736
Views
0
CrossRef citations to date
0
Altmetric
RESEARCH ARTICLE

A comparative analysis of fractional model of second grade fluid subject to exponential heating: application of novel hybrid fractional derivative operator

, , , &
Pages 1-17 | Received 06 Jun 2022, Accepted 25 Nov 2023, Published online: 10 Dec 2023

References

  • Alabedalhadi, M., Al-Smadi, M., Al-Omari, S., Baleanu, D., & Momani, S. (2020). Structure of optical soliton solution for nonliear resonant space-time Schrödinger equation in conformable sense with full nonlinearity term. Physica Scripta, 95(10), 105215. doi:10.1088/1402-4896/abb739
  • Ali, F., Khan, I., & Shafie, S. (2014). Closed form solutions for unsteady free convection flow of a second grade fluid over an oscillating vertical plate. PLoS One. 9(2), e85099. doi:10.1371/journal.pone.0085099
  • Al-Smadi, M., Arqub, O. A., & Hadid, S. (2020). Approximate solutions of nonlinear fractional Kundu-Eckhaus and coupled fractional massive Thirring equations emerging in quantum field theory using conformable residual power series method. Physica Scripta, 95(10), 105205. doi:10.1088/1402-4896/abb420
  • Al-Smadi, M., Djeddi, N., Momani, S., Al-Omari, S., & Araci, S. (2021). An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space. Advances in Difference Equations, 2021(1), 271.). doi:10.1186/s13662-021-03428-3
  • Al-Smadi, M., Freihat, A., Arqub, O. A., & Shawagfeh, N. (2015). A novel multistep generalized differential transform method for solving fractional-order Lü chaotic and hyperchaotic systems. Journal of Computational Analysis and Applications, 19, 713–724.
  • Altawallbeh, Z., Al-Smadi, M., Komashynska, I., & Ateiwi, A. (2018). Numerical solutions of fractional systems of two-point BVPs by using the iterative reproducing kernel algorithm. Ukrainian Mathematical Journal, 70(5), 687–701. doi:10.1007/s11253-018-1526-8
  • Arianna, P., & Gudrun, T. (2005). Boussinesq-type approximation for second-grade fluids. International Journal of Non-Linear Mechanics, 40(6), 821–831.
  • Atangana, A., & Baleanu, D. (2016). New fractional derivative with non local and non-singular kernel: Theory and application to heat transfer model. Thermal Science, 20(2), 763–769. doi:10.2298/TSCI160111018A
  • Baranovskii, E. S. (2021). Optimal boundary control of the boussinesq approximation for polymeric fluids. Journal of Optimization Theory and Applications, 189(2), 623–645. doi:10.1007/s10957-021-01849-4
  • Dinarvand, S., Doosthoseini, A., Doosthoseini, E., & Rashidi, M. M. (2010). Series solutions for unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces. Nonlinear Analysis: Real World Applications. 11(2), 1159–1169. doi:10.1016/j.nonrwa.2009.02.009
  • Erdogan, M. E. (2003). On unsteady motions of a second‐order fluid over a plane wall. Int. J. Nonlinear Mech, 38(7), 1045–1051. doi:10.1016/S0020-7462(02)00051-3
  • Fetecau, C., Fetecau, C., & Rana, M. (2011). General solutions for the unsteady flow of second grade fluid over an infinite plate that applies arbitratry shear to the fluid. Zeitschrift Für Naturforschung A, 66(12), 753–759. doi:10.5560/zna.2011-0044
  • Fetecau, C., Vieru, D., & Fetecau, C. (2011). Effect of side walls on the motion of a viscous fluid induced by an infinite plate that applies an oscillating shear stress to the fluid. Central European Journal of Physics. 9(3), 816–824.
