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Thermal analysis of MHD convective slip transport of fractional Oldroyd-B fluid over a plate

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Abstract

The prime concern of this study is to analyze the generalized time-dependent magnetohydrodynamic (MHD) slip transport of an Oldroyd-B fluid near an oscillating upright plate. The plate is nested in a porous media under the action of ramped heating and nonlinear thermal radiation. Caputo–Fabrizio (CF) and Atangana–Baleanu (ABC) derivatives are utilized to constitute fractional partial differential equations that establish slip flow, shear stress, and heat transfer phenomena. Primarily, Laplace transformation is applied to dimensionless fractional models, and later Stehfest’s numerical algorithm is invoked to anticipate solutions of momentum and heat equations in principal coordinates. Moreover, computed solutions of velocity and energy fields are authenticated by Durbin’s and Zakian’s Laplace inversion algorithms. The relations for skin friction and Nusselt number are evaluated in terms of velocity and temperature gradients to efficiently anticipate shear stress and rate of heat transfer at the solid–fluid interface. The respective outcomes are manifested through tables. A critical examination of the current model is carried out and repercussions of variation in implanted parameters on temperature and momentum profiles are graphically elucidated. For the sake of comparison, three limiting fractional models, named second grade, Maxwell, and viscous models, are proposed for the isothermal and ramped temperature cases. Consequently, the observed outcomes affirm that under the isothermal condition, a generalized Maxwell fluid performs the swiftest slip transport compared to other models. Inversely, a second grade fluid specifies the highest velocity profile under ramped temperature case.

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Acknowledgements

The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science(TaCS-CoE), KMUTT. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005. The first author appreciates the support provided by Petchra Pra Jom Klao PhD Research Scholarship (Grant no. 14/2562).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Talha Anwar

  2. KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, 10140, Thailand

    Poom Kumam

  3. Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Poom Kumam

  4. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Poom Kumam

  5. Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia

    Ilyas Khan

  6. Renewable Energy Research Centre, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, 1518 Pracharat 1 Road, Bangsue, Bangkok, 10800, Thailand

    Phatiphat Thounthong

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Anwar, T., Kumam, P., Khan, I. et al. Thermal analysis of MHD convective slip transport of fractional Oldroyd-B fluid over a plate. Mech Time-Depend Mater 26, 431–462 (2022). https://doi.org/10.1007/s11043-021-09495-z

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