Prabhakar fractional derivative model of sodium alginate (C6H9NaO7) for accelerated plate motions

Prabhakar fractional derivative model of sodium alginate (C6H9NaO7) for accelerated plate motions Ilyas Khan

The Prabhakar fractional derivative model is not studied in the open literature for the Casson fluid model when the vertical plate exhibits linear and quadratic translations with constant heating. Therefore, this study deals with the thermal transport of sodium alginate (C 6 H 9 NaO 7 ) over a vertical plate with a constant temperature. Since the classical PDEs are incapable of analyzing and investigating the physical impact of flow variables with memory effects, a fractional derivative model is developed using the Prabhakar fractional derivative approach. Two different types of plate translations (linear and quadratic) are considered. The non-dimensional governing equations are transformed into a fractional model and solved using the Laplace transformation (L.T) technique. The effects and behavior of significant physical parameters and fractional order parameters are studied graphically and discussed. As a consequence, it is found that as fractional limitations are increased, the thermal and momentum profiles drop. In addition, the momentum profile in the case of quadratic translation (variable acceleration) shows a higher magnitude than the case of linear translation (constantly accelerated plate).
11 8 2022 1013829 10.3389/fenrg.2022.1013829 1 10.3389/crossmark-policy frontiersin.org true https://creativecommons.org/licenses/by/4.0/ 10.3389/fenrg.2022.1013829 https://www.frontiersin.org/articles/10.3389/fenrg.2022.1013829/full https://www.frontiersin.org/articles/10.3389/fenrg.2022.1013829/full Int. J. Appl. Comput. Math. Abdal 7 235 2021 Attribution of multi-slips and bioconvection for micropolar nanofluids transpiration through porous medium over an extending sheet with PST and PHF conditions 10.1007/s40819-021-01137-9 Int. J. Eng. Sci. Aksoy 45 829 2007 Boundary layer equations and stretching sheet solutions for the modified second grade fluid 10.1016/j.ijengsci.2007.05.006 Solit. Fractals Ali 114 478 2018 A novel method for a fractional derivative with non-local and non-singular kernel, Chaos 10.1016/j.chaos.2018.07.032 Chaos, Solit. Fractals Alidousti 134 109688 2020 Dynamic behavior of a fractional order prey-predator model with group defense 10.1016/j.chaos.2020.109688 Dermatol. Ther. Alwawi 22 431 2009 Long‐term efficacy of biologics in the treatment of psoriasis: What do we really know? 10.1111/j.1529-8019.2009.01259.x Int. J. Non-Linear Mech. Andersson 27 929 1992 Magnetohydrodynamic flow of a power-law fluid over a stretching sheet 10.1016/0020-7462(92)90045-9 J. nanofluids Archana 6 232 2017 Influence of nonlinear thermal radiation and magnetic field on three-dimensional flow of a Maxwell nanofluid 10.1166/jon.2017.1320 Chin. J. Phys. Asjad 66 497 2020 New trends of fractional modeling and heat and mass transfer investigation of (SWCNTs and MWCNTs)-CMC based nanofluids flow over inclined plate with generalized boundary conditions 10.1016/j.cjph.2020.05.026 Therm. Sci. Asjad 25 411 2021 Prabhakar fractional derivative and its applications in the transport phenomena containing nanoparticles 10.2298/TSCI21S2411A Math. Methods Appl. Sci. Basit 2021 1 2021 Convective flow of a fractional second grade fluid containing different nanoparticles with Prabhakar fractional derivative subject to non‐uniform velocity at the boundary 10.1002/mma.7461 Alexandria Eng. J. Bilal 61 4341 2022 Finite difference simulations for magnetically effected swirling flow of Newtonian liquid induced by porous disk with inclusion of thermophoretic particles diffusion 10.1016/j.aej.2021.09.054 Frontiers in biomechanics Chuong 117 1986 10.1007/978-1-4612-4866-8_9 Residual stress in arteries Int. J. Eng. Sci. Dash 34 1145 1996 Casson fluid flow in a pipe filled with a homogeneous porous medium 10.1016/0020-7225(96)00012-2 Int. J. Proj. Manag. Derakhshan 37 98 2019 Project