  • Haq, S. U., Sehra, S., Shah, I. A., Jan, S. U. & Khan, I. (2021). MHD flow of generalized second grade fluid with modified Darcy’s law and exponential heating using fractional Caputo-Fabrizio derivatives. Alexandria Engineering Journal, 4, 60, 3845–3854. doi:10.1016/j.aej.2021.02.038
  • He, J.-H., & Abd Elazem, N. Y. (2022). The Carbon nanotube-embedded boundary layer theory for energy harvesting. Facta Universitatis, Series, 20(2), 211–235. doi:10.22190/FUME220221011H
  • He, J.-H., Elgazery, N. S., & Abd Elazem, N. Y. (2023). Magneto-radiative gas near an unsmooth boundary with variable temperature. International Journal of Numerical Methods for Heat & Fluid Flow, 33(2), 545–569. doi:10.1108/HFF-05-2022-0285
  • He, J.-H., Sayed, K., Elagan, K. S., & Li, Z. B. (2012). Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus. Physics Letters A, 376(4), 257–259. doi:10.1016/j.physleta.2011.11.030
  • Islam, M. N., & Akbar, M. A. (2018). Closed form exact solutions to the higher dimensional fractional Schrodinger equation via the modified simple equation method. Journal of Applied Mathematics and Physics, 06(01), 90–102. doi:10.4236/jamp.2018.61009
  • Islam, S., Bano, Z., Haroon, T., & Siddiqui, A. M. (2011). Unsteady poiseuille flow of second grade fluid in a tube of elliptical cross section. Proceedings of the Romanian Academy Series A, 12(4), 291–295.
  • Kahshan, M., Lu, D., & Siddiqui, A. M. (2019). A Jeffrey fluid model for a porous-walled channel: Application to flat plate dialyzer. Scientific Reports, 9(1), 15879. doi:10.1038/s41598-019-52346-8
  • Khan, Z., Tairan, N., Mashwani, W. K., Rasheed, H. U., Shah, H., & Khan, W. (2019). MHD and slip effect on two-immiscible third grade fluid on thin film flow over a vertical moving belt. Open Physics, 17(1), 575–586. doi:10.1515/phys-2019-0059
  • Koo, S. J., He, C. H., Men, X. C., & He, J. H. (2022). Fractal boundary layer and its basic properties. Fractal, 30(9), 2250172.
  • Labropulu, F. (2000). A few more exact solutions of a second grade fluid via inverse method. Mechanics Research Communications. 27(6), 713–720. doi:10.1016/S0093-6413(00)00145-2
  • Li, X. (2023). A fractal-fractional model for complex fluid-flow with nanoparticles. Thermal Science, 27(3 Part A), 2057–2063. doi:10.2298/TSCI2303057L
  • Mohebbi, R., Delouei, A. A., Jamali, A., Izadi, M., & Mohamad, A. A. (2019). Pore-scale simulation of non-Newtonian power-law fluid flow and forced convection in partially porous media: Thermal lattice Boltzmann method. Physica A: Statistical Mechanics and Its Applications. 525, 642–656. doi:10.1016/j.physa.2019.03.039
  • Momani, S., Freihat, A., & Al-Smadi, M. (2014). Analytical study of fractional-order multiple chaotic Fitzhugh-Nagumo neurons model using multistep generalized differential transform method. Abstract and Applied Analysis, 2014, 1–10. doi:10.1155/2014/276279
  • Osman, M. S., Korkmaz, A., Rezazadeh, H., Mirzazadeh, M., Eslami, M., & Zhou, Q. (2018). The unified method for conformable time fractional Schro dinger equation with perturbation terms. Chinese Journal of Physics. 56(5), 2500–2506. doi:10.1016/j.cjph.2018.06.009
  • Rajagopal, K. R. (1993). Mechanics of non‐Newtonian fluids in recent development in theoretical fluid Mechanics. Pitman Res Notes Math, 291, 129–162.
  • Rajagopal, K. R., & Gupta, A. S. (1984). An exact solution for the flow of a non‐Newtonian fluid past an infinite porous plate. Meccanica, 19(2), 158–160. doi:10.1007/BF01560464
  • Rashidi, M. M., Erfani, E., & Rostami, B. (2014). Optimal homotopy asymptotic method for solving viscous flow through expanding or contracting gaps with permeable walls. Transmission IoT Cloud computing, 2(1), 76–100.
  • Rehman, A. U., Awrejcewicz, J., Riaz, M. B., & Jarad, F. (2022a). Mittag-Leffler form solutions of natural convection flow of second grade fluid with exponentially variable temperature and mass diffusion using Prabhakar fractional derivative. Case Studies in Thermal Engineering, 34, 102018. doi:10.1016/j.csite.2022.102018
  • Rehman, A. U., Riaz, M. B., Rehman, W., Awrejcewicz, J., & Baleanu, D. (2022b). Fractional modeling of viscous fluid over a moveable inclined plate subject to exponential heating with singular and non-singular kernels. Mathematical and Computational Applications, 27(1), 8. doi:10.3390/mca27010008
  • Rehman, A. U., Riaz, M. B., Saeed, S. T., Jarad, F., Jasim, H. N., & Enver, A. (2022c). An exact and comparative analysis of MHD free convection flow of water-based nanoparticles via CF derivative. Mathematical Problems in Engineering, 2022, 1–19. doi:10.1155/2022/9977188
  • Rehman, A. U., Shah, Z. H., & Riaz, M. B. (2021). Application of local and non-local kernels: The optimal solutions of water-based nanoparticles under ramped conditions. Progress in Fractional Differentiation & Applications, 7(4), 317–335.
