[granzer]

Is it possible to define the heat transfer coefficient for heat transfer within fluid?. Say I am injecting a stream of hot fluid into a stream of cold fluid, where fluids are of the same type (imagine a small pipe injecting the hot fluid along the flow of cold fluid). Also, let's say the resulting temperature contour is steady.
Heat transfer coefficient (h) is defined as the rate of heat convected from fluid to per area of the surface product when the unit temperature gradient exists between fluid and surface. So, h, characterizes the heat transfer between a surface and a fluid.
i) What about heat transfer between 2 points of a fluid, where a temperature difference exists? Is there a way to characterize the heat flow in such a situation? Can we use h itself?

ii) Also. within the solid we have conductivity, which can be given as a second-order tensor to characterize different heat transfer behavior in different directions from any given point in the solid. Is it possible to have a convective heat transfer coefficient also as a second-order tensor, so it captures differing heat transfer behavior in different directions (near to a wall with heat flux OR if the answer to question (i) is yes, then, within the flow)? OR is h always a zeroth order tensor?

[LuckyTran]

i) technically there is no surface. Now even if you naively apply the analogy, that is what is called conductance, which no surprise is the reciprocal of conductivity
ii) That would just be conductivity again


You should consider what happens if you have a solid that is moving! That is the scenario you are asking about and you can see right away how the advection can be absorbed into an effective conductivity and thereby giving your the (imperfect) analogy between heat transfer coefficient and conductivity.

[granzer]

Thank you LuckyTran!.
i) So is there a way (a non-dimensional number maybe) to characterize the heat transfer within the fluid flow (2 points within the fluid), not near any solid surface?
i.a) when you say "conductance": do you for the fuid this would be some kind of function of fluid properties and flow properties?
ii) Can you please elaborate on the scenario where the solid is moving?
ii.a) When you say analogy between heat transfer coefficient and conductivity in the fluid do you mean the heat transfer coefficient would become a second-order tensor?
ii.b) Is the heat transfer coefficient, in the traditional sense (ie next to a solid surface) always considered a zeroth order tensor (ie it doesn't depend on the direction, or is always considered normal to the surface)

[granzer]

Originally Posted by LuckyTran

i) technically there is no surface. Now even if you naively apply the analogy, that is what is called conductance, which no surprise is the reciprocal of conductivity
ii) That would just be conductivity again


You should consider what happens if you have a solid that is moving! That is the scenario you are asking about and you can see right away how the advection can be absorbed into an effective conductivity and thereby giving your the (imperfect) analogy between heat transfer coefficient and conductivity.

@LuckyTran, was reading your comment again and I get it now. 'Assume an element of fluid to be solid that is moving'!. Thank you. That is very healpful.
But I have not seen a non-dim number of some kind of convective coefficient to characterize the convective heat transfer (except those compare advection to other transfer processes). Like from a heated jet as in my above example or say from the flame boundary (I know convection is a heat transfer mode here, but can w define a h here?).
Is running the CFD the only way to get the heat being transfer out of a point in fluid (not near to solid?)