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On the viscous dissipation modeling of thermal fluid flow in a porous medium

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Abstract

The problem of viscous dissipation and thermal dispersion in saturated porous medium is numerically investigated for the case of non-Darcy flow regime. The fluid is induced to flow upward by natural convection as a result of a semi-infinite vertical wall that is immersed in the porous medium and is kept at constant higher temperature. The boundary layer approximations were used to simplify the set of the governing, nonlinear partial differential equations, which were then non-dimensionalized and solved using the finite elements method. The results for the details of the governing parameters are presented and investigated. It is found that the irreversible process of transforming the kinetic energy of the moving fluid to heat energy via the viscosity of the moving fluid (i.e., viscous dissipation) resulted in insignificant generation of heat for the range of parameters considered in this study. On the other hand, thermal dispersion has shown to disperse heat energy normal to the wall more effectively compared with the normal diffusion mechanism.

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Abbreviations

C :

Empirical constant

d :

Pore diameter

Ge:

Gebhart number

g :

Gravitational constant

K :

Permeability of the porous medium

k :

Thermal conductivity

Nu x :

Local Nusselt number

p :

Pressure

q :

Local heat flux

Ra:

Rayleigh number

\({\bar{{T}}}\) :

Temperature

T :

Non-dimensional temperature

\({\bar{{u}}, \bar{{v}}}\) :

Velocity components in the \({\bar{{x}}}\) and\({\bar{{y}}}\) directions

u, v :

Non-dimensional velocity components in the x and y directions

\({\bar{{x}}, \bar{{y}}}\) :

Cartesian coordinates

x, y :

Non-dimensional Cartesian coordinates

ρ :

Fluid density

μ :

Viscosity

ν :

Fluid kinematic viscosity

α :

Molecular thermal diffusivity

β :

Thermal expansion coefficient

ψ :

Dimensional stream function

w :

Evaluated on the wall

∞:

Evaluated at the outer edge of the boundary layer

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Authors and Affiliations

  1. King Abdullah University of Science and Technology (KAUST), Thuwal, Kingdom of Saudi Arabia

    Amgad Salama, M. F. El-Amin & Shuyu Sun

  2. Mathematics Department, Aswan Faculty of Science, South Valley University, Aswan, 81258, Egypt

    M. F. El-Amin

  3. Mathematics Department, Faculty of Science, Sohag University, Sohag, Egypt

    Ibrahim Abbas

Authors
  1. Amgad Salama
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  2. M. F. El-Amin
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  3. Ibrahim Abbas
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  4. Shuyu Sun
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Correspondence to M. F. El-Amin.

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Salama, A., El-Amin, M.F., Abbas, I. et al. On the viscous dissipation modeling of thermal fluid flow in a porous medium. Arch Appl Mech 81, 1865–1876 (2011). https://doi.org/10.1007/s00419-011-0523-2

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  • DOI: https://doi.org/10.1007/s00419-011-0523-2

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