Cryogenic heat exchanger cooling power

[freddie_mclair]

Hi everyone!

I have a silver plated copper heat exchanger (with an internal embedded circuit where liquid nitrogen flows) attached to a bigger aluminium block in order to cool it down.

First, I want to estimate it's instantaneous cooling power during cool-down to a stable temperature. I have the mass of the Aluminium block, $m$, and I'm measuring its' temperature evolution with time, $dT/dt$. I assumed that the instantaneous cooling power of this heat exchanger, $dP$, can be given by:

$$dP = m\, c_p(T)\, \frac{dT}{dt} \mbox{ [Watt]}$$

Where $c_p(T)$ is a polynomial function of $T$, so a non-linear behavior was introduced.

Question 1: Is this a valid assumption for the instantaneous cooling power?

Question 2: How could I estimate it's cooling power at a given temperature with this data? I don't have a measure of the flow of the liquid nitrogen...

Thanks in advance!
Ciao!

 

[Rx7man]

It's been ages since I've done this, but it seems to me that you're making it more complicated than it needs to be... I would think it's more of a function of the thermal conductivity (thus area and thicknesses) of the materials involved... For there to be any effective power transfer, there has to be a difference in temperature between the two sides of the heat exchanger, the thinnner the walls, and the greater the area and/or temperature difference and/or thermal conductivity of the medium, greater the power transfer

 

[Nidum]

More information is needed before any meaningful calculations of heat transfer can be attempted .

Please post a complete description of the set up and a clear diagram .

 

[freddie_mclair]

Hi!

Thanks for your replies.
Here is a scheme depicting the setup.

Everything is in vacuum (minimizing radiative heat transfer) and some glass fiber epoxy supports were used to install the Aluminium block in the cryostat (minimizing conductive heat transfer). I only have a couple of temperature sensors on the Aluminium block.
The heat exchanger (attached to the Aluminium block) has an embedded circuit inside where pressurized Liquid Nitrogen (LN2) from a Dewar is flowing; it flows through some Swagelok stainless steel flexible tubes.

As I said, to get the instantaneous cooling power, I considered the heat removed from the Aluminium block by measuring $dT/dt$, knowing its mass $m$ and evaluating $c_p(T)$ with the values given by NIST, here.

Thanks! :)

 

[freddie_mclair]

Guys, any further help on this?

Thanks!

 

[Chestermiller]

Please provide the dimensions of the block and the heat exchanger, including the geometry of the coolant channels.

 

[freddie_mclair]

Hi Chester,

Thanks for your reply!
Well, first of all, I just would like to know if the physical principle that I assumed (described in the first post) are correct: is the instantaneous cooling power is defined by $dP = m c_p(T) \frac{dT}{dt}$?

Secondly, I see a lot in literature (and in practical applications) that sometimes the cooling power is defined as, e.g., $50$Watt @ $77$K. How are these values defined?

Thanks again!
Regards!

 

[Chestermiller]

Hi Chester,

Thanks for your reply!
Well, first of all, I just would like to know if the physical principle that I assumed (described in the first post) are correct: is the instantaneous cooling power is defined by $dP = m c_p(T) \frac{dT}{dt}$?

This is correct if T represents the average temperature of the block. But, depending on the operating conditions, the temperature can vary substantially with location within the block. This is the reason I was asking those other questions.

Secondly, I see a lot in literature (and in practical applications) that sometimes the cooling power is defined as, e.g., $50$Watt @ $77$K. How are these values defined?

Regards!

I'm not familiar with this standard. But you should be able to find somewhere in the literature a description of the experimental procedure required to implement this standardized measurement.