Air convection between two plates for low vacuum, 0.1 to 100 mbar

[solarproblem]

Air convection between two (glass) plate for low vacuum, 0.1mbar to 100 mbar

For flat plate solar collection in cold weather half the heat is lost though the front glass.
Radiation losses are handled via selective coatings, low e glass etc. Radiation losses are more or less independent of outside temperatures.
At summer temperatures, efficiency can be 70% but drop due to thermal losses to 40% or less in cold weather

I have read threads ( searched convection vacuum) but can not find a clear result for convection at low vacuum in range for 1mbar to 1 bar (or even 0.1m bar)

Thermal conductivity of air is independent of pressure in this range and only starts to drop below 0.1mbar

http://www.alma.nrao.edu/memos/html-memos/alma554/memo554.pdf

Others noted below 0.1 mbar convection is likely to be small.

It seems the best that a low vacuum can do is eliminate convection and leave the conduction term.
However this is a significant gain if we can make the gap bigger as conduction is linear in thickness.
The main purpose of insulation is to eliminate convection.

At 1 bar the balance between conduction and convection leads to optimum gap of about 1/2 in for double glazing.
Solar energy books have formulas but these seem to be based on empirical formula without a pressure term.

How to compute convection heat transfer for low vacuum to see what can be achieved and optimal gap versus pressure?

 

[gwolf2]

I think you are having trouble finding data/methods because the 0.1 to 100mbar is not a very useful range for the reduction of thermal losses. Most commercial solar collectors either don't use vacuum at all or go to 10-4 mbar or lower to get into the molecular conductivity range where significant insulation is possible.

I have personal experience that whilst 0.1 mbar does give a benefit by virtually eliminating convection, the 10-100mbar range has no measurable benefit at all.

Do a search on molecular conductivity of air to see what you are up against.

gwolf

 

[IRstuff]

The pressure only changes the value, so just use the value in the normal conduction equation

TTFN

FAQ731-376

 

[ione]

We are talking about natural convection, so

h = Nu * k / L

Where :
Nu = Nusselt Number
k= thermal conductivity of the fluid
L = characteristic length.
The Nusselt number is given by:

Nu = 0.54*(Gr* Pr)^0.25 For Ra values between 2x10^4 and 10^6

Or

Nu = 0.15*(Gr* Pr)^0.33 For Ra values between 10^6 and 10^11

Where:
Ra = Rayleigh number = Gr * Pr
Gr =Grashof number = gravity * (coefficient of expansion) * (Tw - Ta) x L^3 / (kinematic viscosity)^2
Tw = wall temperature
Ta = fluid temperature
Pr = Prandtl number = kinematic viscosity / thermal diffusivity

If you have access to the thermal properties of air in the range of pressure of interest, you can calculate how h varies vs pressure

 

[unclesyd]

This paper will be of interest.

http://www.alma.nrao.edu/memos/html-memos/alma554/memo554.pdf

 

[solarproblem]

thanks for replies.

SYMBOLS in roman characters:
h =heat transfer coefficient
Nu=Nusselt Number
k=thermal conductivity of the fluid
L=characteristic length
Ra=Rayleigh number=Gr*Pr
Gr=Grashof number
g=gravity
b=coefficient of expansion (1/T for ideal gas)
alpha=thermal diffusivity=k/( rho cp)
u=absolute or Dynamic viscosity in centipoise g/(cm s)
v=kinematic viscosity in stokes cm^2/s= u/rho
Tw=wall temperature
Ta=fluid temperature
Pr=Prandtl number= u cp/k = (u/rho)/ (k /( rho cp)= v/alpha
cp= specific heat capacity (at constant pressure?)
rho=density=P Mw/(R T) from idea gas law.
P = pressure
T= absolute temperature
Mw= of a compound is the sum of all the atomic weights of the elements \
present in the formula of the compound.Typical unit is g/mol.
R = ideal gas constant

cp is a material property and constant
looking at equations for constant temperature and variable pressure.
k, u are constant for ideal gas at constant temperature
thus Prandtl number is constant = u cp/k

however Gr depends on kinematic viscosity which depends on density hence pressure.
Gr= b g L^3(Tw-Ta)/ v^2
= b g L^3rho^2 (Tw-Ta)/u^2
= g L^3 Mw^2 P^2(Tw-Ta)/ R^2 T^3 u^2

h= 0.15 k (cp g Mw^2 P^2(Tw-Ta)/ k R^2 T^3 u^2)^(1/3)
this seem to indicate it should depend on P ^(2/3) to P^(1/2) so reducing pressure by factor of 10 should reduce h by factor in range 5-3

Have i confused some concept about viscosity in these formula?

 

[HDS]

Gas properties for any pressure.

http://webbook.nist.gov/chemistry/fluid/