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# heat exchange coefficient at 10 mbar CO2 pressure

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## heat exchange coefficient at 10 mbar CO2 pressure

(OP)
Hello everybody

I am busy developing a climate chamber: 4- 12 mbar total pressure of carbon dioxide (CO2; temperature range -40 C + 40 C. These conditions resemble the atmosphere on Mars. A Raman spectrometer system will be placed in this chamber for testing purposes.
The chamber will be refreshed but only 1 or 2 times in an hour. So, wind speed is 0 m/sec an we wil rely completely on natural convective currents inside the chamber for heat exchange.

Some heat transfer modelling is going to develop the chamber but definite values for heat exchange coefficients in a CO2 atmosphere with the (cooled/heated) walls of the chamber is somewhat of an unknown to us.

The way of reasoning up to now is this. At atmospheric pressure natural convection currents have characteristic heat exchange coefficients typically between 1 and 10 watt/m^2.K

At 4 to 12 mbar pressure we still expect to see convective heat transfer because the mean free path length of a CO2 molecule at these pressures is still much smaller than the characteristic system dimension. So we expect to see the same heat transfer coefficients 1-10 (watt/m^2.K)

How can we come to a more precise or realistic value?
Any tips?

Thank you all for reading and thinking

Onno

### RE: heat exchange coefficient at 10 mbar CO2 pressure

If the pressure is lower, then net mass impingement on the object is lower, how can the net energy transfer be the same?

### RE: heat exchange coefficient at 10 mbar CO2 pressure

Listen to IRstuff.  A second problem you will have in correlating your results is that natural convection depends on local acceleration due to gravity; on Mars the number is about 1/4 or so of what it is down here in this well.  The equations for laminar boundary layer natural convection are in just about any good heat transfer textbook; you should be able to plug in the real values for CO2 at low pressure and the Martian low-g field, and come up with more appropriate estimates.

...long, long ago...colleagues and I looked into heat-rejection systems (aka radiators) for heat engines operating on Mars.  We found that radiation heat transfer played a very large role.

### RE: heat exchange coefficient at 10 mbar CO2 pressure

(OP)
Thanks both for replying

IRstuff:"If the pressure is lower, then net mass impingement on the object is lower, how can the net energy transfer be the same?"

The net impingement rate decreases with pressure. You are right with this. However, this is half of the story. There is also a flow leaving the object versus the flow impinging (assuming steady state is reached), a flow which is relevant in calcualting the net heat transport.
This leaving (or desorbing) flow will be obstructed by surrounding high density gas if the pressure is high. If the pressure is lower the desorbing flow is less but the transport of heat through this smaller flow is not obstructed by the surrounding low density gas resulting in comparable heat transport at higher pressures.

The dynamic viscosity at higher pressures is independent on pressure. These "higher pressures" are defined as a pressure at which the free path length is much smaller than the characteristic dimension of the system (0.01 m to 1 m). Around 10 mbar the mean free path length is in the order of 1e-6 to 1e-5 m which clearly indicates there is viscous flow still present. Between 10 mbar and 1000 mbar the dynamic viscosity is constant. Dynamic viscosity and the thermal conduction coefficient are directly related, so between 10 mbar and 1000 mbar the thermal conduction coefficient is also constant.This is eay to know if we want to calculate the Rayleigh number for free convection.

btrueblood

I calculated the Rayleigh number under the following conditions: gas CO2 100 % , characteristic length = 1 m,temperature 273 K, typical temperature difference 5K and at 1/4 of earths gravity 3.8 m/sec^2
and I come to Ray = 6e4  I have to check whether this number indicated the onset of free convection flows in our system (L =1 m and d =0.5 m) or that there is only thermal conduction through the bulk mass of CO2 gas. Since the change from laminar to turbulence occurs roughly at Ray=1e9 I think that we are at the low bottom end of the free convection scale with a value of 6e4.

I'll post something tomorrow I think and will try.

Interesting to hear that you have some practical background on this. Do you remember still some typical convective heat transfer coefficients from your radiator experiments.?

Thanks for reading and with greetings Onno

### RE: heat exchange coefficient at 10 mbar CO2 pressure

(OP)
IRstuff

Thank you for the abstract. That could be very helpfull. I'll get the copy through our library.You are absolutely right:the convective heat transfer efficiency is not the same on Mars. I used some free convection relations from a study book on heat transfer and I come (with the data from above on Rayleigh) to heat exchange coefficients on Mars that are at the bottom end of the Earth scale.
Earth: > 1 watt/m^2.K
Mars: 0.1 - 1 watt/m^2.K
There seems to be some overlap but only at the lower end of the scale.

Thanks for replying and best regards

Onno

### RE: heat exchange coefficient at 10 mbar CO2 pressure

Onno, sorry not to get back to you earlier.  The study I was involved in did not do experimental hx, but was involved in the design of heat engines (specifically heat rejection systems aka radiators) for use on Martian surface.  I will try and dig out our report (300-some pages, done as students on summer sojourn at NASA-LeRC way back in '87), and see if there are any useful numbers for you in there.

### RE: heat exchange coefficient at 10 mbar CO2 pressure

(OP)
Dear all

I would like to add the results of some testing in my laboratory as it seems to clarify the question posed in this thread a little bit.

I mounted a aluminium clad resistor (RH-50,50 W maximum power:length app 3 cm, diamter app. 1 cm))in a stainless steel volume of 70 cm length and 30 cm diameter. The pressure in the tank can be regulated between 4 and 12 mbar. CO2 is used as the flush gas at 20 C. The resistor hangs on it's own weight using (thin) electrical wiring that supply the current, thereby eliminating any significant heat conduction through the wires. Measurements were taken at 0.8 watt electrical power. This power can only be transferred to the surrounding gas.

