heat transfer coefficients when phase change

[sanjig]

HI,
The basic equation for HTC is Q(w)=HTC*Cp*deltaT

How does this equation relate, when there is a phase change of the fluid and there is heat transfer only due to this phase change, and no temp change of fluid occurs?

thanks

 

[25362]

The given "basic" equation is incorrect and cannot relate. It should be: (1) Q = U*A*[Δ]T or (2) Q = m*Cp*[Δ]T. Units' cancellation for (1) is:

W = (W/(m².K) [×] (m²) [×] (K)​

The formula is applicable for phase change as well.

 

[Christine74]

The formula is applicable for phase change as well.

So you're saying that during an isothermal phase change (?T=0), that there's no heat transferred?

 

[Montemayor]

sanjig:

25362 is absolutely correct. I don't know how you feel qualified about making such an assertion, but the equation is bizarre - both in logic and in units.

There are 2 basic mechanisms in direct-contact heat transfer: sensible heat transfer and latent heat transfer.

25362 has given you the sensible heat transfer equation:
Q = m*Cp*?T

The equation for latent heat transfer (phase change) involve no temperature difference (it's zero) and is simply:
Q = m*LHV

where,
m = mass, lb
LHV = Latent Heat of Vaporization, Btu/lb (at the temperature in question)

 

[sanjig]

HI , Ok...so the basic equation was not correct. I should have said A( area) instead of Cp.
But still does not answer question about HTC, when heat transfer results in only phase change...

 

[davefitz]

as montemayor indicated, the heat transfer during phase change is not related to to fluid temperaure difference, but to a rate of boiling of the liquid and the heat of vaporization. It can , however, be related to a temperature difference between themetal surface and the fluid saturation temp.

Usually the boiling heat transfer coeficient is found from lab tests, wherein the metal is inductively heated by a known electrical load. There are normally added chordal thermocouples in the metal, and these are used to determine the onset of the "boiling crisis", ie the max heat flux for which normal film boiling cannot be sustained.

This coeficient would represent the heat flux q/a divided by the temperature difference between the metal surface temperature and the fluid saturation temperature. The max heat flux would occur a the "critical heat flux" value, and the that DT ( metal temp - sat temp) is called the "Liedenfrost" temperature.

Most people are familiar with the Liedenfrost temperature when they spit onto a very hot frying pan- the spit will not boil but simply scamper about because the pan metal temp is above the Leidenfrost temperature. This phenomena is callled "DNB" or departure from nucleate boiling if the fluid sbw is less than about 20%,and called "dryout chf" if the sbw is above about 20%.

 

[Montemayor]

Sanjig:

You can't reasonably expect us to read your mind. If you can't furnish a logical equation, how can you expect us to know what you want to know or learn? Now you come back and state that you want to know about the film heat transfer coefficient ("HTC") during a phase change. You don't state which HTC - in the case of a heat exchanger, for example. Do you expect us to also magically know that you are dealing with an electric resistance heater?

davefitz, in trying to second-guess what it is you are after, has given you an excellent recap on the phenomena of heat transfer during phase change. If you are unaware of what the critical heat flux is or how it comes about in your specifc case, I recommend you read a lot of theory first before tackling the subject. You can start with Don Q. Kern's classical "Process Heat Transfer". He describes the mechanism of heat transfer during a phase change very well.

You haven't told us what you are doing, but in industrial reboilers I have used a heat flux to design the required heating area of a tube bundle - not a heat transfer coefficient.

 

[m777182]

To Montemayor

may I suggest you to make your equation for latent heat transfer (phase change) more general so that the term LHV becomes LHPC-latent heat of phase change or simply k.
It includes then all possible phase changes like crystallization, sublimation, evaporation,condensation, dissolution, solvation, glassy state transition and whatelse possible isothermal transition.
m777182

 

[25362]

I hope Christine74 understood that in formula (1) [Δ]T refers to both sides of the heat exchanger, as the driving force for heat transfer.

In formula (2) better written [Δ]t, in small case to show a difference and avoid confusion, refers to one side only. If it is isothermal use m777182's approach.

