IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v131y2020ics0960077919304357.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919304357
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.109489?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fetecau, C. & Zafar, A.A. & Vieru, D. & Awrejcewicz, J., 2020. "Hydromagnetic flow over a moving plate of second grade fluids with time fractional derivatives having non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    2. Odibat, Zaid & Baleanu, Dumitru, 2023. "A new fractional derivative operator with generalized cardinal sine kernel: Numerical simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 224-233.
    3. Rashid, Saima & Sultana, Sobia & Jarad, Fahd & Jafari, Hossein & Hamed, Y.S., 2021. "More efficient estimates via ℏ-discrete fractional calculus theory and applications," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    4. Abu Shadate Faisal Mahamude & Wan Sharuzi Wan Harun & Kumaran Kadirgama & Devarajan Ramasamy & Kaniz Farhana & Khalid Saleh & Talal Yusaf, 2022. "Experimental Study on the Efficiency Improvement of Flat Plate Solar Collectors Using Hybrid Nanofluids Graphene/Waste Cotton," Energies, MDPI, vol. 15(7), pages 1-27, March.
    5. Salman, B.H. & Mohammed, H.A. & Munisamy, K.M. & Kherbeet, A. Sh., 2013. "Characteristics of heat transfer and fluid flow in microtube and microchannel using conventional fluids and nanofluids: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 28(C), pages 848-880.
    6. Prakash, Amit & Kaur, Hardish, 2021. "Analysis and numerical simulation of fractional Biswas–Milovic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 298-315.
    7. Syahira Mansur & Anuar Ishak & Ioan Pop, 2015. "The Magnetohydrodynamic Stagnation Point Flow of a Nanofluid over a Stretching/Shrinking Sheet with Suction," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-14, March.
    8. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    9. Amaris, Carlos & Vallès, Manel & Bourouis, Mahmoud, 2018. "Vapour absorption enhancement using passive techniques for absorption cooling/heating technologies: A review," Applied Energy, Elsevier, vol. 231(C), pages 826-853.
    10. Abdin, Z. & Alim, M.A. & Saidur, R. & Islam, M.R. & Rashmi, W. & Mekhilef, S. & Wadi, A., 2013. "Solar energy harvesting with the application of nanotechnology," Renewable and Sustainable Energy Reviews, Elsevier, vol. 26(C), pages 837-852.
    11. Sharma, A. & Tripathi, D. & Sharma, R.K. & Tiwari, A.K., 2019. "Analysis of double diffusive convection in electroosmosis regulated peristaltic transport of nanofluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    12. Rahman, Mati ur & Arfan, Muhammad & Shah, Kamal & Gómez-Aguilar, J.F., 2020. "Investigating a nonlinear dynamical model of COVID-19 disease under fuzzy caputo, random and ABC fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    13. Ranga Babu, J.A. & Kumar, K. Kiran & Srinivasa Rao, S., 2017. "State-of-art review on hybrid nanofluids," Renewable and Sustainable Energy Reviews, Elsevier, vol. 77(C), pages 551-565.
    14. Deniz, Sinan, 2021. "Optimal perturbation iteration method for solving fractional FitzHugh-Nagumo equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    15. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
    16. Wu, Xi & Xu, Shiming & Jiang, Mengnan, 2018. "Development of bubble absorption refrigeration technology: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 82(P3), pages 3468-3482.
    17. Shaafi, T. & Sairam, K. & Gopinath, A. & Kumaresan, G. & Velraj, R., 2015. "Effect of dispersion of various nanoadditives on the performance and emission characteristics of a CI engine fuelled with diesel, biodiesel and blends—A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 49(C), pages 563-573.
    18. Aliyu, Aliyu Isa & Inc, Mustafa & Yusuf, Abdullahi & Baleanu, Dumitru, 2018. "A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 268-277.
    19. Eleonora Ponticorvo & Mariagrazia Iuliano & Claudia Cirillo & Angelo Maiorino & Ciro Aprea & Maria Sarno, 2022. "Fouling Behavior and Dispersion Stability of Nanoparticle-Based Refrigeration Fluid," Energies, MDPI, vol. 15(9), pages 1-21, April.
    20. Pawel Rozga & Abderrahmane Beroual & Piotr Przybylek & Maciej Jaroszewski & Konrad Strzelecki, 2020. "A Review on Synthetic Ester Liquids for Transformer Applications," Energies, MDPI, vol. 13(23), pages 1-33, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304357. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.