Thermal resistance of tray to the ambient air temperature.
| $0$ | Black & Harshe |
| $0$ | Saadat2017 |
| $\frac{\rho_{ty}}{2S_{tw,T}+2S_{tw,S}}$ | Cableizer |
| Id | Method | Info |
|---|---|---|
| 0 | Black & Harshe | The method by Stolpe (1971) treats the random mixture of cables in a tray as a homogeneous rectangular mass with uniform heat generation, assuming cables are installed at a uniform depth and that all cables are power cables generating heat uniformly throughout the tray cross-section. Conduction is the governing mode of heat flow within a tightly packed cable mass, so ampacities are placed in proportion to the cross-sectional area of each composite cable. The allowable heat intensity Q (W per unit area of tray) is determined by balancing the temperature drop through the cable mass (treated as a rectangular slab with uniform internal heat generation) and the temperature drop through the surrounding air (by convection and radiation). The three governing equations are solved iteratively for the total allowable heat, after which the ampacity of each individual cable is found from its cross-sectional area. The method assumes one-dimensional vertical heat flow and ignores heat loss from the sides, which is a reasonable simplification for trays 6 inches and wider. This method formed the basis for the ampacity tables in ICEA/NEMA Standard P54-440. |
| 1 | Saadat2017 | The method by Engmann (1984) extends the homogeneous cable mass approach to covered trays by dividing the system into five thermal regions. Regions 1 and 2 cover the packed cable mass below and above the unknown location of the maximum temperature, where heat transfer is by conduction through a mass of constant thermal conductivity with uniform heat generation per unit volume. Region 3 is the air space between the top of the cable mass and the tray cover, where conductive and convective heat transfer are characterised by an empirically derived equivalent thermal conductivity k3 based on the Grashof number, and radiation is treated using a geometry-dependent view factor. Regions 4 and 5 account for heat dissipation from the bottom of the cable mass and tray surface, and from the tray cover to the ambient air, respectively. The simultaneous solution for the distance to the maximum temperature and the allowable heat generation per unit volume is obtained iteratively, and the ampacity is then calculated from the relationship between heat generation and conductor resistance. |
| 2 | Cableizer | The methods by Harshe and Black (1994, 1997) use a mathematical thermal model based on conservation of energy to predict cable operating temperatures in single open-top and single covered trays, respectively. The cable bundle is treated as a uniform mass with an equivalent thermal resistivity, and heat generated within the bundle is transferred to the surface by conduction and then dissipated to ambient by free convection and radiation using classical Nusselt number correlations. Two loading scenarios are accommodated: a uniform model in which heat is distributed evenly across the tray cross-section, and a layered (hot-spot) model in which the most heavily loaded cables are assumed to be concentrated along the centreline and surrounded by more lightly loaded cables, yielding a conservative maximum temperature. For covered trays, an additional energy balance on the cover accounts for the trapped stagnant air layer between the cable mass and the cover, and a derating factor is introduced defined as the ratio of the ampacity in a covered tray to that in an identical uncovered tray. The derating factor is shown to be independent of cable size and composition, and is primarily a function of cable depth. The solution is iterative because convective heat transfer coefficients and electrical resistances are temperature-dependent. The models were verified against laboratory data and a four-year field study in an operating nuclear power plant. |
