Abstract
Pore-scale heat and fluid flow simulation through reconstructed porous media is presented with the aim of investigating the physics of heat flux splitting at the boundary of porous media. As such, the effects of the solid to fluid thermal conductivity ratio, porosity, pore-scale Reynolds number, Prandtl number and heat conduction within the solid matrix are investigated. The results of the present study for heat transfer coefficient and pressure drop are compared with available experimental data and good agreement was observed. The validated results are then used to investigate the validity of the existing volume-averaged models. It was observed that while results based on the volume-averaged models are reasonably close to current predictions for \(\varepsilon \le 0.7\), the discrepancy between the two becomes notable for higher porosities. While existing models rely exclusively on porosity and thermal conductivity ratio, our newly proposed correlations show the effects of Reynolds number on the heat split mechanism for high porosities. On the other hand, the Prandtl number, at least for the range of parameters studies here, is found to be less influential on the boundary heat split mechanism.
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Abbreviations
- \(k_{\mathrm{f}}\) :
-
Fluid phase thermal conductivity (\(\text{ W }\,\text{ m }^{-1}\,\text{ K }^{-1}\))
- \(k_{\mathrm{s}}\) :
-
Solid phase thermal conductivity (\(\text{ W }\,\text{ m }^{-1}\,\text{ K }^{-1}\))
- \(Pr\) :
-
Prandtl number, \(\nu /\alpha \)
- \(q_{\mathrm{f}}\) :
-
Heat flux received by the fluid phase (\(\text{ W }\,\text{ m }^{-2}\))
- \(q_{\mathrm{s}}\) :
-
Heat flux received by the solid phase (\(\text{ W }\,\text{ m }^{-2}\))
- \(q_{{\mathrm{wo}}}\) :
-
Wall prescribed heat flux (\(\text{ W }\,\text{ m }^{-2}\))
- \(Re_{D_{\mathrm{h}}}\) :
-
Reynolds number based on the channel hydraulic diameter, \({\rho uD_{\mathrm{h}}}/\mu \)
- \(Re_{\mathrm{p}}\) :
-
Reynolds number based on the pore diameter, \({\rho ud_{\mathrm{p}} }/\mu \)
- \(T_{{\mathrm{f,in}}}\) :
-
Fluid temperature at the channel inlet (K)
- \(u_{{\mathrm{in}}}\) :
-
Fluid velocity at the channel inlet (\(\text{ m }\,\text{ s }^{-1}\))
- \(\varepsilon \) :
-
Porosity
- \(\varepsilon _{\mathrm{w}}\) :
-
Wall porosity
- \(\rho \) :
-
Fluid density (\(\text{ kg }\,\text{ m }^{-3}\))
- \(\lambda \) :
-
Solid to fluid thermal conductivity ratio, \({k_{\mathrm{s}}}/{k_{\mathrm{f}}}\)
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Imani, G., Maerefat, M. & Hooman, K. Pore-Scale Numerical Experiment on the Effect of the Pertinent Parameters on Heat Flux Splitting at the Boundary of a Porous Medium. Transp Porous Med 98, 631–649 (2013). https://doi.org/10.1007/s11242-013-0164-8
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DOI: https://doi.org/10.1007/s11242-013-0164-8