Abstract
The present work investigates the thermal radiation transport inside porous media under local thermal non-equilibrium conditions. Two different geometrical situations, a two-dimensional channel and a cylindrical geometry, are considered in the analysis. Porous media application is generally associated with high-temperature combustion, and radiative heat transfer is dominant. In this paper, by considering a stream of high-temperature flow in geometries filled with porous medium, the effect of thermal radiation on the solid- and fluid-phase temperature fields is calculated and analyzed. Two radiative heat transfer techniques, the discrete ordinate method (DOM) and the finite volume method (FVM), are tested, and the results are compared with a non-radiative model and with a model-based Rosseland approximation. A sensitivity study for the variation in absorption and scattering coefficients and the effect on the solid- and fluid-phase temperature fields is also undertaken. The effect of the extinction coefficient on the Nusselt number is also examined. The temperatures obtained through the Rosseland model show differences up to + 34% and − 26% compared to temperatures calculated with the DOM or FVM radiation calculation methods. The temperature fields obtained through DOM and FVM are very similar, and some significant differences can only be seen in the cases where a very low number of angular directions are used.
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Abbreviations
- \(c_{\text{F}}\) :
-
Forchheimer coefficient
- \(c_{\text{p}}\) :
-
Constant pressure specific heat of mixture (kJ/kg K)
- d p :
-
Particle diameter (m)
- d m :
-
Mean pore diameter (m)
- \(D_{\text{diff}}\) :
-
Macroscopic diffusion tensor
- \(G\) :
-
Incident radiation function
- h :
-
Interfacial convective heat transfer coefficient (W/m2 K)
- \(h_{\text{v}}\) :
-
Volumetric heat transfer coefficient (W/m3 K)
- \({\mathbf{I}}\) :
-
Unit tensor
- K :
-
Permeability (m2)
- \(k_{\text{f}}\) :
-
Fluid thermal conductivity (W/m K)
- \(k_{\text{s}}\) :
-
Solid thermal conductivity (W/m K)
- \({\mathbf{K}}_{\text{disp}}\) :
-
Dispersion conductivity tensor
- \({\text{K}}_{\text{eff}}\) :
-
Effective thermal conductivity tensor
- \(K_{\text{r}}\) :
-
Local Rosseland mean attenuation coefficient (m−1)
- Nu:
-
Local Nusselt number
- p :
-
Pressure (N/m2)
- T :
-
Temperature (K)
- \({\mathbf{u}}_{\text{D}}\) :
-
Average surface velocity (m/s)
- \(\alpha_{\text{eff}}\) :
-
Effective absorptivity
- \(\varepsilon_{\text{eff}}\) :
-
Effective emissivity
- \(\kappa\) :
-
Absorption coefficient (m−1)
- \(\mu\) :
-
Dynamic viscosity (kg/m s)
- \(\rho\) :
-
Density (kg/m3) or reflectivity (−)
- σ :
-
Stefan–Boltzmann constant (W/m2 K4)
- \(\sigma_{\text{s}}\) :
-
Scattering coefficient (m−1)
- ϕ :
-
\(\phi =\Delta V_{\text{f}} /\Delta V\), porosity
- b:
-
Black body
- f:
-
Fluid
- in:
-
Inlet
- s:
-
Solid
- w:
-
Wall
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Acknowledgements
The authors are thankful to CNPQ, Brazil, for their financial support during the preparation of this work and to the Loughborough University for providing the facilities, equipment, all the support necessary.
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Moro Filho, R.C., Malalasekera, W. An Analysis of Thermal Radiation in Porous Media Under Local Thermal Non-equilibrium. Transp Porous Med 132, 683–705 (2020). https://doi.org/10.1007/s11242-020-01408-x
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DOI: https://doi.org/10.1007/s11242-020-01408-x