A Time Dependent Analytical Analysis of Heat Transfer in A PCB during A Thermal Excursion
A great deal of work has already been done to determine the equilibrium temperature of a PCB when exposed to a heat source such as the thermal environment of reflow soldering. This study will go beyond an equilibrium condition and explore the temperature-time distribution of the board when a variable temperature heat source is applied to both outer surfaces. For simplicity,the model will be a two-sided board. Obviously,the model board has two material interfaces. An interesting observation is that anywhere within the board,including the material interface,thermal energy must be conserved. There is not a similar requirement for the temperature. Consequently,at the material interfaces we can expect the thermal properties’ of the board to change in a profound manner. A similar situation occurs when a fluid passes through a shock wave. This will be reflected in such board properties as the thermal stresses in the various layers and the resulting warp. This phenomenon also explains and quantifies why a thermal shock can be devastating while a slow temperature rise to the same endpoint may well be tolerated.
The analysis will use a one dimensional,time dependent model i.e. there are two independent variables. This necessitates a partial differential equation to describe the temperature variation within the board. The boundary conditions are the outer temperature of the board,which is the temperature of the heat source on both outer surfaces. The third boundary condition is at the copper epoxy interface where conservation of thermal energy is required.