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Cattaneo–Friedrich and Crank–Nicolson analysis of upper-convected Maxwell fluid along a vertical plate

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  • Hanif, Hanifa

Abstract

The concept of fractional derivative is used to solve a variety of viscoelastic fluid problems. However, researchers mostly overlooked the consequences of nonlinear convection in the fractional viscoelastic fluid models and were concerned only with situations where the governing equations are linear. Most importantly, the nonlinear fluid models, whether classical or fractional, are solved for steady-state conditions. To overcome these limitations, this research presents unsteady flow and heat transfer of nonlinear fractional upper-convected Maxwell (UCM) viscoelastic fluid along a vertical plate. The governing equations of the fractional Maxwell fluid are developed by introducing Friedrich shear stress and Cattaneo heat flux models to the classical UCM fluid model. An additional feature to the invention of the constructed fractional model is the consequence of an external magnetic field. Moreover, the considered model comprises nonlinear, coupled, fractional partial differential equations. Therefore, a numerical scheme is developed with the aid of the L1-approximation of Caputo derivative and the Crank–Nicolson method. The effects of different regulating parameters on fluid features have been thoroughly investigated. The obtained results are exhibited graphically and discussed in detail. It is observed that the skin friction increases for the velocity relaxation time parameter, but an opposite behavior is observed against the velocity fractional derivative parameter. Moreover, a significant enhancement is noticed in the Nusselt number for increasing estimates of the Prandtl number.

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  • Hanif, Hanifa, 2021. "Cattaneo–Friedrich and Crank–Nicolson analysis of upper-convected Maxwell fluid along a vertical plate," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
  • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008171
    DOI: 10.1016/j.chaos.2021.111463
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    References listed on IDEAS

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    1. Owolabi, Kolade M., 2017. "Mathematical modelling and analysis of two-component system with Caputo fractional derivative order," Chaos, Solitons & Fractals, Elsevier, vol. 103(C), pages 544-554.
    2. Ahmed A. Afify & Nasser S. Elgazery, 2020. "Impacts of Newtonian heating, variable fluid properties and Cattaneo–Christov model on MHD stagnation point flow of Walters’ B fluid induced by stretching surface," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(09), pages 1-17, September.
    3. Hanif, Hanifa, 2022. "A computational approach for boundary layer flow and heat transfer of fractional Maxwell fluid," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 1-13.
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