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It's the physical property that indicates the degree/intensity of heat present in a substance or an object. It can be expressed and measured according to various scales.
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Transport equation for temperature in a fluid: Heat capacity at constant volume or pressure
I want to understand the temperature equation for a Newtonian viscous fluid from first principles. … My approach is this:
In every point of the fluid, we must have an internal energy given by the temperature T:
$$
\varphi = \int_0^T c_v(T) \, dT.
$$
Thus, we find that:
$$
\frac{\partial \varphi } …