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Effect of the surface thermal radiation on turbulent natural convection in tall cavities of façade elements

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Abstract

The effect of the surface thermal radiation in tall cavities with turbulent natural convection regime was analyzed and quantified numerically. The parameters considered were: the Rayleigh number 109–1012, the aspect ratio 20, 40 and 80 and the emmisivity 0.0–1.0. The percentage contribution of the radiative surface to the total heat transfer has a maximum value of  15.19% (Ra = 109, A = 20) with emissivity equal to 1.0 and a minimum of 0.5% (Ra = 1012, A = 80) with ε* = 0.2. The average radiative Nusselt number for a fixed emissivity is independent of the Rayleigh number, but for a fixed Rayleigh number diminishes with the increase of the aspect ratio. The results indicate that the surface thermal radiation does not modify significantly the flow pattern in the cavity, just negligible effects in the bottom and top of the cavity were observed. Two different temperature patterns were observed a conductive regime Ra = 109 and a boundary layer regime Ra = 1012.

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Abbreviations

A :

aspect ratio (H/L)

C p :

specific heat, J kg−1 K−1

C 1ε , C 2ε , C 3ε , C μ :

constants of the turbulence model

dF Aj–Ak :

view factor between elements j–k

g :

gravitational acceleration, 9.81 m s−2

G k :

buoyancy production/destruction of kinetic energy

H :

height of the cavity, m

k :

turbulence kinetic energy, m2 s−2

L :

length of the cavity, m

Nu :

Nusselt number

P :

pressure, Pa

P K :

turbulence kinetic energy production

q :

heat flux, W m−2

Ra :

Rayleigh number, (gβΔTH 3 /να)

T :

temperature, K

T*:

non-dimensional temperature, (T – T c )/ΔT

u O :

reference velocity, (gβΔTH)0.5 m s−1

u :

horizontal velocity component, m s−1

u*:

non-dimensional horizontal velocity, u/u O

v :

vertical velocity component, m s−1

v*:

non-dimensional vertical velocity, v/u O

x :

horizontal coordinate, m

x*:

non-dimensional horizontal coordinate, x/H

y :

vertical coordinate, m

y*:

non-dimensional vertical coordinate, y/H

α :

thermal diffusivity, m2 s−1

β :

thermal expansion coefficient, K−1

ΔT :

temperature difference, (T h  – T c ) K

ε :

rate of disipation of k

ε*:

emissivity

λ :

thermal conductivity, W m−1 K−1

μ :

dynamic viscosity, kg m−1 s−1

μ t :

turbulent viscosity, kg m−1 s−1

ν :

kinematic viscosity, m2 s−1

ρ :

density, kg m−3

σ :

Stefan–Boltzmann Constant, W m−2 K−4

c:

cold wall

conv:

convective

h:

tot wall

max:

maximum

mean:

average

min:

minimum

rad:

radiative

total:

total quantities

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Authors and Affiliations

  1. Departamento de Ingeniería Mecánica-Térmica, Centro Nacional de Investigación y Desarrollo Tecnológico, CENIDET-DGEST-SEP, Prol. Av. Palmira s/n. Col. Palmira, Cuernavaca, Morelos, CP 62490, Mexico

    J. P. Xamán & J. J. Flores

  2. Departamento de Ingeniería Química y Metalurgia, Universidad de Sonora, Blvd. Luis Encinas y Rosales s/n. Col. Centro, Hermosillo, Sonora, CP 83000, Mexico

    J. F. Hinojosa & R. E. Cabanillas

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  1. J. P. Xamán
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  2. J. F. Hinojosa
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  3. J. J. Flores
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  4. R. E. Cabanillas
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Correspondence to J. P. Xamán.

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Xamán, J.P., Hinojosa, J.F., Flores, J.J. et al. Effect of the surface thermal radiation on turbulent natural convection in tall cavities of façade elements. Heat Mass Transfer 45, 177–185 (2008). https://doi.org/10.1007/s00231-008-0393-5

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  • DOI: https://doi.org/10.1007/s00231-008-0393-5

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