A finite element method for heat transfer of power-law flow in channels with a transverse magnetic field

Huandi Shi, Ping Lin (Lead / Corresponding author), Botong Li, Liancun Zheng

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    Heat transfer of a power-law non-Newtonian incompressible fluid in channels with porous walls has not been carefully studied using a proper numerical method despite a few constructions of approximate analytic solutions through the similarity transformation and perturbation method for Newtonian fluids (i.e. power-law index being one). In this paper, we propose a finite element method for the thermal incompressible flow equations. The incompressible condition is treated by a penalty formulation. Numerical solutions are validated by comparing them with an approximate analytic solution of the Navier-Stokes equation in the Newtonian fluid case. Then, the method is used to simulate the heat transfer of various power-law fluids. Additionally, unlike previous studies, we allow the thermal diffusivity to be a function of temperature gradient. The effect of different values of the parameters on the temperature and velocity is also discussed in this paper.
    Original languageEnglish
    Pages (from-to)1121-1129
    Number of pages9
    JournalMathematical Methods in the Applied Sciences
    Volume37
    Issue number8
    DOIs
    Publication statusPublished - 30 May 2014

    Fingerprint

    Newtonian Fluid
    Analytic Solution
    Heat Transfer
    Power Law
    Transverse
    Finite Element Method
    Magnetic Field
    Magnetic fields
    Heat transfer
    Finite element method
    Thermal Diffusivity
    Power-law Fluid
    Fluids
    Similarity Transformation
    Non-Newtonian Fluid
    Perturbation Method
    Incompressible Flow
    Incompressible Fluid
    Penalty
    Navier-Stokes Equations

    Cite this

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    abstract = "Heat transfer of a power-law non-Newtonian incompressible fluid in channels with porous walls has not been carefully studied using a proper numerical method despite a few constructions of approximate analytic solutions through the similarity transformation and perturbation method for Newtonian fluids (i.e. power-law index being one). In this paper, we propose a finite element method for the thermal incompressible flow equations. The incompressible condition is treated by a penalty formulation. Numerical solutions are validated by comparing them with an approximate analytic solution of the Navier-Stokes equation in the Newtonian fluid case. Then, the method is used to simulate the heat transfer of various power-law fluids. Additionally, unlike previous studies, we allow the thermal diffusivity to be a function of temperature gradient. The effect of different values of the parameters on the temperature and velocity is also discussed in this paper.",
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    A finite element method for heat transfer of power-law flow in channels with a transverse magnetic field. / Shi, Huandi; Lin, Ping (Lead / Corresponding author); Li, Botong; Zheng, Liancun.

    In: Mathematical Methods in the Applied Sciences, Vol. 37, No. 8, 30.05.2014, p. 1121-1129.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - A finite element method for heat transfer of power-law flow in channels with a transverse magnetic field

    AU - Shi, Huandi

    AU - Lin, Ping

    AU - Li, Botong

    AU - Zheng, Liancun

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