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Numerical analysis of interaction between non-gray radiation and forced convection flow over a recess using the full-spectrum k-distribution method

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Abstract

In the present work, the interaction between non-gray radiation and forced convection in a laminar radiating gas flow over a recess including two backward and forward facing steps in a duct is investigated numerically. Distributions of absorption coefficients across the spectrum (50 cm−1 < η < 20,000 cm−1) are obtained from the HITRAN2008 database. The full-spectrum k-distribution method is used to account for non-gray radiation properties, while the gray radiation calculations are carried out using the Planck mean absorption coefficient. To find the divergence of radiative heat flux distribution, the radiative transfer equation is solved by the discrete ordinates method. The effects of radiation–conduction parameter, wall emissivity, scattering coefficient and recess length on heat transfer behaviors of the convection–radiation system are investigated for both gray and non-gray mediums. In addition, the results of gray medium are compared with non-gray results in order to judge if the differences between these two approaches are significant enough to justify the usage of non-gray models. Results show that for air mixture with 10 % CO2 and 20 % H2O, use of gray model for the radiative properties may cause significant errors and should be avoided.

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Abbreviations

a :

Weight function for full-spectrum k-distribution method

c p :

Specific heat (J kg−1 K−1)

CR:

Contraction ratio

ER:

Expansion ratio

f :

k-Distribution (m)

g:

Cumulative k-distribution

I:

Radiation intensity (W m−2)

k :

Absorption coefficient variable (m−1)

k P :

Planck-mean absorption coefficient (m−1)

Nu c :

Convective Nusselt number

\(\overline{{Nu_{c} }}\) :

Average convective Nusselt number

Nu r :

Radiative Nusselt number

\(\overline{{Nu_{r} }}\) :

Average radiative Nusselt number

Nu t :

Total Nusselt number

\(\overline{{Nu_{t} }}\) :

Average total Nusselt number

q c :

Convective heat flux (W m−2)

q r :

Radiative heat flux (W m−2)

q t :

Total heat flux (W m−2)

Re:

Reynolds number

RC:

Radiation–conduction parameter

s:

Height of step (m)

T:

Temperature (K)

T ave :

Average temperature (K)

\(U_{{^\circ }}\) :

Average velocity of the incoming flow at the inlet section (m/s)

u, v:

x- and y-Components of velocity (m/s)

U, V:

Dimensionless x- and y-component of velocity

x, y:

Horizontal and vertical distance, respectively (m)

X, Y:

Dimensionless horizontal and vertical coordinate, respectively

x r :

Reattachment length (m)

\(\alpha\) :

Thermal diffusivity (m2 s−1)

\(\sigma\) :

Stefan Boatsman’s constant = 5.67 × 10−8 (W m−2 K−4)

\(\sigma_{a\eta }\) :

Spectral absorbing coefficient (m−1)

\(\sigma_{s}\) :

Scattering coefficient (m−1)

\(\varepsilon\) :

Wall emissivity

\(\varphi\) :

Step inclination angle

\(\mu\) :

Dynamic viscosity (N s/m2)

\(\rho\) :

Density (kg/m3)

\(\Theta\) :

Dimensionless temperature

\(\Theta_{b}\) :

Mean bulk temperature

\(\kappa\) :

Thermal conductivity (W m−1 K−1)

\(\theta_{1} ,\theta_{2}\) :

Dimensionless temperature parameters

\(\eta\) :

Wavenumber (cm−1)

b:

Black body

c:

Convective, or cold wall

g:

Cumulative k-distribution

h:

Hot wall

in:

Inlet section

r:

Radiative

t:

Total

w:

Wall

\(\eta\) :

Wavenumber (cm−1)

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Authors and Affiliations

  1. Mechanical Engineering Department, School of Engineering, Shahid Bahonar University, Kerman, Iran

    M. Atashafrooz & S. A. Gandjalikhan Nassab

  2. Mechanical Engineering Department, Graduate University of Advanced Technology, Kerman, Iran

    K. Lari

Authors
  1. M. Atashafrooz
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  2. S. A. Gandjalikhan Nassab
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  3. K. Lari
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Correspondence to S. A. Gandjalikhan Nassab.

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Atashafrooz, M., Gandjalikhan Nassab, S.A. & Lari, K. Numerical analysis of interaction between non-gray radiation and forced convection flow over a recess using the full-spectrum k-distribution method. Heat Mass Transfer 52, 361–377 (2016). https://doi.org/10.1007/s00231-015-1561-z

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