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ABSTRACT
In this study the physical system under consideration is a three-dimensional (3D) cabinet with arrays of block heat sources mounted on one of the walls of the cabinet. The block heat sources dissipate heat to the surrounding cabinet through conjugate conduction and natural convection. The results illustrate that the difference in hot spot temperature (θH) for situations with and without consideration of thermal interaction between the system and its surrounding area is higher for smaller Rayleigh number (Ra), and can be up to 94.73% with Ra = 105. In addition, heat transfer characteristics depend strongly on the dimensionless heat conductivity of the cabinet wall (Kwf), heat conductivity of the block (Kbf), and length of cabinet (Cx). The maximum reduction in θH is 70.01% when Kwf varies from 10 to 1,000, 12.7% for 10 ≦ Kbf ≦ 1,000, and 30.07% for 0.5 ≦ Cx ≦ 1. The variation in hot spot temperature of blocks is not sensitive to cabinet angle (Φ).
Nomenclature
| Bx | = | dimensionless length of block, bx/cy |
| By | = | dimensionless height of block, by/cy |
| Bz | = | dimensionless width of block, bz/cy |
| Bsx | = | dimensionless spacing between blocks in X direction, bsx/cy |
| Bsy | = | dimensionless spacing between blocks in Y direction, bsy/cy |
| Ct | = | dimensionless thickness of cabinet wall, ct/cy |
| Cx | = | dimensionless length of cabinet, cx/cy |
| cy | = | height of cabinet |
| Cz | = | dimensionless width of cabinet, cz/cy |
| g | = | gravity acceleration |
| h | = | heat transfer coefficient |
| Kbf | = | ratio of block to air thermal conductivities, kb/kf |
| Kwf | = | ratio of cabinet wall to air thermal conductivities, kw/kf |
| Nu | = | local Nusselt number, Eq. (14) |
| = | line-average Nusselt number in X direction, Eq. (15) | |
| = | line-average Nusselt number in Y direction, Eq. (16) | |
| n | = | dimensionless coordinate outward normal to heat transfer surface |
| P | = | dimensionless pressure, (p − p∞)/( |
| Pr | = | Prandtl number, νf/αf |
| = | heat generation rate per each block | |
| Ra | = | Rayleigh number, gβ |
| T | = | temperature |
| T∞ | = | temperature at region distant to cabinet |
| U | = | dimensionless velocity in x direction, ucy/ αf |
| V | = | dimensionless velocity in y direction, vcy/ αf |
| W | = | dimensionless velocity in z direction, wcy/ αf |
| X | = | dimensionless longitudinal coordinate, x/cy |
| Xl | = | X location of left surface of block |
| Y | = | dimensionless vertical coordinate, y/cy |
| Yb | = | Y location of bottom surface of block |
| Z | = | dimensionless lateral coordinate, z/cy |
| αf | = | thermal diffusivity of air |
| β | = | coefficient of thermal expansion |
| θ | = | dimensionless temperature, (T − T∞)/( |
| θb | = | dimensionless temperature of block |
| θf | = | dimensionless temperature of air stream inside or outside the cabinet |
| θH | = | dimensionless hot spot temperature of block |
| θmax | = | dimensionless maximum temperature of block |
| θw | = | dimensionless temperature of cabinet wall |
| νf | = | kinematic viscosity of air |
| ρf | = | density of air |
| Φ | = | angle of cabinet |
Nomenclature
| Bx | = | dimensionless length of block, bx/cy |
| By | = | dimensionless height of block, by/cy |
| Bz | = | dimensionless width of block, bz/cy |
| Bsx | = | dimensionless spacing between blocks in X direction, bsx/cy |
| Bsy | = | dimensionless spacing between blocks in Y direction, bsy/cy |
| Ct | = | dimensionless thickness of cabinet wall, ct/cy |
| Cx | = | dimensionless length of cabinet, cx/cy |
| cy | = | height of cabinet |
| Cz | = | dimensionless width of cabinet, cz/cy |
| g | = | gravity acceleration |
| h | = | heat transfer coefficient |
| Kbf | = | ratio of block to air thermal conductivities, kb/kf |
| Kwf | = | ratio of cabinet wall to air thermal conductivities, kw/kf |
| Nu | = | local Nusselt number, Eq. (14) |
| = | line-average Nusselt number in X direction, Eq. (15) | |
| = | line-average Nusselt number in Y direction, Eq. (16) | |
| n | = | dimensionless coordinate outward normal to heat transfer surface |
| P | = | dimensionless pressure, (p − p∞)/( |
| Pr | = | Prandtl number, νf/αf |
| = | heat generation rate per each block | |
| Ra | = | Rayleigh number, gβ |
| T | = | temperature |
| T∞ | = | temperature at region distant to cabinet |
| U | = | dimensionless velocity in x direction, ucy/ αf |
| V | = | dimensionless velocity in y direction, vcy/ αf |
| W | = | dimensionless velocity in z direction, wcy/ αf |
| X | = | dimensionless longitudinal coordinate, x/cy |
| Xl | = | X location of left surface of block |
| Y | = | dimensionless vertical coordinate, y/cy |
| Yb | = | Y location of bottom surface of block |
| Z | = | dimensionless lateral coordinate, z/cy |
| αf | = | thermal diffusivity of air |
| β | = | coefficient of thermal expansion |
| θ | = | dimensionless temperature, (T − T∞)/( |
| θb | = | dimensionless temperature of block |
| θf | = | dimensionless temperature of air stream inside or outside the cabinet |
| θH | = | dimensionless hot spot temperature of block |
| θmax | = | dimensionless maximum temperature of block |
| θw | = | dimensionless temperature of cabinet wall |
| νf | = | kinematic viscosity of air |
| ρf | = | density of air |
| Φ | = | angle of cabinet |