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Conjugate Phase Change Heat Transfer in an Inclined Compound Cavity Partially Filled with a Porous Medium: A Deformed Mesh Approach

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Abstract

In this paper, the melting process of a PCM inside an inclined compound enclosure partially filled with a porous medium is theoretically addressed using a novel deformed mesh method. The sub-domain area of the compound enclosure is made of a porous layer and clear region. The right wall of the enclosure is adjacent to the clear region and is subject to a constant temperature of Tc. The left wall, which is connected to the porous layer, is thick and thermally conductive. The thick wall is partially subject to the hot temperature of Th. The remaining borders of the enclosure are well insulated. The governing equations for flow and heat transfer, including the phase change effects and conjugate heat transfer at the thick wall, are introduced and transformed into a non-dimensional form. A deformed grid method is utilized to track the phase change front in the solid and liquid regions. The melting front movement is controlled by the Stefan condition. The finite element method, along with Arbitrary Eulerian–Lagrangian (ALE) moving grid technique, is employed to solve the non-dimensional governing equations. The modeling approach and the accuracy of the utilized numerical approach are verified by comparison of the results with several experimental and numerical studies, available in the literature. The effect of conjugate wall thickness, inclination angle, and the porous layer thickness on the phase change heat transfer of PCM is investigated. The outcomes show that the rates of melting and heat transfer are enhanced as the thickness of the porous layer increases. The melting rate is the highest when the inclination angle of the enclosure is 45°. An increase in the wall thickness improves the melting rate.

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Abbreviations

A :

Area

A s,i :

Scaled absolute tolerance for degrees of freedom i

C p :

Specific heat capacity

d :

Wall length

Da :

Darcy number

E Y :

Estimate of the local error (absolute error)

g :

Gravitational acceleration

k :

Thermal conductivity

L :

Cavity length

M :

Number of fields

N j :

Number of degrees of freedom in a field

Pr :

Prandtl number

R :

Relative tolerance

Ra :

Rayleigh number

s :

Porous media length

Ste :

Stefen number

t :

Dimensional time

T :

Dimensional temperature

u, v :

Components of dimensional velocity along x and y directions

U, V :

Components of non-dimensional velocity along x and y velocity

x, y :

Dimensional cartesian coordinates

X, Y :

Non-dimensional cartesian coordinatess

Y i :

Scaled solution vector

α :

Thermal diffusivity

β :

Volume expansion coefficient

γ :

Inclination angle

ε :

Porosity

ζ :

Basis function

θ :

Dimensionless temperature

ν f :

Kinematic viscositys

ρ :

Density

τ :

Dimensionless time

c :

Cold

h :

Hot

i, j :

Degrees of freedom, field number

l :

Liquid

m :

Melt

p :

Property of metal foam

s :

Solid

w :

Wall

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Authors and Affiliations

  1. Young Researchers and Elite Club, Yasooj Branch, Islamic Azad University, Yasooj, Iran

    S. A. M. Mehryan

  2. Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Kasra Ayoubi-Ayoubloo

  3. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran

    Mohammad Shahabadi

  4. Metamaterials for Mechanical, Biomechanical and Multiphysical Applications Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Mohammad Ghalambaz

  5. Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Mohammad Ghalambaz & Pouyan Talebizadehsardari

  6. Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Pouyan Talebizadehsardari

  7. Mechanical Engineering Department, Prince Mohammad Endowment for Nanoscience and Technology, Prince Mohammad Bin Fahd University, Al-Khobar, 31952, Saudi Arabia

    Ali Chamkha

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  1. S. A. M. Mehryan
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  2. Kasra Ayoubi-Ayoubloo
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  3. Mohammad Shahabadi
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  4. Mohammad Ghalambaz
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  6. Ali Chamkha
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Correspondence to Mohammad Ghalambaz or Pouyan Talebizadehsardari.

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Mehryan, S.A.M., Ayoubi-Ayoubloo, K., Shahabadi, M. et al. Conjugate Phase Change Heat Transfer in an Inclined Compound Cavity Partially Filled with a Porous Medium: A Deformed Mesh Approach. Transp Porous Med 132, 657–681 (2020). https://doi.org/10.1007/s11242-020-01407-y

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