In this paper we present how the graph theory can be used in the field of thermal study. We have developed a method which can describe the heat conduction ability of big Surface Mounted Devices (SMDs) during the reflow soldering process. Our method established that the heat conduction ability of the materials can be described with time coefficients. These time coefficients are determined by the thermal resistance and the heat capacity of the examined materials. We implemented our method in a Matlab 7.0 program which generates a directed and weighted graph from the discrete thermal model of the investigated SMD. The program uses Dijsktra Algorithm to find the shortest “conduction path” between the different parts of the component. With our method, the following effects can be studied during the reflow soldering process: from which points and which paths can the most effective heating of a chosen contact surface be achieved, the differences between the shortest conduction paths and the effect of heat distraction.
Keywords: Thermal modelling, reflow soldering, Dijsktra algorithm, heat conduction, Surface Mounted Devices, time coefficients, thermal resistance, heat capacity, conduction path, SMT, PWBs, solder alloy, solder pads, thermal cells, temperature, thermodynamic equilibrium, thermal node theory, thermal conductivity, algorithm, optimization
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