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Numerical Study of Natural Convection Heat Transfer in an Inclined Porous Cavity with Time-Periodic Boundary Conditions

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Abstract

Kalabin et al. (Numer. Heat Transfer A 47, 621-631, 2005) studied the unsteady natural convection for the sinusoidal oscillating wall temperature on one side wall and constant average temperature on the opposing side wall. The present article is on the unsteady natural convective heat transfer in an inclined porous cavity with similar temperature boundary conditions as those of Kalabin et al. The inclined angle \({\varphi}\) of the cavity is varied from 0° to 80°. The flow field is modeled with the Brinkman-extended Darcy model. The combined effects of inclination angle of the enclosure and oscillation frequency of wall temperature are studied for Ra* = 103, Da = 10−3, \({\varepsilon =0.6}\) , and Pr=1. Some results are also obtained with the Darcy–Brinkman–Forchheimer model and Darcy’s law and are compared with the present Brinkman-extended Darcy model. The maximal heat transfer rate is attained at the oscillating frequency f = 46.7π and the inclined angle \({\varphi = 42.2^{\circ}}\) .

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Abbreviations

c :

Specific heat

c a :

Acceleration coefficient of the porous medium

Da :

Darcy number

f :

Dimensionless oscillating frequency

F :

Inertia coefficient

H :

Height of cavity

k :

Thermal conductivity

K :

Permeability

Nu av :

Time-averaged Nusselt number in one period

Nu R :

Average Nusselt number at right wall

P :

Dimensionless pressure

p :

Pressure

Pr :

Prandtl number

\({\rm {R^{\ast}_a}}\) :

Rayleigh–Darcy number

t :

Time

T :

Temperature

u, v :

Velocity components along x- and y-axes, respectively

v :

Velocity vector

U, V :

Dimensionless velocity components along X- and Y-axes, respectively

|V|:

Magnitude of velocity vector

x, y :

Cartesian coordinates

X, Y :

Dimensionless Cartesian coordinates

αf :

Thermal diffusivity

αm :

Modified thermal diffusivity of the porous medium

\({\varepsilon}\) :

Porosity

θ :

Dimensionless temperature

μ :

Viscosity

ν f :

Fluid kinematic viscosity

ρ :

Density

τ :

Dimensionless time

τ p :

Dimensionless period of oscillation

σ :

Specific heat ratio

ω :

Oscillating frequency

\({\varphi}\) :

Inclined angle of the cavity

f:

Fluid

m:

Fluid-saturated porous medium

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Authors and Affiliations

  1. State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Gang Wang, Qiuwang Wang, Min Zeng & Hiroyuki Ozoe

  2. School of Civil Engineering, Lanzhou University of Technology, Lanzhou, 730050, China

    Gang Wang

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  1. Gang Wang
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  2. Qiuwang Wang
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  3. Min Zeng
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  4. Hiroyuki Ozoe
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Correspondence to Qiuwang Wang.

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Wang, G., Wang, Q., Zeng, M. et al. Numerical Study of Natural Convection Heat Transfer in an Inclined Porous Cavity with Time-Periodic Boundary Conditions. Transp Porous Med 74, 293–309 (2008). https://doi.org/10.1007/s11242-007-9198-0

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