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Numerical simulation of self-similar thermal convection from a spinning cone in anisotropic porous medium

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Abstract

Self-similar steady natural convection thermal boundary layer flow from a rotating vertical cone to anisotropic Darcian porous medium is investigated theoretically and numerically. The transformed non-dimensional two-point boundary value problem is reduced to a system of coupled, highly nonlinear ordinary differential equations, which are solved subject to robust surface and free stream boundary conditions with the MAPLE 17 numerical quadrature software. Validation with earlier non-rotating studies is included, and also further verification of rotating solutions is achieved with a variational finite element method (FEM). The rotational (spin) parameter emerges as an inverse function of the Grashof number. The influence of this parameter, primary Darcy number, secondary Darcy number and Prandtl number on tangential velocity and swirl velocity, temperature and heat transfer rate are studied in detail. It is found that the dimensionless tangential velocity increases whilst the dimensionless swirl velocity and temperature decrease with the swirl Darcy number, tangential Darcy number and the rotational parameters. The model finds applications in chemical engineering filtration processing, liquid coating and spinning cone distillation columns.

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Authors and Affiliations

  1. Spray Research Group, Petroleum and Gas Engineering Division, Room G77, Newton Building, School of Computing, Science and Engineering (CSE), University of Salford, M54WT, UK

    O. Anwar Bég

  2. Department of Mathematics, American International University-Bangladesh, Dhaka, Bangladesh

    M. J. Uddin

  3. Engineering Mechanics Associates, Dickenson Road, Manchester, M16, England

    T. Bég

  4. Department Mechanical Engineering, Cleveland State University, Cleveland, Ohio, USA

    R. Reddy Gorla

Authors
  1. O. Anwar Bég
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  2. M. J. Uddin
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  3. T. Bég
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  4. R. Reddy Gorla
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Corresponding author

Correspondence to M. J. Uddin.

Additional information

Biography: O. Anwar BÉG (1969-), Male, Ph. D., Professor

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Bég, O.A., Uddin, M.J., Bég, T. et al. Numerical simulation of self-similar thermal convection from a spinning cone in anisotropic porous medium. J Hydrodyn 28, 184–194 (2016). https://doi.org/10.1016/S1001-6058(16)60620-0

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  • DOI: https://doi.org/10.1016/S1001-6058(16)60620-0

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