# Convection coefficient for an annular finned pipe

1. May 28, 2016

### mech-eng

Hi. I am stuck on a project on calculation of heat convection transfer coefficient for a annular finned pipe.

All parameters [Diameter of pipe, diameter of fins for each case, the distance between fins, fin thickness, pipe length and fin number] are determined. And I have two book Fundamentals of Heat and Mass Transfer by Incropera/Dewitt and Heat and Mass Transfer by Çengel. I cannot determine how I will proceed. Should I refer to the conduction heat transfer for this project as well?

Would you like to give some guidance please?

Thank you.

2. May 29, 2016

### BvU

Not really my expertise. Who knows @SteamKing is good at this too...
I do have Incropera at work, as well as Bird Stewart and Lightfoot; they might have some info too. Tomorrow at best.

3. May 29, 2016

### mech-eng

I would like to learn what your job is? And do you refer to the books while you are working?

Thank you.

4. May 29, 2016

### BvU

I'm a physicist and I make computer models of chemical processes, so now and then I dabble with heat transfer.

5. May 29, 2016

### mech-eng

I would be very happy if I could cope with this project which bonds my hands and I know your helps are precious. So I will wiat for tomorrow.

Thank you.

6. May 29, 2016

### Staff: Mentor

Can you please provide a diagram. That would be very helpful. Apparently, a fluid is flowing through the annulus, but what is inside the inner pipe and what is happening outside the outer pipe? What is the flow rate and what is the fluid? What are the actual data?

7. May 30, 2016

### mech-eng

. Inner and outer diameters of the pipe is 33 mm and 35 mm, respectively and inner temperature of the pipe is 60 Celcius. Thickness of the fins 1 mm, length of the pipe is 15 cm, the distance between fins 5 mm. So in every 5 mm there is one fin so there are 30 fins. These were constants. And now is the cases.

The temperature of air is optional as well.

1) Diameter of the fin 40mm, radius 20 mm

2) Diameter of the fin 42.5 mm, radius 21.25 mm

3) Diameter of the fin 45 mm, radius 22.5 mm

The velocity of the flow is optional, i.e I would like to choose the easiest and the most untedious one, the kind of fluid is optional as well.

Is everything O.K now?

P.S Eventhough I have studied convetion for two days, I am still for the situation of how I will derive the h, the convention coefficient.

Thank you.

8. May 30, 2016

### mech-eng

My idea is first to calculate the heat conduction to calculate temperature of outer surface of the pipe, then assuming an environmental temperature I can calculate the film temperature surrounding the pipe. With this film temperature and knowing the environmental temperature I can calculate heat flux. But

1) With what equation, I can calculate the heat conduction and outer temperature of the pipe with specified number of fins?

2) With knowing, outer temperature and environmental temperature, I can calculate the film temperature, by those temperatures.

3) With what equation, I can calculate the convection heat transfer from the pipe with fins, knowing and using that film temperature and environmental temperature?

Thank you.

Last edited: May 30, 2016
9. May 30, 2016

### BvU

Thanks for the description.
Looks a lot like what this guy works through. Pretty hefty with Bessel functions and such.

[obsolete: put together before I was interrupted]:

I agree with Chet (as always ): the subject appears so broad that a little focusing is more than welcome.

What's the aim and the scope of you project ? Steady state or dynamic ? pipes with annular fins ?
Where is it that you get stuck ?

Generally fins are used to improve the heat transfer on the side with the lowest heat transfer coefficient, so design is considering the fin efficiency.

In very thorough books (in german ) I do find the Biot number popping up (you had a thread on that -- but a lot of the books don't use the name Biot).

10. May 30, 2016

### Staff: Mentor

You have a single finned tube with air blowing over it, correct? If you knew the heat transfer coefficient on the air side, would you be able to determine the overall heat transfer coefficient for a single fin? What have you learned so far about heat transfer to finned tubes?

11. May 30, 2016

### mech-eng

First of all I think there is no need for Bessel functions and it's strange that I have never seen them in heat transfer. It should be steady state, making everything much easier, and pipes with annular i.e circular fins. I stuck at the beginning. I have never seen such an example. I have looked at the example questions in the mentioned sourced but I cannot see such a thing. As I said before I try to find the equation or derive the h. To do so, I have thought some steps that I write in #8.

Thank you.

12. May 30, 2016

### Staff: Mentor

I can help you through this if you are willing to answer my questions in post #10. If not, have a nice day.

13. May 31, 2016

### mech-eng

Sory for late.

Yes, I have a single pipe/tube airblowing over it, but it has 30 fins on surrounding it.

I don't know exactly answer of this question because I do not get the difference between the heat transfer coefficient on the air side and the overall heat transfer coefficient. Would you like the explain this difference so that I could take more steps.

I have two heat transfer books one is by Çengel and one is by Incropera/Dewitt. I have looked finned surfaces in these books but there isn't any example on calculation of overall conduction/heat transfer coefficient. The books focused just on increase of heat transfer due to fins. They have no information on calculation over all conduction heat transfer coefficient. I have speak to an instructor and said that it was a special case and I could just find them in the internet, not in the essential/fundamental heat transfer books. So, now I am searching for those studies.

Thank you.

Last edited: May 31, 2016
14. May 31, 2016

### Staff: Mentor

The overall heat transfer coefficient U is based on the overall heat flow Q, the inside area of the pipe $A=\pi D_iL$, and the total temperature driving force between the inside surface of the pipe and the air, namely 40 C: $$Q=UA(40)$$.

If you knew the temperature at the base of an annular fin and the heat transfer coefficient between the fin and the surrounding air $h_a$, would you be able to determine the radial temperature profile within the fin and the rate of heat loss from the fin to the air?

15. May 31, 2016

### mech-eng

I try to understand this post. I cannot understand the base of fin, and what is happening there? Please would you like to provide some information for the base of the fin.

Thank you.

16. May 31, 2016

### Staff: Mentor

The base of the fin is where it is attached to the pipe. Suppose you somehow knew the temperature at this location.

17. May 31, 2016

### mech-eng

I think I should assume the base of the fin and inner surface of the pipe at the same temperature, i.e 60 celcius.

As I already know them, I still cannot determine the temperature profile within the fin and rate of heat loss from the fin to the air. I am not such skillful but I can conduct a study for them. Can I find them in the book of Çengel or in the book of Incropera/Dewitt? Or would like to give an instructive link for it? I have started to search it just now.

Thank you.

18. May 31, 2016

### Staff: Mentor

There is no need to assume anything right now. Just do it algebraically, and call the temperature $T_b$.
I am not familiar with these books. Do you understand the heat conduction equation? Have you ever seen an analysis of cooling fin heat transfer? I have no idea what level of understanding your are starting from. Have you studied differential equations?

19. May 31, 2016

### mech-eng

I understand heat conduction equation. It is a simple algebraic equation and I can apply boundary conditions to the differential equations. I can solve linear differential equations and separable differential equations.

I try to study analysis of cooling fin right now.

Thank you.

20. May 31, 2016

### Staff: Mentor

Excellent!!!!!!