If, as I believe, Sanjig is interested only in formula (1) consider the overall HTC would depend on many factors as detailed by Art Montemayor.

I'd like to emphasize that an isothermal process is not represented by the fact that one side enters and leaves at the same temperature, the temperature should be steadily constant all along the heat exchange process to be considered isothermic. For example, one has to weigh different factors in the case of non-isothermal chemical reactions taking place along the heat exchanging apparatus, even when the entering and leaving temperatures on the reacting side are the same.

 

[sanjig]

Hi Guys,
Let me explain in more detail what I need.
Consider a automotive a/c system.
One of the components is the evaporater ( a finned heatexchanger).
The refregerant enters it as a mixture of cold liquid and cold vapor( mainly liquid though), and gains heat due to heat exchange with warm air blowing on the other side. This causes liquid refregerant to evaporate inside the heat exchanger. It finally exits as saturated vapor.
So on the refregerant side, this process is mostly isothermal.
Now if I had all the test data for this process, how would I calculate the heat transfer coefficient on the refregerant side? ( the reason I need to calculate this is because its needed as input to a simulation software)

Thanks,

 

[davefitz]

For the specific case you described, the resistance to heat transfer for each element should be calculated, referenced to the inside diameter of the refrigerant tube.

The resistance due to boiling is nearly zero, espescially when compared to the influence of inside fouling , outside fouling, outside air flow unbalance, and error in prediction of outside convective heat transfer coeficient.

If you need to use a number for the inside boiling coefficient, I would use 1000 BTU/hr ft2 F, or calculate it from old standard correlations ,, such as Davis and David:
(hD/k,l)=0.06(rho,l/rho,v)^0.28 *(DG/2/u,l)^0.87 * Pr,l^0.4

I am sure better values are avaialbe from refrigerant vendors and from commerical a/c mfr's, but the uncertainties mentioned above dominate the simulation.

 

[Montemayor]

sanjig:

Your failure to correctly state your question and give us all the basic data is what has wasted a lot of time and caused confusion to some extent. Now, you return a third time to reveal that all you're dealing with is a DX (direct expansion) type of mechanical refrigeration cycle - as opposed to a submerged (flooded) evaporator. The DX is a "cost-efficient" version of a refrigerant evaporator that has economics as its driving force. The trade-off is bad controls and even worse ability to calculate its effective fluid and heat transfer characteristics. It is a 2-phase flow nightmare come-to-life. As davefitz correctly infers, the results of such an evaporator are best derived empirically. Any attempt at a "rational" and formal calculation on the heat transfer coefficients is a good mathematical and heat transfer exercise - at best! The calculated results cannot be taken seriously for actual design; it would be very foolish to believe that one could predict or even guess at the flow regimes (or types) taking place differentially within such a 2-phase region.

I can only speculate that there is still more on "the rest of the story"; but if you already have test data, why are you wasting time attempting to formally calculate theoretical film coefficients that, at best, may be 50% off? Why don't you go with your empirical values instead, and be done with it? You are trying to apply theoretical heat transfer to an area where research is still being done. Additionally, if this is an automotive A/C unit, why try to re-invent the wheel? The design problem has already been resolved - many times over. Are you trying to optimize or re-invent?

 

[sterl]

Well Said, Art: but the problem for Mr. Sanjig has now been compounded as any Automotive A/C unit has a very high rate of dehumidification as compare to normal AC, the Body Count per Sq Ft being what it is. And that makes (2) latent processes...

Automotive AC is its own specific bag of cookies because the compressor speed is so variable and the standby conitions are so variant. Designing a well controlled, tolerant system is not simple to model.

DX Finned Coil heat transfer on both sides of the Nominal Area line has been well studied. Published data on very specific devices and circuits has been done by Ford, Toyota, Parker Hannifin, Alco controls and so on. Most have the benefit of both Test Cell and real-environment data acquisition.

Mr. Sanjig: Do a little Web Search on Automotive AC and you will find a lot of data. A gentleman at the University of Illinois named Jacobi has published a huge amount; running "automotive air conditioning research heat transfer Ford" on Google had 94,000 hits...