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Energy balance with variable density

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Hello everyone,

I am interested in finding the temperature in a system that changes the density in time and I would like to formulate the energy balance using this variable density.

What I have in mind is to use

Cp * d( rho T)/dt = Q

but I find it pretty tricky to implement it in COMSOL, because of the derivative. Does anyone have any experience with this?

Nomenclature: Cp is the specific heat, rho is the density (rho = f(t)), T is the temperature and Q is the heat source in W/m3, which can be any number (just for reference)]

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