{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T23:56:57Z","timestamp":1740182217494,"version":"3.37.3"},"reference-count":45,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T00:00:00Z","timestamp":1722384000000},"content-version":"vor","delay-in-days":28,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Foreign Expert Project","award":["QN2023001001"]},{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["IS23046\/ZW001A00202301"],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Beijing Postdoctoral Research Activities","award":["Q6001A00202301"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,7,3]]},"abstract":"Abstract<\/jats:title>\n Nanoparticles have gained recognition for significantly improving convective heat transfer efficiency near boundary layer flows. The characteristics of both momentum and thermal boundary layers are significantly influenced by the Prandtl number, which holds a crucial role. In this vein, the current study conducted a detailed computational analysis of the mixed convection flow of $\\gamma$Al$_2$O$_3$-H$_2$O and $\\gamma$Al$_2$O$_3$-C$_2$H$_6$O$_2$ nanofluids over a stretching surface. This research integrates an effective Prandtl number, utilizing viscosity and thermal conductivity models based on empirical findings. Additionally, a unique double-fractional constitutive model is debuted to accurately evaluate the effective Prandtl number\u2019s function in the boundary layer. The equations\u00a0were solved using a numerical technique that combined the finite-difference method with the L$_1$ algorithm. This investigation presents numerical findings related to the velocity, temperature distributions, wall shear stress coefficient, and heat transfer coefficient, contrasting scenarios with and without the effective Prandtl number. The research shows that integrating nanoparticles into the base fluids reduces the temperature of the nanofluid with an effective Prandtl number while enhancing the heat transfer rate irrespective of its presence. Nonetheless, the introduction of a fractional parameter reduced the heat transfer efficiency within the system. Notably, the $\\gamma$Al$_2$O$_3$-C$_2$H$_6$O$_2$ nanofluid demonstrates superior heat transfer enhancement capabilities compared to its $\\gamma$Al$_2$O$_3$-H$_2$O counterpart but also exacerbates the drag coefficient more significantly. Many practical applications of this study include electronics cooling, industrial process heat exchangers, and rotating and stationary gas turbines in power plants, and efficient heat exchangers in aircraft.<\/jats:p>","DOI":"10.1093\/jcde\/qwae071","type":"journal-article","created":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T00:37:21Z","timestamp":1722472641000},"page":"319-331","source":"Crossref","is-referenced-by-count":2,"title":["Fractional numerical analysis of \u03b3-Al2O3 nanofluid flows with effective Prandtl number for enhanced heat transfer"],"prefix":"10.1093","volume":"11","author":[{"given":"Mumtaz","family":"Khan","sequence":"first","affiliation":[{"name":"Faculty of Science, Jiangsu University , Zhenjiang, Jiangsu 212013 , PR China"}]},{"given":"Dianchen","family":"Lu","sequence":"additional","affiliation":[{"name":"Faculty of Science, Jiangsu University , Zhenjiang, Jiangsu 212013 , PR China"}]},{"given":"Ghulam","family":"Rasool","sequence":"additional","affiliation":[{"name":"College of Mechanical and Energy Engineering, Beijing University of Technology , Beijing 100124 , China"}]},{"given":"Wejdan","family":"Deebani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science & Arts, King Abdul Aziz University , Rabigh 21911 , Saudi Arabia"}]},{"given":"Shaaban M","family":"Shaaban","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Engineering, Northern Border University , Arar 91431 , Saudi Arabia"}]}],"member":"286","published-online":{"date-parts":[[2024,7,30]]},"reference":[{"key":"2024081615053983300_bib1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s44189-023-00044-6","article-title":"A review on thermochemical seasonal solar energy storage materials and modeling methods","volume":"32","author":"Abdullah","year":"2024","journal-title":"International Journal of Air-Conditioning and Refrigeration"},{"key":"2024081615053983300_bib4","doi-asserted-by":"crossref","first-page":"035211","DOI":"10.1088\/1402-4896\/ab4ba9","article-title":"Numerical study of transport phenomena in a nanofluid using fractional relaxation times in Buongiorno model","volume":"95","author":"Anwar","year":"2020","journal-title":"Physica Scripta"},{"key":"2024081615053983300_bib3","doi-asserted-by":"crossref","first-page":"1690","DOI":"10.1016\/j.cjph.2017.05.011","article-title":"A microscopic study of MHD fractional inertial flow through Forchheimer medium","volume":"55","author":"Anwar","year":"2017","journal-title":"Chinese Journal of Physics"},{"key":"2024081615053983300_bib5","doi-asserted-by":"crossref","first-page":"1072","DOI":"10.3390\/mi14051072","article-title":"Heat transfer enhancement using Al$_2$O$_3$-MWCNT