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ABSTRACT
Steady-state laminar natural convection in a rectangular cavity surface mounted with two identical heaters on the bottom wall is studied numerically. Natural convection is studied for three cooling configurations: (1) cooling at the left vertical wall, (2) cooling at both the left and right vertical walls, and (3) cooling at the top horizontal wall. The cold walls are cooled isothermally while the other cavity walls are kept adiabatic. The effects of Rayleigh number and cavity inclination on natural convection for the above-mentioned three configurations are studied in detail, and the cooling performances of the configurations are compared in terms of the maximum component temperature. Both the wall cooling and the top wall cooling performances show asymmetric flow and thermal patterns for high Rayleigh numbers, despite the geometric and thermal symmetry of the configurations. The cooling performance of left wall cooling is found to be highly sensitive to cavity inclination. Correlations for dimensionless maximum temperature are presented.
Nomenclature
| avg. Nu | = | average Nusselt number |
| cp | = | specific heat at constant pressure (J/kg K) |
| g | = | gravitational acceleration (m/s2) |
| G | = | spacing between heaters (m) |
| h | = | heat-transfer coefficient (W/m2 K) |
| H, Hh | = | height of the cavity and heaters, respectively (m) |
| k | = | thermal conductivity (W/m K) |
| L | = | spacing between heater and its nearest cavity vertical wall (m) |
| Nu | = | local Nusselt number |
| p | = | pressure (N/m2) |
| p∞ | = | ambient pressure (N/m2) |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| q | = | heat flux at the heaters (W/m2) |
| Ra | = | Rayleigh number |
| T | = | temperature (°C) |
| Tc | = | cold wall temperature (°C) |
| u, v | = | velocity components in x and y-directions, respectively (m/s) |
| U, V | = | dimensionless velocity components in x- and y-directions, respectively |
| W, Wh | = | width of the cavity and heaters, respectively (m) |
| x, y | = | Cartesian coordinates (m) |
| X, Y | = | dimensionless Cartesian coordinates |
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient (K−1) |
| γ | = | cavity inclination |
| ν | = | kinematic viscosity (m2/s) |
| ρ | = | density (1/specific volume) (kg/m3) |
| θ | = | dimensionless temperature |
| Subscripts | = | |
| avg. | = | average |
| c | = | cold wall |
| h | = | heater |
| max | = | maximum |
| w | = | wall |
Nomenclature
| avg. Nu | = | average Nusselt number |
| cp | = | specific heat at constant pressure (J/kg K) |
| g | = | gravitational acceleration (m/s2) |
| G | = | spacing between heaters (m) |
| h | = | heat-transfer coefficient (W/m2 K) |
| H, Hh | = | height of the cavity and heaters, respectively (m) |
| k | = | thermal conductivity (W/m K) |
| L | = | spacing between heater and its nearest cavity vertical wall (m) |
| Nu | = | local Nusselt number |
| p | = | pressure (N/m2) |
| p∞ | = | ambient pressure (N/m2) |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| q | = | heat flux at the heaters (W/m2) |
| Ra | = | Rayleigh number |
| T | = | temperature (°C) |
| Tc | = | cold wall temperature (°C) |
| u, v | = | velocity components in x and y-directions, respectively (m/s) |
| U, V | = | dimensionless velocity components in x- and y-directions, respectively |
| W, Wh | = | width of the cavity and heaters, respectively (m) |
| x, y | = | Cartesian coordinates (m) |
| X, Y | = | dimensionless Cartesian coordinates |
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient (K−1) |
| γ | = | cavity inclination |
| ν | = | kinematic viscosity (m2/s) |
| ρ | = | density (1/specific volume) (kg/m3) |
| θ | = | dimensionless temperature |
| Subscripts | = | |
| avg. | = | average |
| c | = | cold wall |
| h | = | heater |
| max | = | maximum |
| w | = | wall |