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ABSTRACT
A numerical investigation is carried out to understand the effect of natural convection, surface thermal radiation, and wall thermal conduction on the heat transfer from a plate heat source located at the bottom of a three-dimensional rectangular enclosure. The distributions of convective, radiative, and total Nusselt numbers and the average Nusselt number at the surface of the heat source are obtained for the ranges of parameters of 1 × 102 ≤ Ra ≤ 1 × 106, 0 ≤ ϵ ≤ 1, 1 ≤ kr ≤ 15, and 0.5 ≤ AR ≤ 1.5. The increase of thermal radiation restrains the convective heat transfer, but increases the total heat transfer and the overall heat transfer uniformity. Useful correlations have been developed for the average and the standard deviation of the Nusselt numbers at the heat source.
Nomenclature
| Bi | = | Biot number |
| cp | = | specific heat of the fluid |
| Fi-j | = | view factor from element i to element j |
| g | = | gravitational acceleration |
| H | = | height of the cavity |
| k | = | thermal conductivity |
| l | = | thickness of the wall |
| L | = | width of the cavity |
| Nrad | = | radiation number, defined by Eq. (11) |
| Nu | = | local Nusselt number |
| = | average Nusselt number | |
| P | = | dimensionless pressure |
| Pr | = | Prantdl number |
| Qrad | = | dimensionless radiative heat flux |
| R | = | dimensionless radiosity |
| Ra | = | Rayleigh number |
| T | = | temperature |
| = | dimensionless velocity vector | |
| x,y,z | = | coordinate system |
| α | = | thermal diffusivity |
| β | = | coefficient of volumetric expansion |
| ϵ | = | surface emissivity |
| υ | = | kinematic viscosity |
| ξ | = | temperature parameter (= Tam/Ths). |
| ρ | = | density of the fluid |
| σ | = | standard deviation |
| τ | = | dimensionless time |
| Subscripts | = | |
| am | = | ambient |
| con | = | convective |
| f | = | fluid |
| hs | = | heat source |
| r | = | the ratio of the solid to fluid properties |
| rad | = | radiative |
| s | = | solid |
| tot | = | total |
Nomenclature
| Bi | = | Biot number |
| cp | = | specific heat of the fluid |
| Fi-j | = | view factor from element i to element j |
| g | = | gravitational acceleration |
| H | = | height of the cavity |
| k | = | thermal conductivity |
| l | = | thickness of the wall |
| L | = | width of the cavity |
| Nrad | = | radiation number, defined by Eq. (11) |
| Nu | = | local Nusselt number |
| = | average Nusselt number | |
| P | = | dimensionless pressure |
| Pr | = | Prantdl number |
| Qrad | = | dimensionless radiative heat flux |
| R | = | dimensionless radiosity |
| Ra | = | Rayleigh number |
| T | = | temperature |
| = | dimensionless velocity vector | |
| x,y,z | = | coordinate system |
| α | = | thermal diffusivity |
| β | = | coefficient of volumetric expansion |
| ϵ | = | surface emissivity |
| υ | = | kinematic viscosity |
| ξ | = | temperature parameter (= Tam/Ths). |
| ρ | = | density of the fluid |
| σ | = | standard deviation |
| τ | = | dimensionless time |
| Subscripts | = | |
| am | = | ambient |
| con | = | convective |
| f | = | fluid |
| hs | = | heat source |
| r | = | the ratio of the solid to fluid properties |
| rad | = | radiative |
| s | = | solid |
| tot | = | total |