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A Transient Flow of a Non-Newtonian Fluid Modelled by a Mixed Time-Space Derivative: An Improved Integral-Balance Approach

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Book cover Mathematical Methods in Engineering

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 24))

Abstract

Transient flow of second-grade fluid, modelled by mixed time-space derivative, due to sudden change of the boundary condition (Stokes first problem) has been solved by an improved integral-balance method utilizing double integration technique. Two versions of mixed time-space derivative, integer-order and fractional in time (Riemann-Liouville), have been considered. The solution uses the concept of finite penetration depth of diffusing momentum from the interface into the fluid bulk. The solutions provide straightforwardly the functional relationship of the penetration depth controlled by two similarity variables: related to the Newtonian flow behaviour and the Deborah number relevant to the elastic fluid performance.

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Authors and Affiliations

  1. Department of Chemical Engineering, University of Chemical Technology and Metallurgy, Sofia, Bulgaria

    Jordan Hristov

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  1. Jordan Hristov
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Correspondence to Jordan Hristov .

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Editors and Affiliations

  1. Department of Mathematics, Cankaya University, Ankara, Turkey

    Kenan Taş

  2. Department of Mathematics, Çankaya University, Ankara, Turkey

    Dumitru Baleanu

  3. Instituto Superior de Engenharia do Porto, Porto, Portugal

    J. A. Tenreiro Machado

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Hristov, J. (2019). A Transient Flow of a Non-Newtonian Fluid Modelled by a Mixed Time-Space Derivative: An Improved Integral-Balance Approach. In: Taş, K., Baleanu, D., Machado, J. (eds) Mathematical Methods in Engineering. Nonlinear Systems and Complexity, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-319-90972-1_11

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  • DOI: https://doi.org/10.1007/978-3-319-90972-1_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-90971-4

  • Online ISBN: 978-3-319-90972-1

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