# Estimate the local heat transfer flux

1. May 4, 2017

### electr

1. The problem statement, all variables and given/known data

Liquid ammonia is heated as it flows at a mean velocity of 2 m s–1 through
a circular pipe. The pipe, which has an internal diameter of
75 mm, is at a uniform temperature of 27°C, and the ammonia at a section
1.2 m from the inlet to the pipe has a temperature of –23°C. Use the
following information to estimate the local heat transfer flux at l = 1.2 m.
Note, the properties of ammonia liquid have been taken at –23°C, except
where stated.
Liquid ammonia properties:
Density = 600 kg m–3
Specific heat capacity = 4.86 kJ kg–1 K–1
Dynamic viscosity (at 27°C) = 1.19 × 10–4 kg m–1 s–1
Dynamic viscosity = 2.05 × 10–4 kg m–1 s–1
Thermal conductivity = 5.11 × 10–4 kW m–1 s–1
Heat transfer correlations:

Nu=1.86Re^1/3 Pr^1/3 (d/l)^1/3 (μ/μw)^0.14 for laminar flow
Nu= 0.023Re^0.8Pr^0.14 for turbulent flow

2. Relevant equations

3. The attempt at a solution

Re =600 x 2 x 0.075/2.05 x10^-4 = 4.39 x 10^5 which is > 2000 so turbulent flow
Pr=2.05 x 10 ^-4 x 4.86 x 10^3 / 5.11 x 10 ^-4 x 10^3 = 1,949

Nu=0.023 (4,39 x 10^5)^0.8 x (1.949)^0.33 = 936.132

Nu=hd/k => h=936.132 x 5.11 x 10^-4 x 10 ^3 / 0.075 =6378.183 w/m^2k

Q=h x π χ d x l x (Ts - To) =>6378.183 x π χ 0.075 x 1.2 x (27 - (-23)) = 90.16 kw

is this correct?if not i would like your help,thank you

Last edited: May 4, 2017
2. May 4, 2017

### haruspex

Your answer strikes me as much too high. I can't check it, though, because I am not an expert in this subject matter and you have not quoted the Relevant Equations you are depending on.
What is Pr? Working from the variables you seem to have used to calculate it (except the 1000 at the end... I assume that's some conversion between kilo and non-kilo units) it appears to have units of s/K, which I cannot connect with anything I know.

3. May 4, 2017

### electr

Re is reynolds number and PR=Cpμ/κ is the Prandtl number..........i thought this is a forum to help people not give exams,someone that knows about this can understand what i m doing and dont need to write the equation because i substitude with the values so its the same thing,i see many people dont write them ,if you dont know thank you for your time and hope someone that knows about it can answer if i m wrong ,i posted it here just to be 100 % sure

4. May 4, 2017

### haruspex

The "relevant equations" section of the template is there for a reason and should be filled in. It allows a far broader audience to offer assistance. I frequently respond to questions in areas of which I have no prior knowledge yet manage to resolve the issue. Mostly the student is not having a problem with the subject matter but with the application of equations and the handling of the algebra.

This is what threw me. I believe you mean kW m–1 K–1. That makes Pr dimensionless, as it should be.
Is that a decimal comma? It's about 1.9, right?
You wrote that ^(1/3) is for is laminar flow. But that only makes a small difference to the Nusselt number.
I note that it says "at", not along. I.e. it sounds like they are asking for the heat transfer rate per linear metre at the 1.2m mark. That means you would multiply 1m, not 1.2m, but again that is just a small difference. Besides, if they mean that there seems no point in specifying 1.2m as the position, so I could be wrong.
If it does mean along the first 1.2m then isn't there a problem with the calculation? The temperature difference would have been greater closer to the source.

So although I cannot find a significant flaw in your calculation, 90kW still seems huge to me.
If you get no other help, try pinging Chestermiller. He's very good on thermodynamics.

Edit: I calculated the temperature rise expected in the gas based on 90kW/m. I get 7K per m travelled. So I now accept that 90kW might be reasonable.

Last edited: May 4, 2017
5. May 4, 2017

### Staff: Mentor

It all looks OK to me, except that the exponent in the Sieder Tate equation should be 0.4, and, the last equation is incorrect. The local heat flux should just be $q = h\Delta T$

6. May 5, 2017

### electr

thank you for your replies,chester what you mean by 0.4 ,i didnt understand it sorry,and for the Q only be Q=6378.183 x (27 - (-23)) =31890915 ??

7. May 5, 2017

### haruspex

There does not seem to be universal agreement on the terminology. I see some authors use heat flux for the total rate of heat flow (over whatever area it happens to be) and heat flux density for the flow rate per unit area. But most seem to agree with Chet that heat flux is per unit area.
I would say that latter is how it is being used in this question, since we do not know the temperature of the gas along the first 1.2m of pipe.

8. May 5, 2017

### Staff: Mentor

Nu= 0.023Re^0.8Pr^0.4 for turbulent flow, not Nu= 0.023Re^0.8Pr^0.14 or Nu= 0.023Re^0.8Pr^0.33

When they ask for the local heat flux in a heat transfer context, they mean the local rate of heat flow per unit area. That is just $q=h\Delta T$, not the overall cumulative rate of heat flow over the entire length of pipe.

9. May 5, 2017

### electr

now i see ,sorry my bad, write it wrong...... your correct about the Nu= 0.023Re^0.8Pr^0.33 (when i was writing the question saw the laminar value...),so the 90 kw is not the correct one and all i need to do is the q=hΔT for my final answer? and something else chest,i have one more question but some guys already posted it here and i dont know if i have to post it again,because i did tha mistake before,but i would like to post my answer for you to check

10. May 5, 2017

### electr

and thank you too haruspex for taking the time to help me

11. May 5, 2017

### Staff: Mentor

Bird, Stewart, and Lightfoot, Transport Phenomena, give the following equation for Re > 20000:
$$Nu=0.026 Re^{0.8}Pr^{1/3}\left(\frac{\mu _B}{\mu _0}\right)^{0.14}$$where $\mu_B$ is the bulk viscosity and $\mu_0$ is the wall viscosity.

12. May 5, 2017

### electr

so chest is my solution ok?and should i post the other question too?like i said some other guys already posted it here but still want u to check it

13. May 5, 2017

### electr

its just my last questions to finish the HNC thats why i m a m a bit impatient to finish

14. May 5, 2017

### Staff: Mentor

15. May 5, 2017

### electr

ok,i posted it if you have time take a look,and for this question am i correct or should i give it a try again?

16. May 5, 2017

### Staff: Mentor

Where is it posted?

17. May 6, 2017