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Heat and mass transfer in Maxwell fluid in view of local and non-local differential operators

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Abstract

Study of heat and mass transfer in Maxwell fluid is carried out near a vertical plate. It is proven in many already published articles that the heat and mass transfer does not really or always follow the classical mechanics process that is known as memoryless process. Therefore, the model using classical differentiation based on the rate of change cannot really replicate such dynamical process very accurately; thus, a different concept of differentiation is needed to capture such process. Very recently, new classes of differential operators were introduced and have been recognized to be efficient in capturing processes following the power law, the decay law and the crossover behaviors. For the study of heat and mass transfer, we applied the newly introduced differential operators to model such flow. The Laplace transform, inversion algorithm and convolution theorem were used to derive the exact and semi-analytical solutions for all cases. The obtained analytical solutions were plotted for different values of fractional order \(\alpha \), Maxwell fluid parameter \(\lambda \), thermal Grashof number Gr, mass Grashof number Gm, Prandtl number Pr and Schmidt number Sc on concentration and velocity fields. In comparison, velocity of Atangana–Baleanu fractional derivative is greater than that of Caputo and Caputo–Fabrizio for \(\alpha \), \(\lambda \), Gr and Gm. With the increase in Pr and Sc, there is a decrease in velocity. For fractional parameter, the effect of concentration field for ABC model is more than for C and CF. Moreover, from the present solutions already published results were found as limiting cases.

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Authors and Affiliations

  1. Department of Mathematics, University of Management and Technology, Lahore, Pakistan

    Muhammad Bilal Riaz

  2. Institute for Groundwater Studies, University of the Free State, Bloemfontein, South Africa

    Muhammad Bilal Riaz & Abdon Atangana

  3. Department of Medical Research, China Medical University Hospital, China Medical University, Taizhong, Taiwan, People’s Republic of China

    Abdon Atangana

  4. Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, Lahore, Pakistan

    Nazish Iftikhar

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  1. Muhammad Bilal Riaz
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Riaz, M.B., Atangana, A. & Iftikhar, N. Heat and mass transfer in Maxwell fluid in view of local and non-local differential operators. J Therm Anal Calorim 143, 4313–4329 (2021). https://doi.org/10.1007/s10973-020-09383-7

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