Yes. It does the way you described. Heat is directly associated with the kinetic energy of fluid particles, thus it is included in the mathematical description for flow dynamics! Therefore, behavior of hot fluids flowing to cooler flow zones can be understood.
If we will compare heat energy with liquid and gas, we can do this with help of notion thermoconductivity. This property is behaving very different in liquids and in gases: in gases thermoconductivity rises with growth of themperature, in liquids - decreases. Heat energy is closely connected with aggregate state of matter.
The heat energy behaves as an atypical fluid (=Liquid + Gas) undergoing kinetic diffusive processes governed the Fourier heat flow equation (like the Fick diffusion equation).
In addition, "heat" might be nicely and justifiably treated in the framework of "radiation hydrodynamics" in most of the realistic astronomical situations.
Look for details into
"Foundations of Radiation Hydrodynamics", by
Dimitri Mihalas and
Barbara Weibel Mihalas.
Thanks for replies. As of now, what is then the absolute definition of "heat"?
An overview in thermodynamics,
a) Heat energy is a kind of energy whether it is in transfer or not, which is the energy of thermal motion, a non-conserved quantity.
b) Heat energy is the function of the two independent variables T and V, q=q(T,V), which is a state function.
c) The entropy of heat energy dq is equal to dq/T, the entropy of other kinds of the internal energy are equal to zero.
d) Since heat energy is a non-conserved quantity, there are the two sources of the changes in heat energy, heat transfer deq=δQ and heat production diq, we have dq=deq+diq.
The heat equation derived from Fourier's law does not include heat production diq, which can be extend to a general equation, you can see Eq.(24), (25) in my paper arXiv:1201.4284(v6).
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