Hi everyone, I am struggling with the following question.
"A device is mounted on a heatsink. It is started from cold and run for five minutes before being switched off. The device produces 30W of losses and the thermal resistance between the device and the heatsink is 1.7C/W. The thermal capacitance of the heatsink is 100J/C. The ambient temperature is 40C. Calculate the temperature of the heatsink when the device is switched off after five minutes."
My approach so far has been to model the semiconductor device as a "current source" since thermal power is analogous to electric current. I have modelled the heatsink as a parallel RC section and I have modelled the ambient temperature as a constant voltage source, since temperature is analogous to voltage.
This yields a first order differential equation, however the differential part has a constant term on top which I am not sure how to deal with. I have even toyed with the idea of using a laplace transform to solve the equation but I don't know how to deal with the fact that the top of the differential term is d(Tj - 40) as opposed to just d(Tj)
I have attached my attempt so far.
"A device is mounted on a heatsink. It is started from cold and run for five minutes before being switched off. The device produces 30W of losses and the thermal resistance between the device and the heatsink is 1.7C/W. The thermal capacitance of the heatsink is 100J/C. The ambient temperature is 40C. Calculate the temperature of the heatsink when the device is switched off after five minutes."
My approach so far has been to model the semiconductor device as a "current source" since thermal power is analogous to electric current. I have modelled the heatsink as a parallel RC section and I have modelled the ambient temperature as a constant voltage source, since temperature is analogous to voltage.
This yields a first order differential equation, however the differential part has a constant term on top which I am not sure how to deal with. I have even toyed with the idea of using a laplace transform to solve the equation but I don't know how to deal with the fact that the top of the differential term is d(Tj - 40) as opposed to just d(Tj)
I have attached my attempt so far.
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