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Analysis of coupled conduction and radiation heat transfer in presence of participating medium- using a hybrid method

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Abstract

The current study addresses the mathematical modeling aspects of coupled conductive and radiative heat transfer in presence of absorbing, emitting and isotropic scattering gray medium within two-dimensional square enclosure. The walls of the enclosure are considered to be opaque, diffuse and gray. The enclosure comprised of isothermal vertical walls and insulated horizontal walls. A new hybrid method where the concepts of modified differential approximation employed by blending discrete ordinate method and spherical harmonics method, has been developed for modeling the radiative transport equation. The finite volume method has been adopted as the numerical technique. The effect of various influencing parameters i.e., radiation-conduction parameter, surface emissivity, single scattering albedo and optical thickness has been illustrated. The compatibility of the method with regard to solving coupled conduction and radiation has also been addressed.

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Abbreviations

AW, AE, AS, AN:

Four face areas (West, East, South, North)

I :

Radiation intensity (watt/m2)

I b :

Black body radiation intensity (=σT4/π)

k :

Thermal conductivity (watt m−1 K−1)

H :

Characteristic length (m)

q R :

Radiation heat flux (watt/m2)

Q T :

Total heat flux

q r :

Radiative heat flux

q c :

Conductive heat flux

RC:

Radiation-conduction parameter (=σ T 3 H H/k)

T :

Absolute temperature (K)

T H, T_C :

Hot and cold wall temperatures

X, Y :

Dimensionless co-ordinate.

w i :

Quadrature weight associated with in any direction si

αa:

Absorption coefficient (1/m)

αs:

Scattering coefficient (1/m)

β:

Extinction co-efficient (=αs +αa)

Ω:

Solid angle [sr]

σ:

Stefan Boltzman’s constant [5.67×10−8  watt  m−2  K−4]

ε:

Wall emissivity

ξ, η:

X and Y direction cosines

ω:

Single scattering albedo (αs/β)

ρ:

Reflectivity of the surface.

τ:

Total optical depth (=β H)

θ:

Dimensionless temperature (T/TH)

c:

- Conduction transfer

R:

- Radiation transfer

H, C, L:

- Hot wall, Cold wall, Bottom wall

w, m:

- wall, medium

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Authors and Affiliations

  1. Mechanical Engg. Deptt., University College of Engineering, Burla, Orissa, India

    SK Mahapatra & P Nanda

  2. Burla Engineering College Campus, Qrs No. 3R/32, Professor Colony, 768018, Orissa, India

    SK Mahapatra

  3. Mechanical Engg. Deptt., Jadavpur University, Kolkata, India

    A Sarkar

Authors
  1. SK Mahapatra
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  2. P Nanda
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  3. A Sarkar
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Correspondence to SK Mahapatra.

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Mahapatra, S., Nanda, P. & Sarkar, A. Analysis of coupled conduction and radiation heat transfer in presence of participating medium- using a hybrid method. Heat Mass Transfer 41, 890–898 (2005). https://doi.org/10.1007/s00231-004-0587-4

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