http://orcid.org/0000-0002-8430-6917
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Abstract
The flow structure and temperature field of the conjugate turbulent mixed convection in an open cavity were investigated numerically. Results including the local and average temperatures as well as Nusselt number were obtained and compared for the Reynolds number of 1200, the Rayleigh numbers of 1.25 × 1012 ≤ Ra ≤ 2.5 × 1013, the thermal conductivity ratios of 1 ≤ ≤ 1 × 105, and the reduced wall thickness of 0.05 ≤ δ ≤ 0.5. The conjugate model as well as two commonly used simplified heat conduction models, that is, one-dimensional and lumped-parameter methods, were used to solve the issue of heat transfer within the solid walls. The effects of the buoyancy, thermal conductance ratio, and reduced thickness on the errors in predicting the dimensionless temperature profile and Nusselt number using two simplified wall conduction models are discussed in detail. The results show that the one-dimensional method accurately predicts the flow field and temperature distribution for all cases considered. The lumped-parameter method shows a lower temperature distribution but a closer average Nusselt number with the conjugate method. The errors in the simplified models also increase with the increasing buoyancy force.
Nomenclature
| g | = | gravity acceleration (m/s2) |
| L | = | height and length of the cavity (m) |
| l | = | thickness of the side wall (m) |
| k | = | thermal conductivity (W/K·m) |
| kr | = | thermal conductivity ratio |
| Nu | = | Nusselt number |
| p | = | pressure (Pa) |
| Pr | = | Prandtl number |
| q | = | heat flux (W/m2) |
| Ra | = | Rayleigh number |
| Re | = | Reynolds number |
| T | = | temperature (K) |
| t | = | time (s) |
| ui | = | velocity component (m/s) |
| X, Z | = | spatial direction |
| Greek symbols | ||
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient (1/K) |
| θ | = | dimensionless temperature |
| ρ | = | density (kg/m3) |
| μ | = | dynamic viscosity (Pa·s) |
| ν | = | kinematic viscosity (m2/s) |
| δ | = | reduced thickness |
| Subscripts | ||
| f | = | fluid |
| s | = | solid |
| in | = | inlet condition |
| out | = | outlet condition |
| local | = | local value |
| avg | = | average value |
Nomenclature
| g | = | gravity acceleration (m/s2) |
| L | = | height and length of the cavity (m) |
| l | = | thickness of the side wall (m) |
| k | = | thermal conductivity (W/K·m) |
| kr | = | thermal conductivity ratio |
| Nu | = | Nusselt number |
| p | = | pressure (Pa) |
| Pr | = | Prandtl number |
| q | = | heat flux (W/m2) |
| Ra | = | Rayleigh number |
| Re | = | Reynolds number |
| T | = | temperature (K) |
| t | = | time (s) |
| ui | = | velocity component (m/s) |
| X, Z | = | spatial direction |
| Greek symbols | ||
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient (1/K) |
| θ | = | dimensionless temperature |
| ρ | = | density (kg/m3) |
| μ | = | dynamic viscosity (Pa·s) |
| ν | = | kinematic viscosity (m2/s) |
| δ | = | reduced thickness |
| Subscripts | ||
| f | = | fluid |
| s | = | solid |
| in | = | inlet condition |
| out | = | outlet condition |
| local | = | local value |
| avg | = | average value |