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Convection in a Lid-Driven Heat-Generating Porous Cavity with Alternative Thermal Boundary Conditions

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Abstract

Mixed convection flow in a two-sided lid-driven cavity filled with heat-generating porous medium is numerically investigated. The top and bottom walls are moving in opposite directions at different temperatures, while the side vertical walls are considered adiabatic. The governing equations are solved using the finite-volume method with the SIMPLE algorithm. The numerical procedure adopted in this study yields a consistent performance over a wide range of parameters that were 10−4 ≤ Da ≤ 10−1 and 0 ≤ Ra I ≤ 104. The effects of the parameters involved on the heat transfer characteristics are studied in detail. It is found that the variation of the average Nusselt number is non-linear for increasing values of the Darcy number with uniform or non-uniform heating condition.

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Abbreviations

H :

Enclosure length (m)

K e :

Effective thermal conductivity of porous medium (Wm−1K−1)

Nu :

Local Nusselt number

Nu avg :

Average Nusselt number

q′′′:

Volumetric heat generation

Ra E :

External Rayleigh number (Gr·Pr)

T :

Dimensionless temperature, \({\frac {\theta-\theta_c}{\theta_h-\theta_c}}\)

U 0 :

Lid-driven velocity (m/s)

U c :

Dimensionless velocity in the x-direction at the mid-plane of the cavity

u, v:

Velocities in x- and y-directions

V c :

Dimensionless velocity in the y-direction at the mid-plane of the cavity

x, y:

Cartesian coordinates

α e :

Effective thermal diffusivity of the porous medium (m2s−1)

β :

Coefficient of thermal expansion of fluid (K−1)

Δθ :

Temperature difference

θ :

Temperature (°C)

K :

Permeability of porous medium (m2)

μ :

Effective dynamic viscosity (Pa s−1)

ν :

Effective kinematic viscosity, μ/ρ

ρ :

Fluid density (kgm−3)

avg:

Average

C :

Cold wall

H :

Hot wall

l :

Local

References

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Correspondence to M. Muthtamilselvan.

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Muthtamilselvan, M., Das, M.K. & Kandaswamy, P. Convection in a Lid-Driven Heat-Generating Porous Cavity with Alternative Thermal Boundary Conditions. Transp Porous Med 82, 337–346 (2010). https://doi.org/10.1007/s11242-009-9429-7

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Keywords

  • Mixed convection
  • Heat generation
  • Porous medium
  • Finite-volume method