At 4 mbar CO2 average temperature    60.4 C
At 1000 mbar CO2 average temperature 42.5 C
At 1000 mbar Air average temperature 43.6 C

There does not seem to be much difference in heat exchange between CO2 and air at 1000 mbar.

If I define: Q_res [W] = A [m^2] * alpha [watt/m^2.K] *(T_resistor-20 C)

60.4-20 = 40.4 C and 60.4-43.6 = 16.8 C

The heat exchange coefficient at 6 mbar CO2 pressure is
16.8/40.4 = 0.42 times smaller than the one at 1000 mbar air/CO2 pressure.

If one assumes the heat transfer coefficients for natural convection in air at 1000 mbar to lie between 1  - 10 watt/m2*K , than at 6 mbar Co2 we have 0.4 - 4 watt/m^2.K

This is not the difference one might expect intuitively for a gas at 6 mbar pressure. Nature is full of wonders.

Of course any dicsusion or additional input more than welcome.

Best regards

Onno

### RE: heat exchange coefficient at 10 mbar CO2 pressure

Interesting, but it's not obvious to me that you're actually measuring "convection" as is conventionally defined.  From your description, the CO2 is 20ºC ONLY at the start of the run.  The conventional definition of convection requires essentially an infinite sink of cold side gas, which could not occur in your closed chamber, at least, not with the walls of the chamber being held at 20ºC.

How did you prevent your gas from being heated from chamber walls?  Were they held at 20ºC or were they warmer?

And why 20ºC?  The average surface temperature on Mars is ~-46ºC.

How did you account for radiated emission?  A blackbody at 60ºC could dump up to 0.6W into a 20ºC black environment

### RE: heat exchange coefficient at 10 mbar CO2 pressure

Take a look again at the Rayleigh number for your setup (characteristic dimension 0.01 m), are you sure you have any significant natural convection occurring?  Can you calculate a 1-d or 2-d approximation for conduction transient through the gas over the duration of your experiment, and how do those numbers (convection only) compare to your data?  Try and calculate the real-world (gray body) radiation values too, as IR suggests.  Finally, pull a full vacuum to give yourself a good "control" value, i.e. conduction thru leads and radiation only.

### RE: heat exchange coefficient at 10 mbar CO2 pressure

(OP)
Dear all

I think I have not been at my best with the last response.

IRstuff is very right in questioning whether natural convection actually occurs in the test set up. I have flushed the tank with 160 mL/min CO2 gas. Considering the volume of the tank, 50 L, it is immediately clear that these conditions cannot correspond with the ones for natural convection.

IRstuff, you are also right in stating that a blackbody at 60C can already dump 0.6 watt at the 20 C walls.

On Mars temperatures show great range: -80 C +60 C. Since, at the moment I only have the tank of 50 L at roomtemperature I cannot set any other condition.

I now come to btrueblood's remark to produce a good vacuum. I have a tank, pressure gauges and I can control the pressure. Today I am going to install a vacuum pump for 1e-6 mbar and beyond end pressure. This will enable me to take into account the resitor body radiation loss and conduction through the leads, following directly btrueblood's suggestion.

To follow up on the experiments I will use a gas filled tank, to 6 mbar CO2 pressure, but no flushing. I will also measure the gas temperature during heating of the test resistor.

Well, thanks for making me think a lot further and putting a number of things in perspective. I will restart this thread as soon as I have new, more solid results.

Best regards

Onno

### RE: heat exchange coefficient at 10 mbar CO2 pressure

Good luck...  Thermal measurements are quite non-trivial, hence, NIST gets the big bucks to do that sort of characterization and development of methodologies.

You might try and see if one of the standards organizations has a standard methodology for this sort of test.

### RE: heat exchange coefficient at 10 mbar CO2 pressure

(OP)
Dear all

I promised I would be back with some measurement results on this question.

I tried to measure heat transfer between 4 and 1000 mbar in a CO2 atmosphere. As a first idea I used an aluminium clad power resistor of 50 Watt, type Dale 15,2 ohm, L = 50 mm, h=15 mm. I hang this up in a tank of L=70cm and d=50 cm. The electrical power could be set using a power supply between 0,9 and 3,9 watt.
The resistor temperature, the CO2 temperature and the tank wall temperatures were measured using thermocouples type K.
In vacuum (P<3.8e-5 mbar) the emissive area was measured. Radiation equation:q=eps.A*sigma_Boltzm*(TH^4-TL^4).

eps.A is defined as emissve area [m^2] and defines the emissive property of the resistor. At higher pressures (p>4 mbar) the emissive area is used to calculate the radiation [watt] from the resistor body. The convective heat transfer is the electrical power put in, minus the radiative power.

In summary the results are shown in the graph. Errors overshadow the accuracy achieved at 4-10 mbar pressure: gas desorption form resistor body,temperature measurement, heat loss through wires and the uncertainty in the emissive area. Shown in the graph are fractions convective/radiative heat transfer of the total electrical power put in.

The errors are large and limit my conclusion: the fraction convective heat transfer at 4- 10 mbar CO2 pressure is between 1 and 29 % of the total electrical power put in. In short, the measurement procedure will lead to proper numbers if the error contributions could be limited.The result however is tempting in that the pressure ratio (1000/4=250) might not be expressed linearly in the value for convective heat transfer at 4 - 10 mbar.

To come to a real convective heat transfer coefficient [watt/m^2.K] is impossible due to large uncertainties in the actual surface area of the resistor and the difficulty im measuring the temperature difference between resistor body and CO2 gas temperature.

Thanks for reading and with greetings

Onno

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