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A Galerkin approach to analyze MHD flow of nanofluid along converging/diverging channels

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Abstract

In this article, we numerically analyzed the MHD flow of a nanofluid in converging/diverging channels through the Galerkin approach. The walls are assumed to be stretchable. The governing equations of flow are reduced to nonlinear ODE system by using the appropriate nondimensionalized technique. The results are simulated numerically by means of Galerkin method. A detailed evaluation of outcomes obtained by Galerkin scheme with the fourth-order Runge–Kutta technique (RK-4) is available to support our numerical results. The significant effects of the various physical parameters are presented graphically. Prandtl numbers cause an increase in the temperature profile, while they cause a decrease in the concentration profile. The shrinking decreases the fluid velocity nearby the channel walls, while the stretching of diverging channel provides an enhancement in flow nearby the channel walls. An identical behavior is found for the convergent channel. The influence of Grashof numbers is negligible but effect of opposing flow forces is a little dominant than assisting flow forces. The comparative study with existing literature and RK-4 as well as convergence analysis indicates that the proposed method is an efficient mathematical tool to analyze the problems arising in mechanics.

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Acknowledgements

The first author (M. Hamid) acknowledges the support of Fudan University through the International Exchange Post-Doctoral Fellowship. This work was supported by China Postdoctoral Science Foundation (No. 2020M681135) and partially supported by the National Natural Science Foundation of China (No. 11872151). The corresponding author (M. Usman) is grateful to Peking University for providing support through the BOYA fellowship.

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Authors and Affiliations

  1. Department of Mechanics and Engineering Science, Fudan University, Shanghai, 200433, People’s Republic of China

    Muhammad Hamid & Zhenfu Tian

  2. BIC-ESAT, College of Engineering, Peking University, Beijing, 100871, People’s Republic of China

    Muhammad Usman

  3. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, People’s Republic of China

    Muhammad Usman

  4. Institute of Ocean Research, Peking University, Beijing, 100871, People’s Republic of China

    Muhammad Usman

  5. Department of Electrical Engineering, Bahria University, Islamabad, 44000, Pakistan

    Rizwan Ul Haq

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  1. Muhammad Hamid
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Correspondence to Muhammad Usman or Zhenfu Tian.

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Hamid, M., Usman, M., Ul Haq, R. et al. A Galerkin approach to analyze MHD flow of nanofluid along converging/diverging channels. Arch Appl Mech 91, 1907–1924 (2021). https://doi.org/10.1007/s00419-020-01861-6

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  • DOI: https://doi.org/10.1007/s00419-020-01861-6

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