hybrid-nanofluid inside a tube\/shell heat exchanger with different tube shapes","volume":"14","author":"Bouselsal","year":"2023","journal-title":"Micromachines"},{"key":"2024081615053983300_bib6","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.aml.2019.03.036","article-title":"Unsteady boundary layer flow of viscoelastic MHD fluid with a double fractional Maxwell model","volume":"95","author":"Chen","year":"2019","journal-title":"Applied Mathematics Letters"},{"key":"2024081615053983300_bib7","first-page":"99","article-title":"Enhancing thermal conductivity of fluids with nanoparticles","volume":"231","author":"Choi","year":"1995","journal-title":"ASME FED"},{"key":"2024081615053983300_bib8","doi-asserted-by":"crossref","first-page":"2785","DOI":"10.1007\/s00231-017-1985-8","article-title":"Modeling of heat conduction via fractional derivatives","volume":"53","author":"Fabrizio","year":"2017","journal-title":"Heat and Mass Transfer"},{"key":"2024081615053983300_bib9","first-page":"1","article-title":"Exploring the influence of nanolayer morphology on magnetized tri-hybrid nanofluid flow using artificial neural networks and Levenberg\u2013Marquardt optimization","volume":"85","author":"Faisal","year":"2024","journal-title":"Numerical Heat Transfer, Part B: Fundamentals"},{"key":"2024081615053983300_bib10","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.cjph.2020.05.006","article-title":"On overall behavior of Maxwell mechanical model by the combined Caputo fractional derivative","volume":"66","author":"Feng","year":"2020","journal-title":"Chinese Journal of Physics"},{"key":"2024081615053983300_bib11","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1016\/j.apt.2016.01.015","article-title":"A comparative theoretical study on $Al_2{\\rm O}_3-H_2{\\rm O}$ and $\\gamma-{\\rm Al}_2{\\rm O}_3$ nanoparticles with different base fluids over a stretching sheet","volume":"27","author":"Ganesh","year":"2016","journal-title":"Advanced Powder Technology"},{"key":"2024081615053983300_bib12","doi-asserted-by":"crossref","first-page":"100413","DOI":"10.1016\/j.csite.2019.100413","article-title":"Numerical study of MHD effective Prandtl number boundary layer flow of $\\gamma$-Al$_2$O$_3$ nanofluids past a melting surface","volume":"13","author":"Ganesh","year":"2019","journal-title":"Case Studies in Thermal Engineering"},{"key":"2024081615053983300_bib13","doi-asserted-by":"crossref","first-page":"871","DOI":"10.2298\/TSCI16S3871G","article-title":"Fractional Maxwell fluid with fractional derivative without singular kernel","volume":"20","author":"Gao","year":"2016","journal-title":"Thermal Science"},{"key":"2024081615053983300_bib14","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.jmaa.2011.02.047","article-title":"Well posedness of a linearized fractional derivative fluid model","volume":"380","author":"Heibig","year":"2011","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"2024081615053983300_bib15","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s11012-008-9176-9","article-title":"Boundary layer flow and heat transfer over an unsteady stretching vertical surface","volume":"44","author":"Ishak","year":"2009","journal-title":"Meccanica"},{"key":"2024081615053983300_bib16","doi-asserted-by":"crossref","first-page":"2049","DOI":"10.1093\/jcde\/qwad090","article-title":"Inherent irreversibility in unsteady magnetohydrodynamic nanofluid flow past a slippery permeable vertical plate with fractional-order derivative","volume":"10","author":"Khan","year":"2023","journal-title":"Journal of Computational Design and Engineering"},{"key":"2024081615053983300_bib17","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1115\/1.2825978","article-title":"Enhanced thermal conductivity of nanoparticle-fluid mixtures","volume":"121","author":"Lee","year":"1999","journal-title":"Journal of Heat Transfer"},{"key":"2024081615053983300_bib18","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1016\/0021-9517(63)90004-6","article-title":"Catalytic aluminas i. surface chemistry of eta and gamma alumina","volume":"2","author":"Maciver","year":"1963","journal-title":"Journal of Catalysis"},{"key":"2024081615053983300_bib19","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.jcde.2019.03.003","article-title":"Exact and statistical computations of radiated flow of nano and Casson fluids under heat and mass flux conditions","volume":"6","author":"Mackolil","year":"2019","journal-title":"Journal of Computational Design and Engineering"},{"key":"2024081615053983300_bib20","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1016\/j.spmi.2003.09.012","article-title":"Heat transfer behaviours of nanofluids in a uniformly heated tube","volume":"35","author":"Maiga","year":"2004","journal-title":"Superlattices and Microstructures"},{"key":"2024081615053983300_bib21","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1016\/j.ijheatfluidflow.2005.02.004","article-title":"Heat transfer enhancement by using nanofluids in forced convection