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Caputo–Fabrizio fractional derivatives modeling of transient MHD Brinkman nanoliquid: Applications in food technology

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  • Ali, Farhad
  • Ali, Farman
  • Sheikh, Nadeem Ahmad
  • Khan, Ilyas
  • Nisar, Kottakkaran Sooppy

Abstract

Amongst the several definitions of fractional operator (memory operator), these days the Caputo–Fabrizio operator (CF) without singular kernel is a useful extension of the classical Caputo derivative operator as the latter includes a singular mathematical expression also known as the kernel in its definition, leading to some difficulties in finding solutions to the corresponding differential equation, whereas the kernel of the former (CF) is non-singular. In this paper, the idea of CF derivative has been applied to solve a Brinkman nanoliquid (suspension of nanomaterials in a base fluid) problem. More exactly, the present article studies the effect of copper nanoparticles on the MHD free convection transient motion of C6H9NaO7 Brinkman nanoliquid lies over a vertical surface with time-dependent velocity, temperature, and concentration. Formulation of the problem in the fractional form (CF) is done and then closed-form solution is obtained. Graphs are drawn for different embedded parameters and variations in Nusselt number, skin friction and Sherwood number are shown in tabular form. C6H9NaO7 is a food product taken from seaweed or brown algae. C6H9NaO7 is used in the food industry for making gel-like foods such as pimento stuffing in prepared cocktail olives. In a liquid, C6H9NaO7 also acts as a thickener. C6H9NaO7 Brinkman nanoliquid in this direction (food technology) using CF derivative has not been investigated yet. This study will further provide new directions to carry this research using Atangana–Baleanu fractional derivatives for other non-Newtonian C6H9NaO7 nanoliquids used in different foods.

Suggested Citation

  • Ali, Farhad & Ali, Farman & Sheikh, Nadeem Ahmad & Khan, Ilyas & Nisar, Kottakkaran Sooppy, 2020. "Caputo–Fabrizio fractional derivatives modeling of transient MHD Brinkman nanoliquid: Applications in food technology," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304357
    DOI: 10.1016/j.chaos.2019.109489
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    References listed on IDEAS

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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. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    3. Saidur, R. & Leong, K.Y. & Mohammad, H.A., 2011. "A review on applications and challenges of nanofluids," Renewable and Sustainable Energy Reviews, Elsevier, vol. 15(3), pages 1646-1668, April.
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    1. Liao, Xiaozhong & Wang, Yong & Yu, Donghui & Lin, Da & Ran, Manjie & Ruan, Pengbo, 2023. "Modeling and analysis of Buck-Boost converter with non-singular fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.

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