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# Convective heat transfer coefficient vs. gas density (pressure)3

## Convective heat transfer coefficient vs. gas density (pressure)

(OP)
Hello,
I am here to ask a simple, basic question about heat exchangers which is puzzling me.

Whenever I look for approximated values for convective heat transfer coefficients, I just find tables depending of phase of matter (liquid/gas), type of flow (laminar/turbulent) or type of gas (monatomic or not).

But I never find any parameter associated to the pressure or density of the gas.
My understanding is that air at 100 bars should get much higher convective heat transfer that air at 1 bar, as the number of molecules hitting the solid barrier is much higher.

Am I missing something? Are there any formulas related to convective heat transfer coefficient which take gas density or pressure as a parameter?

### RE: Convective heat transfer coefficient vs. gas density (pressure)

(OP)
1503-44,
so, If I am understanding ok the Prandt number, Air heat transfer is dominated by thermal diffusivity (as air Prandt's number is 0.71).
And that situation does not change with pressure, as I have seen in the formulas and tables.

So I am checking thermal diffusivity of air at varying pressure, and I find the the values are dramatically lower when the pressure is higher.

Consequence would be (for a given area) heat transfer being lower the higher the gas density, then?

### RE: Convective heat transfer coefficient vs. gas density (pressure)

Think about the distinction between 'thermal conductivity' and 'convection' in a gas. They are not the same thing. Thermal conductivity of a gas is fairly constant with pressure. At higher pressure, there are more frequent collisions of gas molecules with the wall, but the mean free path of the molecules between collisions is smaller.

Helium is used for heat transfer, Krypton is used to insulate double pane windows. High pressure increases gas density an increase convective heat flow. Fiberglass-type insulation is used to reduce convection.

### RE: Convective heat transfer coefficient vs. gas density (pressure)

There was a lot of research into the use of a "supercharged" boiler in the 1960's which operates at 10-15 atm , and the heat transfer surfaces can be very compact due to the much higher convective heat transfer coeficient at elevated pressure. There were built a couple of "boilers in a bottle" back in the 1990's as pressurized fluidized bed boilers, but the downstream gas turbine had trouble digesting the dust and corrosive flue gas.

"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick

### RE: Convective heat transfer coefficient vs. gas density (pressure)

OP, please read 1503-44 and pierreicks's posts again, and try to understand them. Density is a factor in Reynolds No., but plays no part at all in Prandtl No. You mention thermal diffusivity, which plays no part in Prandtl No. at all, though it is a factor in Grashof No., which applies only to natural convection heat transfer. Are you talking about forced or natural convection, the two are quite different situations. If your interest is in a gas at 100 bar, I'm guessing you are talking forced convection in a flow situation, and gas density is only a very minor factor in that circumstance.

### RE: Convective heat transfer coefficient vs. gas density (pressure)

(OP)
AlmostRetired,
ye, I am interested in heat transfer in heat exchangers (forced convection).
I have seen many examples of conductive heat transfer examples here and there, but they never mention pressure, which I find puzzling.

I am not interested in an specific pressure, just in the general correlations (if any) between conductive heat transfer and gas density (using forced convection, both laminar and turbulent).

I am looking at pierreicks's material, but there is a lot there to chew for me. I will keep trying.

### RE: Convective heat transfer coefficient vs. gas density (pressure)

(OP)
While I am not being able to work the equations, let me rephrase the question a bit better.

Given a heat exchanger surface and constant mass transfer rate (ie, 1 m2, 1 kg/s of air),
does convective heat transfer coefficient change significantly with air density?
Can a simple rule of thumb be extracted, like "eight times the pressure, double the convective heat transfer coefficient"?

### RE: Convective heat transfer coefficient vs. gas density (pressure)

The two are treated separately. Convection includes the direct effect of velocity. Conduction includes all direct effects of pressure-density.
.
Convective heat transfer is dependent on velocity and temperature difference, but as velocity has dependencies on density and density of a gas is very dependent on pressure, convected heat transfer rate could be said to have at least some indirect dependencies on density, but only as far as providing the motive force required to reach the given velocity; not towards affecting the convective heat transfer rate.

Otherwise the conductive process includes all of the direct effects of pressure-density.
https://www.engineeringtoolbox.com/air-properties-...

If you have "high pressure convection", you really have conduction happening at the same time and need to include that process too.

A black swan to a turkey is a white swan to the butcher ... and to Boeing.

### RE: Convective heat transfer coefficient vs. gas density (pressure)

In heat transfer in a heat exchanger, conduction is a very small factor and is not even considered. The heat transfer coefficient contains all of the mportant factors. Conduction requires the thickness of the wall or the diameter of the flow channel to be the major factor, which you don't find in the equations. The diameter affects fluid velocity, which affects heat transfer greatly, but that is included in the Reynolds number used to determine the transfer coefficient.

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