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Analytical Solutions of Fractional Walter’s B Fluid with Applications

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  • Qasem Al-Mdallal
  • Kashif Ali Abro
  • Ilyas Khan

Abstract

Fractional Walter’s Liquid Model-B has been used in this work to study the combined analysis of heat and mass transfer together with magnetohydrodynamic (MHD) flow over a vertically oscillating plate embedded in a porous medium. A newly defined approach of Caputo-Fabrizio fractional derivative (CFFD) has been used in the mathematical formulation of the problem. By employing the dimensional analysis, the dimensional governing partial differential equations have been transformed into dimensionless form. The problem is solved analytically and solutions of mass concentration, temperature distribution, and velocity field are obtained in the presence and absence of porous and magnetic field impacts. The general solutions are expressed in the format of generalized Mittag-Leffler function and Fox- function satisfying imposed conditions on the problem. These solutions have combined effects of heat and mass transfer; this is due to free convections differences between mass concentration and temperature distribution. Graphical illustration is depicted in order to bring out the effects of various physical parameters on flow. From investigated general solutions, the well-known previously published results in the literature have been recovered. Graphs are plotted and discussed for rheological parameters.

Suggested Citation

  • Qasem Al-Mdallal & Kashif Ali Abro & Ilyas Khan, 2018. "Analytical Solutions of Fractional Walter’s B Fluid with Applications," Complexity, Hindawi, vol. 2018, pages 1-10, February.
    • Handle: RePEc:hin:complx:8131329
    DOI: 10.1155/2018/8131329
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    1. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    2. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    3. Alkahtani, Badr Saad T. & Atangana, Abdon, 2016. "Analysis of non-homogeneous heat model with new trend of derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 566-571.
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    4. Guangming Shao & Biao Liu & Yueying Liu, 2018. "The Unique Existence of Weak Solution and the Optimal Control for Time-Fractional Third Grade Fluid System," Complexity, Hindawi, vol. 2018, pages 1-12, November.
    5. Abdeljawad, Thabet, 2019. "Fractional difference operators with discrete generalized Mittag–Leffler kernels," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 315-324.
    6. Abro, Kashif Ali & Abro, Irfan Ali & Yıldırım, Ahmet, 2020. "A comparative analysis of sulfate SO4−2 ion concentration via modern fractional derivatives: An industrial application to cooling system of power plant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
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    8. Asifa, & Kumam, Poom & Tassaddiq, Asifa & Watthayu, Wiboonsak & Shah, Zahir & Anwar, Talha, 2022. "Modeling and simulation based investigation of unsteady MHD radiative flow of rate type fluid; a comparative fractional analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 486-507.
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    10. Al-Mdallal, Qasem M., 2018. "On fractional-Legendre spectral Galerkin method for fractional Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 261-267.

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