governance and stakeholders: A literature review 10.1016/j.ijproman.2018.10.007 Int. J. Numer. Methods Heat. Fluid Flow. Durairaj 27 156 2017 Heat generating/absorbing and chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium 10.1108/HFF-08-2015-0318 Nonlinear Dyn. Garrappa 102 567 2020 Stability of fractional-order systems with Prabhakar derivatives 10.1007/s11071-020-05897-9 Commun. Nonlinear Sci. Numer. Simul. Giusti 56 138 2018 Prabhakar-like fractional viscoelasticity 10.1016/j.cnsns.2017.08.002 Sea-Level Changes: An Integrated Approach Haq 1988 10.2110/pec.88.01.0071 Mesozoic and Cenozoic chronostratigraphy and cycles of sea-level change Appl. Math. Model. Hassanien 20 779 1996 Flow and heat transfer on a continuous flat surface moving in a parallel free stream of power-law fluid 10.1016/0307-904x(96)00082-0 Int. J. Mod. Phys. B Hayat 25 2863 2011 Mass transfer effects on the unsteady flow of UCM fluid over a stretching sheet 10.1142/s0217979211101375 J. Heat. Transf. Jasmine Benazir 138 112005 2016 Comparison between Casson fluid flow in the presence of heat and mass transfer from a vertical cone and flat plate 10.1115/1.4033971 Eur. Phys. J. Spec. Top. Khan 226 3791 2017 Application of time-fractional derivatives with non-singular kernel to the generalized convective flow of Casson fluid in a microchannel with constant walls temperature 10.1140/epjst/e2018-00097-5 Discrete Continuous Dyn. Syst. - S Khan 13 769 2020 Channel flow of fractionalized H2O-based CNTs nanofluids with Newtonian heating 10.3934/dcdss.2020043 Proc. Institution Mech. Eng. Part E J. Process Mech. Eng. Li 095440892210824 2022 Applications of fractional derivatives in MHD free-convective oscillating flow of a blood based CNTs nanofluid across a porous medium 10.1177/09544089221082489 J. Mol. Liq. Mythili 216 466 2016 Influence of higher order chemical reaction and non-uniform heat source/sink on Casson fluid flow over a vertical cone and flat plate 10.1016/j.molliq.2016.01.072 Biotechnol. Adv. Nadeem 32 429 2014 The role of mycorrhizae and plant growth promoting rhizobacteria (PGPR) in improving crop productivity under stressful environments 10.1016/j.biotechadv.2013.12.005 Panchal 2016 K-hilfer-prabhakar fractional derivatives and applications Fract. Differ. Calc. Polito 6 73 2016 Some properties of Prabhakar-type fractional calculus operators 10.7153/fdc-06-05 Alexandria Eng. J. Qureshi 61 12925 2022 Mathematical analysis about influence of Lorentz force and interfacial nano layers on nanofluids flow through orthogonal porous surfaces with injection of SWCNTs 10.1016/j.aej.2022.07.010 Proc. Institution Mech. Eng. Part A J. Power Energy Raza 236 974 2022 Transport properties of mixed convective nano-material flow considering the generalized Fourier law and a vertical surface: Concept of Caputo-Time Fractional Derivative 10.1177/09576509221075110 Front. Phys. Samraiz 23 309 2020 Hilfer-Prabhakar fractional derivative with applications to mathematical physics 10.3389/fphy.2020.00309 Int. J. Non-Linear Mech. Sadeghy 39 1265 2004 Local similarity solution for the flow of a “second-grade” viscoelastic fluid above a moving plate 10.1016/j.ijnonlinmec.2003.08.005 Int. J. Heat Mass Transf. Sajid 50 1723 2007 Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet 10.1016/j.ijheatmasstransfer.2006.10.011 Mathematics Sandev 5 66 2017 Generalized Langevin equation and the Prabhakar derivative 10.3390/math5040066 Symmetry Saqib 12 768 2020 Application of fractional derivative without singular and local kernel to enhanced heat transfer in CNTs nanofluid over an inclined plate 10.3390/sym12050768 Eur. Phys. J. Spec. Top. Sivaraj 228 35 2019 Investigation of cross-diffusion effects on Casson fluid flow in existence of variable fluid properties 10.1140/epjst/e2019-800187-3 Case Stud. Therm. Eng. Wang 32 101904 2022 Thermal outcomes for blood-based carbon nanotubes (SWCNT and MWCNTs) with Newtonian heating by using new Prabhakar fractional derivative simulations 10.1016/j.csite.2022.101904