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- Stąpór, Paweł (1)
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- extended finite element method (1)
  
  level set method (1)
  
  natural convection (1)
  
  phase change (1)
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Non-Newtonian fluid flow between parallel plates filled with an anisotropic porous medium

Amit Kumar Krishna Prasad Madasu

Archive of Mechanical Engineering | 2024 | vol. 71 | No 2 | 273-294

Słowa kluczowe anisotropic porous medium permeability ratio anisotropic angle micropolar fluid slip

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Abstrakt

Micropolar fluid flow through an anisotropic porous medium between two horizontally oriented impermeable plates under the effect of slip conditions for velocity and microrotation vectors at both plates are analysed in this paper. The permeability of an anisotropic porous medium is along two principal axes of permeability K₁ and K₂. The principal axis with permeability K₂ forms an angle ψ with the horizontal direction called anisotropic (or orientation) angle. It is observed that the velocity and the microrotation profiles decrease as permeability ratio K and orientation angle ψ increase. Velocity slip (β₁ and β₂) parameters show the effect on the velocity profile near upper and lower plates but have a strong influence on the microrotation profile. The spin slip (σ₁ and σ₂) parameters showed minor enhancement in the velocity profile but had an increasing effect on the microrotation vector. The decrease in permeability ratio and anisotropic angle results in an increase in skin friction. The impact of other parameters like Darcy number Da, micropolar parameter N on velocity and microrotation vectors are presented graphically and discussed. The presence of the slip effect helps to reduce the impact of friction due to plates causing fluid flow to enhance.

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Autorzy i Afiliacje

Amit Kumar

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Krishna Prasad Madasu

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National Institute of Technology Raipur, Raipur, India

The modified XFEM for solving problems of a phase change with natural convection

Paweł Stąpór

Archive of Mechanical Engineering | 2019 | vol. 66 | No 3 | 273-294 | DOI: 10.24425/ame.2019.129676

Słowa kluczowe phase change natural convection extended finite element method level set method

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Abstrakt

This paper presents an extended finite element method applied to solve phase change problems taking into account natural convection in the liquid phase. It is assumed that the transition from one state to another, e.g., during the solidification of pure metals, is discontinuous and that the physical properties of the phases vary across the interface. According to the classical Stefan condition, the location, topology and rate of the interface changes are determined by the jump in the heat flux. The incompressible Navier-Stokes equations with the Boussinesq approximation of the natural convection flow are solved for the liquid phase. The no-slip condition for velocity and the melting/freezing condition for temperature are imposed on the interface using penalty method. The fractional four-step method is employed for analysing conjugate heat transfer and unsteady viscous flow. The phase interface is tracked by the level set method defined on the same finite element mesh. A new combination of extended basis functions is proposed to approximate the discontinuity in the derivative of the temperature, velocity and the pressure fields. The single-mesh approach is demonstrated using three two-dimensional benchmark problems. The results are compared with the numerical and experimental data obtained by other authors.

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Autorzy i Afiliacje

Paweł Stąpór

Faculty of Management and Computer Modelling, Kielce University of Technology, Kielce, Poland.