![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
ABSTRACT
Natural convection from a duct into the quiescent ambient is investigated. Heat transfer and dynamics of natural convection from the duct are discussed using a simple scaling analysis and the corresponding scaling relations are obtained. Additionally, numerical simulation for a wide range of Rayleigh numbers from 100 to 106 and the duct aspect ratios from 0 to 4 with the Prandtl number of 0.71 (air) is performed. The development of natural convection may approach a steady or an unsteady state in a fully developed stage, which is determined by the Rayleigh number and the duct aspect ratio. It is demonstrated that heat transfer of natural convection is improved by the duct for high Rayleigh numbers but depressed for low Rayleigh numbers. The scaling relations of natural convection from the duct have been validated in comparison with numerical results. The scaling predictions are consistent with the numerical results. Furthermore, the formulae of the Nusselt number, the Reynolds number, and the flow rate quantifying natural convection from the duct are presented.
Nomenclature
| A | = | aspect ratio |
| Cp | = | specific heat |
| f | = | frequency |
| g | = | acceleration due to gravity |
| H | = | height of the duct |
| k | = | thermal conductivity |
| Nu | = | Nusselt number |
| Pr | = | Prandtl number, ν/κ |
| qcd | = | heat flux though the duct by thermal diffusion |
| qcv | = | heat flux though the duct by convection |
| Q | = | volumetric flow rate |
| Ra | = | Rayleigh number, gβΔTW3/νκ |
| Re | = | Reynolds number, vaveW/ν |
| t | = | time |
| Δt | = | time step |
| tc | = | time scale when convective heat transfer is larger than conductive one |
| tH | = | time scale when the plume arrives at the duct outlet |
| T | = | temperature |
| ΔT | = | temperature difference between the duct inlet and the ambient |
| Ta | = | temperature of the ambient |
| Ti | = | temperature of the duct inlet |
| u | = | x-velocity |
| v | = | y-velocity |
| vave | = | average velocity of the duct outlet |
| vH | = | y-velocity scale when the plume arrives at the duct outlet |
| W | = | width of the duct |
| x, y | = | horizontal and vertical coordinates |
| β | = | coefficient of thermal expansion |
| κ | = | thermal diffusivity |
| ν | = | kinematic viscosity |
| ρ | = | density |
| δ | = | thickness of the thermal layer at the front of the plume |
Nomenclature
| A | = | aspect ratio |
| Cp | = | specific heat |
| f | = | frequency |
| g | = | acceleration due to gravity |
| H | = | height of the duct |
| k | = | thermal conductivity |
| Nu | = | Nusselt number |
| Pr | = | Prandtl number, ν/κ |
| qcd | = | heat flux though the duct by thermal diffusion |
| qcv | = | heat flux though the duct by convection |
| Q | = | volumetric flow rate |
| Ra | = | Rayleigh number, gβΔTW3/νκ |
| Re | = | Reynolds number, vaveW/ν |
| t | = | time |
| Δt | = | time step |
| tc | = | time scale when convective heat transfer is larger than conductive one |
| tH | = | time scale when the plume arrives at the duct outlet |
| T | = | temperature |
| ΔT | = | temperature difference between the duct inlet and the ambient |
| Ta | = | temperature of the ambient |
| Ti | = | temperature of the duct inlet |
| u | = | x-velocity |
| v | = | y-velocity |
| vave | = | average velocity of the duct outlet |
| vH | = | y-velocity scale when the plume arrives at the duct outlet |
| W | = | width of the duct |
| x, y | = | horizontal and vertical coordinates |
| β | = | coefficient of thermal expansion |
| κ | = | thermal diffusivity |
| ν | = | kinematic viscosity |
| ρ | = | density |
| δ | = | thickness of the thermal layer at the front of the plume |
Acknowledgments
The authors would like to thank the National Natural Science Foundation of China (11572032 and 11272045), the 111 Project (B13002), and the Fundamental Research Funds for the Universities (2015JBC015) for their financial support.