Error! Reference source not found. and Error! Reference source not found. give the temperature variation with distance at a heat sink fixed thermal resistance of 0.1K/W while Error! Reference source not found. and Error! Reference source not found. give the temperature variation for Rth = 30K/W. As power increases, the temperature rise increases with a larger gradient as the distance between the heat sources decreases. As stated in the previous study, all 4 graphs show that for distances smaller than 4mm to 5mm, the temperature rise is exponential establishing our conclusion that the ideal distance of separation between the heat sources is 4mm to 5mm. Since most power electronics fail at temperatures above 85-100°C, 1W is the optimum heat flow for this heat sink. For powers above 1W, the increase in midpoint temperature is greater than the increase in maximum temperature and this suggest a very strong thermal crossover that affects the junction temperatures of adjoining heat sources and thus causes the entire module to heat up.
The temperature difference between the maximum temperature and the midpoint temperature on the substrate shows how much heat has travelled from the heat source laterally to the center of the substrate and raised its temperature due to all heat sources. At 1W power per heat source, the thermal conductivity of the heat sink is decreased from 385W/mK to 1.2833W/mK while the thermal conductivity of the substrate (Aluminum Nitride) is fixed at 130W/mK. Fig 51 shows how the temperature difference varies with the thermal resistance of heat sink for different distances x, where x is the distance between the center of a heat source and the center of the substrate. For 14mm center separation, as the heat sink thermal resistance increases from 0.1K/W to 30K/W, the temperature difference between TMAX and TMID increases. At 0.1K/W, the heat sink is an excellent conductor of heat and heat escapes from the back of the heat sink without significantly affecting the center point. As the thermal resistance of the heat sink increases, the heat sink resists the heat flow and heat is accumulated around the heat source and is forced to flow laterally (heat spreading effect). Time required to lose the heat and reach steady state decreases and the temperature of the heat source increases sharply. At such a large distance, the lateral heat flow has minimal effect in increasing TMID at the center of the substrate (i.e. the heat spreading effect has relatively less impact at x = 14mm). This localization causes the heat source temperature to rise sharply as compared to the midpoint temperature. Thus, at x = 14mm, temperature difference is maximum at Rth = 0.1K/W. For 10mm separation, a similar effect is observed till Rth = 10K/W, after which the thermal resistance increases the heat accumulation beyond the critical point where the heat spreading effect due to the 4 heat sources increases the temperature of the center point severely. It is important to note that no matter what the separation is, higher thermal resistance always increases the absolute heating at any point. For 4mm separation, temperature difference was taken for additional thermal resistances between 0.1K/W and 1K/W. The orange curve in Error! Reference source not found. peaks at Rth = 0.77K/W corresponding to a thermal conductivity of 50 W/mK. This is seen in Error! Reference source not found. Further increasing the thermal resistance of the heat sink beyond 0.77K/W for x = 4mm, increases the heat accumulation beyond the critical point where the heat spreading effect due to the 4 heat sources increases the temperature of the center point severely. This increase is greater than the increase in the temperature of the heat source due to increasing Rth of the heat sink. The green and dark blue lines in fig 51 show the temperature difference variation for x = 3mm and x =1.1mm respectively. As seen from the graphs, at distances of 3mm and below, the heat sources are so close to each other that the thermal crossover effect is significant for all values of thermal conductivities as seen from the continuously decreasing temperature difference. Thus x = 4mm is the optimal separation distance for the given configuration of 4 heat sources with heat sink having thermal conductivity more than 50 W/mK. When the temperature difference between the heat source and the center point is maximum, rate of flow of heat per unit area is maximum and hence the heat flux is maximum. Fig 63 shows that for 4mm separation, heat flux is maximum for Rth = 1K/W and falls on either side. This agrees with the temperature difference being maximum at Rth = 1K/W.
The maximum heat sources study designs a guideline for choosing the number of heat sources after fixing the center distance at x = 4mm for a fixed heat sink size of varying thermal resistance. For 1W power, for the entire spectrum of Rth, 8 heat sources can be arranged without exceeding 85 °C. Thus, a power of 1W should be used. As seen from figure 1,2, for the entire range of thermal resistance i.e. Rth = 0.1K/W to 30K/W, the maximum junction temperature is lower for a linear pattern. Since the power, heat sink and boundary conditions for both patterns are the same, it can be concluded that the thermal crossover effect in the circular pattern is more than the thermal crossover effect in the linear pattern. The rate of increase of thermal crossover effect with respect to the thermal resistance is also more in a circular pattern. Note that in both patterns, the center of the substrate has no heat source, and this surface portion can be used to clamp the COB module.
Fig 70 shows that 4mm is the optimum distance for LED arrays with silicone covering (refer to sec for explanation). As seen from figure 71, the graph corresponding to LED with silicone covering lies below the graph corresponding to LED without silicone covering, indicating an increased thermal crossover effect due to the silicone coating as shown by the decrease in temperature difference between heat source and center. The junction temperature and center temperature graphs for LED with silicone lies above the junction temperature graph for LED without silicone.