Four heat sources with surface area 1mm were modelled in ANSYS Workbench. Heat flow varying from 0.25W to 4W was given at the top surface of each heat source and a heat sink was used for heat dissipation. Heat sinks reduce the thermal resistance and hence lower down the junction temperature by providing a path for the heat to travel from the source to the ambient. . Heat is dissipated through conduction (depends predominantly on the thermal conductivity of the material), convection (depends on material, number of fins, fin arrangement, air flow etc.) and radiation (depends on the temperature of heat sink and the surroundings, and surface properties). Compared to conduction and convection, radiation is negligible and can be neglected. These variables make selection of heat sink a daunting task. In this experiment, a concept of thermal resistance was introduced that combines these variables into a single thermal resistance (Rth). By definition, thermal resistance is the resistance to the flow of heat by a material and is measured in K/W;
\(R_{th\ }=\ \frac{t}{kA}\)
where t is the thickness of the material (measured parallel to the heat flow) (m), A is the cross-sectional area (perpendicular to the path of heat flow) (m2) and k is the thermal conductivity of the material (W/mK). To model the heat sink, a copper block was used with an area A, and a thickness t. The base face was given a fixed temperature of 25°C. After fixing these parameters, the only variable is the thermal conductivity that determines the defined thermal resistance. The thermal resistance, and hence the thermal conductivity of the heat sink was varied and the corresponding heat spreading effect was studied.
The distance between the center and the midpoint of each heat source (center distance) was increased from 1.1mm to 14mm in steps. Temperature probes were used to measure the temperature on the heat source surface (\(T_{MAX}\)) and on the substrate, at the point coinciding with the center of the square or the circle in either arrangements (\(T_{MID}\)). The experiment was repeated by changing the heat sink thermal resistance from 0.1 to 30K/W. TMAX and TMID were plotted against distance for all thermal resistances. For every distance, the difference between TLED and TMID was calculated and was plotted against the thermal resistance. The difference is an indication of thermal crossover effect. When the thermal crossover effect is high, heat flux from the 4 heat sources overlap at the center causing a sharp rise in temperature at the center. This rise in temperature leads to decrease in the temperature difference between the LED junction and the crossover point. Similarly, a higher temperature difference signifies a smaller crossover with more heat conducted down through the heat sink than sideways to affect the junction temperatures of adjoining heat sources. The complete design of experiment is given in Table 8.
Based on the results, an optimum separation distance of 4mm was selected which gave the minimum crossover effect within the size constraints and the selection was verified by studying the heat flux. Although thermal crossover effect affects the temperature, it is more closely related to the heat flux since probing heat flux at specific points as shown in \ref{833400}, indicate the rate of transfer of heat and thus complements the temperature rise in a direction. By definition, heat flux is the rate of transfer of heat energy through a surface at a given time. For heat flux measurement at a certain point, we take a limiting condition where the size of the surface becomes infinitesimally smaller. Four center distances (3mm, 4mm, 5mm and 10mm) were considered and compared for heat flux measurements. Since 4mm was our optimum point, 1mm on both side and the extreme distances were of interest to understand the heat transfer. The distance between the center of the heat source and the center of the module was divided into intervals and heat flux was probed at the points on the substrate at the intervals. The lateral heat transfer was analyzed that contributes to the thermal crossover.