  • Rehman, A.U., Riaz, M.B., Saeed, S. T. & Yao, S. Dynamical Analysis of Radiation and Heat Transfer on MHD Second Grade Fluid. Computer Modeling in Engineering & Sciences, 129(2),689–703(2021). doi:10.32604/cmes.2021.014980
  • Riaz, M. B., Abro, K. A., Abualnaja, K. M., Akgül, A., Rehman, A. U., Abbas, M., & Hamed, Y. S. (2021a). Exact solutions involving special functions for unsteady convective flow of magnetohydrodynamic second grade fluid with ramped conditions. Advances in Difference Equations, 2021(1), 408. doi:10.1186/s13662-021-03562-y
  • Riaz, M. B., Awrejcewicz, J., & Rehman, A. U. (2021b). Functional effects of permeability on Oldroyd-B fluid under magnetization: A comparison of slipping and non-slipping solutions. Appl. Sci, 11(23), 11477. doi:10.3390/app112311477
  • Riaz, M. B., Awrejcewicz, J., Rehman, A. U., & Abbas, M. (2021c). Special functions-based solutions of unsteady convective flow of a MHD Maxwell fluid for ramped wall temperature and velocity with concentration. Advances in Difference Equations, 2021(1), 500. doi:10.1186/s13662-021-03657-6
  • Riaz, M. B., Awrejcewicz, J., Rehman, A. U., & Akgül, A. (2021d). Thermophysical investigation of Oldroyd-B Fluid with functional effects of permeability: memory effect study using non-singular kernel Derivative approach. Fractal and Fractional, 5(3), 124. doi:10.3390/fractalfract5030124
  • Riaz, M. B., Rehman, A. U., Awrejcewicz, J., & Akgül, A. (2021e). Power law kernel analysis of MHD maxwell fluid with ramped boundary conditions: transport phenomena solutions based on special functions. Fractal and Fractional, 5(4), 248. doi:10.3390/fractalfract5040248
  • Shah, N. A., & Khan, I. (2016). Heat transfer analysis in a second grade fluid over and oscillating vertical plate using fractional Caputo-Fabrizio derivatives. The European Physical Journal, C.76, 362.
  • Song, Y. Q., Raza, A., Al-Khaled, K., Farid, S., Khan, M. I., Khan, S. U., … Khan, M. I. (2021). Significances of exponential heating and Darcy’s law for second grade fluid flow over oscillating plate by using Atangana-Baleanu fractional derivatives. Case Studies in Thermal Engineering, 27, 101266.
  • Tawari, A. K., & Ravi, S. K. (2009). Analytical studies on transient rotating flow of a second grade fluid in a porous medium. Advances in Theoretical and Applied Mechanics, 2, 23–41.
  • Wang, K. L., & He, C. H. (2019). A remark on Wang’s fractal variational principle. Fractals, 27(08), 1950134. doi:10.1142/S0218348X19501342
  • Wu, P. X., Yang, Q., & He, J. H. (2022). Solitary waves of the variant Boussinesq-Burgers equation in a fractal dimensional space. Fractals, 30(03), 2250056-380. doi:10.1142/S0218348X22500566
  • Wu, P., Ling, W., Li, X., He, X., & Xie, L. (2022). Dynamics research of Fangzhu’s nanoscale surface. Journal of Low Frequency Noise, Vibration and Active Control, 41(2), 479–487. doi:10.1177/14613484211052753
  • Yavuz, M., Sene, N., & Yıldız, M. (2022). Analysis of the influences of parameters in the fractional second-grade fluid dynamics. Mathematics, 10(7), 1125. doi:10.3390/math10071125
  • Zuo, Y. (2021). Effect of SiC particles on viscosity of 3–D print paste: A fractal rheological model and experimental verification. Thermal Science, 25(3 Part B), 2405–2409. doi:10.2298/TSCI200710131Z