":"publisher","first-page":"101815","DOI":"10.1016\/j.tsep.2023.101815","volume":"41","author":"F Gamaoun","year":"2023","unstructured":"Gamaoun F, Ullah Z, Ahammad NA, Fadhl BM, Makhdoum BM, Khan AA. Effects of thermal radiation and variable density of nanofluid heat transfer along a stretching sheet by using Keller Box approach under magnetic field. Therm Sci Eng Prog. 2023;41:101815.","journal-title":"Therm Sci Eng Prog"},{"key":"4947_CR26","first-page":"101413","volume":"20","author":"Z Ullah","year":"2023","unstructured":"Ullah Z, Abbas A, El-Zahar ER, Seddek LF, Akgul A, Hassan AM. Significance of thermal density and viscous dissipation on heat and mass transfer of chemically reactive nanofluid flow along stretching sheet under magnetic field. Res Eng. 2023;20:101413.","journal-title":"Res Eng"},{"key":"4947_CR27","doi-asserted-by":"publisher","first-page":"105260","DOI":"10.1016\/j.csite.2024.105260","volume":"63","author":"Z Ullah","year":"2024","unstructured":"Ullah Z, Alam MM, Tariq U, Mahrous YM, Merga FE, Albouchi F, Haider I, Faqihi AA. Variable density and heat generation impact on chemically reactive carreau nanofluid heat-mass transfer over stretching sheet with convective heat condition. Case Stud Therm Eng. 2024;63:105260.","journal-title":"Case Stud Therm Eng"},{"key":"4947_CR28","doi-asserted-by":"publisher","first-page":"106168","DOI":"10.1016\/j.csite.2025.106168","volume":"71","author":"NB Khedher","year":"2025","unstructured":"Khedher NB, Ullah Z, Alam MM, Al Arni S, Elbadawi I, Makinde OD, Boujelbene M. Significance of thermal conductivity and variable density on heat and mass transfer of MHD second-grade nanofluid along high-temperature polymer surface. Case Stud Therm Eng. 2025;71:106168.","journal-title":"Case Stud Therm Eng"},{"key":"4947_CR29","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.matcom.2021.02.018","volume":"187","author":"AM Megahed","year":"2021","unstructured":"Megahed AM. Improvement of heat transfer mechanism through a Maxwell fluid flow over a stretching sheet embedded in a porous medium and convectively heated. Math Comput Simul. 2021;187:97\u2013109.","journal-title":"Math Comput Simul"},{"key":"4947_CR30","doi-asserted-by":"publisher","first-page":"102768","DOI":"10.1016\/j.csite.2023.102768","volume":"42","author":"M Alrehili","year":"2023","unstructured":"Alrehili M. Improvement for engineering applications through a dissipative Carreau nanofluid fluid flow due to a nonlinearly stretching sheet with thermal radiation. Case Stud Therm Eng. 2023;42:102768.","journal-title":"Case Stud Therm Eng"},{"key":"4947_CR31","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1007\/s12648-018-1196-2","volume":"92","author":"ST Mohyud Din","year":"2018","unstructured":"Mohyud Din ST, Zubair T, Usman M, Hamid M, Rafiq M, Mohsin S. Investigation of heat and mass transfer under the influence of variable diffusion coefficient and thermal conductivity. Indian J Phys. 2018;92:1109\u201317.","journal-title":"Indian J Phys"},{"key":"4947_CR32","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1007\/s10891-012-0658-1","volume":"85","author":"S Siddiqa","year":"2012","unstructured":"Siddiqa S, Asghar S, Hossain MA. Radiation effects in mixed convection flow of a viscous fluid having temperature-dependent density along a permeable vertical plate. J Eng Phys Thermophys. 2012;85:339\u201348.","journal-title":"J Eng Phys Thermophys"},{"key":"4947_CR33","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1007\/s10808-009-0111-1","volume":"50","author":"MAA Mahmoud","year":"2009","unstructured":"Mahmoud MAA, Megahed AM. Effects of viscous dissipation and heat generation (absorption) in a thermal boundary layer of a non-Newtonian fluid over a continuously moving permeable at plate. J Appl Mech Tech Phys. 2009;50:819\u201325.","journal-title":"J Appl Mech Tech Phys"},{"key":"4947_CR34","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/s11012-011-9448-7","volume":"47","author":"MS Abel","year":"2012","unstructured":"Abel MS, Tawade JV, Nandeppanavar MM. MHD flow and heat transfer for the upper-convected Maxwell fluid over a stretching sheet. Meccanica. 2012;47:385\u201393.","journal-title":"Meccanica"}],"container-title":["Discover Nano"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s11671-026-04947-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s11671-026-04947-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s11671-026-04947-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T07:00:19Z","timestamp":1790665219000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1186\/s11671-026-04947-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,29]]},"references-count":34,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["4947"],"URL":"https:\/\/doi.org\/10.1186\/s11671-026-04947-2","relation":{},"ISSN":["2731-9229"],"issn-type":[{"value":"2731-9229","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,29]]},"assertion":[{"value":"2 July 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 September 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 September 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Not applicable.","order":1,"name":"Ethics","label":"Ethical approval","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","label":"Consent to publish","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":3,"name":"Ethics","label":"Consent to participate","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":4,"name":"Ethics","label":"Clinical trial number","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":5,"name":"Ethics","label":"Competing interests","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"478"}}