Link between pressure and convection heat transfer ?

Hello everyone,

For the purpose of my study I would like to know the relation between Pressure and Convection Heat Transfer. Especially the rough pressure when the convection becomes less significant. I did not find satisfying results on the forum.

I have to study the global heat transfer through the wall (5 mm) of a cold chamber at 5 degree C, low pressure, and the environment at 22 degree C, atmospheric pressure.

Thank you very much for any help or suggestion.

NguyenDV

Gold Member
The problem is that it isn't a pressure-dependent phenomenon. The best way to get the convective heat transfer is by using the Nusselt number and its many empirical correlations, and they all scale with Reynolds number and a handful of other parameters depending on the situation (e.g. Prandtl number, Rayleigh number). Pressure doesn't enter into the equations.

May be not pressure but specific mass does, no ?
The less you have pressure the less you have molecules so less you have specific mass ?
It is about buoyancy force after all, I cannot imagine that it is not Pressure dependent.

NguyenDV
Gold Member
First of all, it is easier to think in terms of density instead of specific mass. Second, yes, it depends on density because it depends on Reynolds number. The point is that pressure itself has no bearing on the heat transfer. If density is an important parameter, you could change that either with pressure or with temperature. There is no magic Reynolds number where suddenly becomes less significant. There are various situations where a critical Reynolds number might signal when convection becomes insignificant, but that is going to depend on the situation and what your definition of insignificant is.

Thank you very much.

Ok, let me give you more input, and you may be able to give me more suggestion on how to solve it by myself, avoiding wrong simplification.

What I cannot change:
The inside of the box has to be kept at 5 degree C and the outside temperature is at 22 degree C. Then I have a box with dimension equal to 0.5 x 0.5 x 0.5 [m] in aluminium and the thickness of the panels is equal to 10 mm. There is no forced convection, neither inside or outside the box.

I though about two solutions to make a better insulation. The two solutions are apparently not good according to what I read in some posts, but it does not matter I would like to know how to break these idea.

1) Vacuum panel : low pressure available cannot be less than 500 Pa. So a simple sandwich layers : alu 1 mm, vacuum 8 mm, alu 1 mm.

2) Vacuum inside the box : low pressure available cannot be less than 500 Pa.

As far as I investigated a 500 Pa pressure will not affect at all conduction, and the convection will then depends on the characteristic length, for instance the solution "vacuum box" is then probably worth than the first one. Right ?
And basically, if I remove convection effect (e.g. with honey comb) I can keep atm pressure and thus simplify the solution.

I saw as well that radiation could be the main heat transfer sometimes, does it could be the case here ? Is there a way to neglect it without checking it properly ?

Thank you very much.

Gold Member
There is no way that radiation is important here. Generally, radiation doesn't become important until you reach several thousand Kelvins.

Since you are talking about natural convection, the important parameter is the Rayleigh number. In the case of thermal convection, the Rayleigh number is defined as:
$$Ra = \dfrac{\rho_0 g \beta \Delta T L^3}{\alpha \mu}$$
where
$\rho_0$ is a reference density, usually the average density of the fluid
$g$ is the acceleration of gravity
$\beta$ is coefficient of thermal expansion of the fluid
$\Delta T$ is the temperature difference between the surface and the reservoir
$L$ is the characteristic length scale, like the side length in your case, or the spacing between walls if you are using a vacuum plenum
$\alpha$ is the thermal diffusivity
$\mu$ is the dynamic viscosity

Once the Rayleigh number reaches a critical value, convection becomes the dominant heat transfer mechanism over conduction for a given system. What that critical number is exactly depends on the specifics of your system. Go check out a good heat transfer textbook to get an idea of how to determine that critical Rayleigh number.

NguyenDV