flows","volume":"26","author":"Maiga","year":"2005","journal-title":"International Journal of Heat and Fluid Flow"},{"key":"2024081615053983300_bib22","doi-asserted-by":"crossref","first-page":"1066","DOI":"10.3390\/en16031066","article-title":"Review on nano enhanced PCMs: Insight on nePCM application in thermal management\/storage systems","volume":"16","author":"Mebarek-Oudina","year":"2023","journal-title":"Energies"},{"key":"2024081615053983300_bib23","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1093\/jcde\/qwaa078","article-title":"Comprehensive numerical study of the effect of nanoparticle additives on the cutting transport performance in horizontal boreholes","volume":"8","author":"Minakov","year":"2021","journal-title":"Journal of Computational Design and Engineering"},{"key":"2024081615053983300_bib24","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1093\/jcde\/qwaa021","article-title":"Computational analysis of bioconvective flow of nanofluid containing gyrotactic microorganisms over a nonlinear stretching sheet with variable viscosity using HAM","volume":"7","author":"Mondal","year":"2020","journal-title":"Journal of Computational Design and Engineering"},{"key":"2024081615053983300_bib25","first-page":"188\u2212193","article-title":"Analysis of laminar-to-turbulent threshold with water $\\gamma$-Al$_2$O$_3$ and ethylene glycol- $\\gamma$-Al$_2$O$_3$ nanofluids in free convection","volume-title":"Proceedings of the 5th IASME\/WSEAS Int. Conference on Heat Transfer, Thermal Engineering and Environment","author":"Popa","year":"2007"},{"key":"2024081615053983300_bib26","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.jcde.2016.06.003","article-title":"Thermal diffusion and diffusion thermo effects on an unsteady heat and mass transfer magnetohydrodynamic natural convection Couette flow using FEM","volume":"3","author":"Raju","year":"2024","journal-title":"Journal of Computational Design and Engineering"},{"key":"2024081615053983300_bib27","doi-asserted-by":"crossref","first-page":"376","DOI":"10.24200\/sci.2022.58629.5822","article-title":"Computational analysis on radiative non-Newtonian Carreau nanofluid flow in a microchannel under the magnetic properties","volume":"30","author":"Ramesh","year":"2023","journal-title":"Scientia Iranica"},{"key":"2024081615053983300_bib28","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1016\/j.ijheatmasstransfer.2016.03.006","article-title":"Influences of an effective Prandtl number model on nano boundary layer flow of $\\gamma$-Al$_2$O$_3$\u2013H$_2$O and$\\gamma$-Al$_2$O$_3$\u2013C$_2$H$_6$O$_2$ over a vertical stretching sheet","volume":"98","author":"Rashidi","year":"2016","journal-title":"International Journal of Heat and Mass Transfer"},{"key":"2024081615053983300_bib29","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1016\/j.matcom.2020.10.011","article-title":"A brief comparative study of gamma alumina\u2013water and gamma alumina\u2013EG nanofluids flow near a solid sphere","volume":"181","author":"Salahuddin","year":"2021","journal-title":"Mathematics and Computers in Simulation"},{"key":"2024081615053983300_bib30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sajce.2023.07.003","article-title":"Entropy generation and current density of tangent hyperbolic Cu-C$_2$H$_6$O$_2$ and ZrO$_2$-Cu\/C$_2$H$_6$O$_2$ hybridized electromagnetic nanofluid: A thermal power application","volume":"46","author":"Salawu","year":"2023","journal-title":"South African Journal of Chemical Engineering"},{"key":"2024081615053983300_bib31","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1093\/jcde\/qwaa041","article-title":"Nonlocal vibration of carbon\/boron-nitride nano-hetero-structure in thermal and magnetic fields by means of nonlinear finite element method","volume":"7","author":"Sedighi","year":"2020","journal-title":"Journal of Computational Design and Engineering"},{"key":"2024081615053983300_bib32","doi-asserted-by":"crossref","first-page":"103186","DOI":"10.1016\/j.csite.2023.103186","article-title":"Case study of thermal and solutal aspects on non-Newtonian Prandtl hybrid nanofluid flowing via stretchable sheet: Multiple slip solution","volume":"49","author":"Shamshuddin","year":"2023","journal-title":"Case Studies in Thermal Engineering"},{"key":"2024081615053983300_bib33","doi-asserted-by":"crossref","first-page":"12083","DOI":"10.1007\/s10973-023-12465-x","article-title":"Bioconvective treatment for the reactive Casson hybrid nanofluid flow past an exponentially stretching sheet with Ohmic heating and mixed convection","volume":"148","author":"Shamshuddin","year":"2023","journal-title":"Journal of Thermal Analysis and Calorimetry"},{"key":"2024081615053983300_bib35","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1108\/HFF-03-2023-0128","article-title":"Homotopic simulation of MHD bioconvective flow of water-based hybrid nanofluid over a thermal convective exponential stretching surface","volume":"34","author":"Shamshuddin","year":"2024","journal-title":"International Journal of Numerical Methods for Heat & Fluid Flow"},{"key":"2024081615053983300_bib34","doi-asserted-by":"crossref","first-page":"55206","DOI":"10.1088\/1402-4896\/ad35f8","article-title":"Ferromagnetic and Ohmic effects on nanofluid flow via permeability rotative disk: significant interparticle radial and nanoparticle radius","volume":"99","author":"Shamshuddin","year":"2024","journal-title":"Physica Scripta"},{"key":"2024081615053983300_bib36","first-page":"Article 162961","article-title":"Experimental study of the freezing point of $\\gamma$-Al$_2$O$_3$\u2013H$_2$O water nanofluid","volume":"2012","author":"Sow","year":"2012","journal-title":"Advances in Mechanical Engineering"},{"key":"2024081615053983300_bib37","doi-asserted-by":"crossref","first-page":"474","DOI":"10.2514\/2.6486","article-title":"Thermal conductivity of nanoparticles-fluid mixture","volume":"13","author":"Wang","year":"1999","journal-title":"Journal of Thermophysics and Heat Transfer"},{"key":"2024081615053983300_bib38","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1590\/S0104-66322008000400001","article-title":"A review of nanofluids \u2013 part 1; theoretical and numerical investigations","volume":"25","author":"Wang","year":"2008","journal-title":"Brazilian Journal of Chemical Engineering"},{"key":"2024081615053983300_bib39","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1590\/S0104-66322008000400002","article-title":"A review of nanofluids \u2013 part 2; experiments and applications","volume":"25","author":"Wang","year":"2008","journal-title":"Brazilian Journal of Chemical Engineering"},{"key":"2024081615053983300_bib40","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.mechmat.2016.06.016","article-title":"An equivalence between generalized Maxwell model and fractional Zener model","volume":"100","author":"Xiao","year":"2016","journal-title":"Mechanics of Materials"},{"key":"2024081615053983300_bib42","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.apm.2019.11.017","article-title":"Flow and heat transfer of double fractional Maxwell fluids over a stretching sheet with variable thickness","volume":"80","author":"Yang","year":"2020","journal-title":"Applied Mathematical Modelling"},{"key":"2024081615053983300_bib41","doi-asserted-by":"crossref","first-page":"107335","DOI":"10.1016\/j.aml.2021.107335","article-title":"Unsteady natural convection boundary layer flow and heat transfer past a vertical flat plate with novel constitution models","volume":"120","author":"Yang","year":"2021","journal-title":"Applied Mathematics Letters"},{"key":"2024081615053983300_bib43","doi-asserted-by":"crossref","first-page":"20230202","DOI":"10.1515\/phys-2023-0202","article-title":"Optimized framework numerical solution for swirling hybrid nanofluid flow with silver\/gold nanoparticles on a stretching cylinder with heat source\/sink and reactive agents","volume":"22","author":"Yasmin","year":"2024","journal-title":"Open Physics"},{"key":"2024081615053983300_bib2","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.3390\/math11051170","article-title":"Role of nanofluid and hybrid nanofluid for enhancing thermal conductivity towards exponentially stretching curve with modified Fourier law inspired by melting heat effect","volume":"11","author":"Zeeshan","year":"2023","journal-title":"Mathematics"},{"key":"2024081615053983300_bib44","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40314-020-01394-2","article-title":"Finite volume method for mixed convection boundary layer flow of viscoelastic fluid with spatial fractional derivatives over a flat plate","volume":"40","author":"Zhao","year":"2021","journal-title":"Computational and Applied Mathematics"},{"key":"2024081615053983300_bib45","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1016\/j.ijheatmasstransfer.2016.02.059","article-title":"Unsteady natural convection boundary layer heat transfer of fractional Maxwell viscoelastic fluid over a vertical plate","volume":"97","author":"Zhao","year":"2016","journal-title":"International Journal of Heat and Mass Transfer"}],"container-title":["Journal of Computational Design and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jcde\/advance-article-pdf\/doi\/10.1093\/jcde\/qwae071\/58696334\/qwae071.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/advance-article-pdf\/doi\/10.1093\/jcde\/qwae071\/58836051\/qwae071.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/advance-article-pdf\/doi\/10.1093\/jcde\/qwae071\/58836051\/qwae071.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,16]],"date-time":"2024-08-16T15:31:47Z","timestamp":1723822307000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jcde\/article\/11\/4\/319\/7724383"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,3]]},"references-count":45,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,7,3]]}},"URL":"https:\/\/doi.org\/10.1093\/jcde\/qwae071","relation":{},"ISSN":["2288-5048"],"issn-type":[{"type":"electronic","value":"2288-5048"}],"subject":[],"published-other":{"date-parts":[[2024,8]]},"published":{"date-parts":[[2024,7,3]]}}}