Interpretation of U (Overall heat transfer Coefficient) 2

[mucour]

I am reading on heat exchangers to prepare me for future challenges.

One of the text books I am reading define U as barrier resistance or overall heat transfer coefficient.

I am trying to make a sense of U (Overall Heat transfer Coefficient) if I come across "U" typical data for different services in shell and tube exchangers.

To clarify myself, because I know how to solve for U, I want somebody to confirm to me that the higher the U figure, the lower the barrier resistance.

An example is in electricity, the higher the "R" figure the higher the resistance to current flow.

In liquid, the higher the API figure, the lower the density of the liquid.

Please correct me if I am getting things missed-up.

 

[poetix99]

The electrical analogies can be helpful.

q = U*(delta T)

U = summation of [(1/(h(1)*A)sub-i + (x/(k*A))sub-i]; These are the convective and conductive components of a series heat transfer network; "sub-i" is my best attempt at representing subscripts.

By electrical analogy, R ~ 1/U.

U is called the heat TRANSFER coefficient, not the heat resistance coefficient.

 

[mucour]

thanks poetix99, but your formula for U is not what I find in design manuals.

It is written as:

1/U = 1/ho + ro + rw + 1/hi * (Ai/Ao) + ri * (Ai/A)

However, in posting this thread and reading your response I was able to get the picture better.

If you look at the formula you will find that ro and rw stand for inside resistance and wall resistance. While ho and hi are the film coefficients.

So if the resistances on the right hand side is not made as inverse then,

U ~ 1/R (~ approx.)

Thanks, poetix99, for helping me to get the picture clearer.

 

[poetix99]

Yeah, I should have inverted "U" and written 1/U, as you have correctly provided it.

It does indeed seem that the equation you've given is a more generalized equation in that your equation is per unit area. The inside parameters (ri, hi) are being "normalized" to the ratio of inside area to outside area (in case it is not a flat plate, with heat transfer at right angles to the plane surface).

However, it is also necessary to recognize that your "r" = x/k.

In any case, the real "fun" is in actually determining the values of k and h; particularly h - the convective film coefficient(s) of heat transfer. Lots of fluid mechanics. Lots of correlations. Lots of engineering judgement required for any real world situation where heat transfer calculations are needed.

Many threads have provided some good reference heat transfer texts. If your might want such, I suggest that you do a keyword search ("heat transfer", "film coefficient", "convection",...).

 

[TD2K]

The higher the value of U, the lower the 'resistance' as you put it to heat transfer. The easiest way IMO is to simply look at the units:

BTU/hr/ft2/degF. Which is esentially your heat flow, BTU/hr, across an area, ft2, per driving force, deg F. So, the higher the value of U, the more heat transfer you will expect to get. Same thing with more area or a higher temperature driving force, you get more heat transferred.

Another way is remember your equation for heat transfer:

Q = UAdT. You'll get more heat transferred, Q, as U, A or dT increases.

 

[abeltio]

mucour,
the formula you are writing is the formula stated in the TEMA stds for overall heat transfer coefficient.
the overall heat transfer coeff is calculated (per the stds) at the outside of the tube. That is why you see the corrections (it has a great influence in the case of finned tubes where A0 >> Ai).
Regarding what does U mean... both postings are quite clear I just may add that:
if you consider all the terms in the equation you posted read them as resistances in series... in fact the "r"'s in the equation are actually called: fouling resistance or tube wall resistance...
1/U is the total resistance to heat flow...you can interpret U then as the conductance... i.e. the higher the resistance the lower the conductance (duh!).
HTH
Saludos.
a.

 

[mucour]

abeltio,

Thanks for the post. However, it confused me the more.

My understanding so far is that(from the previous postings)

1/U ~ R.

This implies that the higher the U in the formula (1/U ~ R), the lower the resistance. Then the better the heat transfer rate (or if I use conductance as an expression, then the better the conductance).

An example is in a HEX calculation, the arrived at

U = 201 for "clean" or no fouling state.

But for the fully fouled state, U = 130

From the above, U figure for the no fouled stae is higher than the fouled state.

And the no fouled state is of better heat transfer.

 

[abeltio]

mucour,
you are correct.
the added resistance due to fouling makes U smaller.
if you can, get a hold of the TEMA Stds... has a pretty good explanation on the calculation.
a.

 

[saxon]

mcour, The classic and fundamental heat transfer calculation is as follows:

Q= U*A*T WHERE:
Q=Total heat transmitted (btu/hr)
U= Overall coeff. of heat tans.
(btu/hr/ft^2/degF)
A= Amount of heating/cooling surface (ft^2)
T= Log Mean temp. diff. between hot& cold
fluids (degF)

It follows from this, that with increasing U, Q increases; with decreasing U, Q decreases. Simple and elegant Eh!

Hope this answers your question.

saxon

 

[25362]

As an additional note, U is always smaller than the individual ho and hi of both sides of the heat exchange surface. In fact, it is smaller than the smallest of these values.