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.