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Newton's law of Heating and Cooling issues


New member
Feb 3, 2018
I understand how to solve the ODE used in newtons law of cooling, assuming that the ambient temperature remains constant, but what are you supposed to do when the ambient temperature is itself a function of time? Say we have an ODE (dT/dt) = K(T-Ta(t)), where the ambient temperature (Ta) varies with time, as well as the temperature of the object in question. I am having difficulty getting the equation to separate or getting it into standard form so that I can use the integrating factors technique to solve the ODE. Anyone know how to solve this?


Staff member
Apr 12, 2005
Most importantly, after building a good model, you should solve the equation using ANY method at your disposal.

1) What model are you contemplating?
2) Can you solve it? Note: There may be some negotiation, here. If you can't solve it, you may opt for a simpler model that you can solve.