Heat Transfer: Finding T2 for a Cooled Stainless Steel Pipe

[FChebli]

1. The problem statement:

(a)Concider a stainless steel hollow pipe containing a saturated steam and has length L, cooled by convection & radiation. Find formula for T2.

(b) Another question "Not related to the previous one": How would I know if a gas has gone turbulent?

Homework Equations

:[/B]
For (a): Q = 2 Pai K (T1 - T2) / ln (r2 / r1)

For (b): Re = e u l / M ??

The Attempt at a Solution

:[/B]

(a) Do I ignore the saturated steam, and re-write the equation (a) with respect to T2 only??

Thank you!

 

[Mindscrape]

Hmm, where does that equation come from? In my previous work with convection, granted it was through a course in partial differential equations, I never had a convective formula work out so nicely. What is r2 and r1, is k Boltzmann's constant? Why does the problem give you length L when it doesn't appear in your formula?

Same with the second equation you posted. I'm guessing that most people on this site, maybe mechanical engineers excluded, will not know what your equations are and that's why you haven't been helped.

 

[FChebli]

The equation comes from Fourir's law for convection.
K is the thermal conductivity (kW/mK) r2 is the outer radius (m) & r1 is the inner radius (m)...
Sorry for the typing mistake: Q = 2 Pai K L (T1 - T2) / ln (r2 / r1)

The second equation is Reynold's Number.

 

[Mindscrape]

Ah, okay, after a bit of research I see where the first equation comes from.

$$Q = 2k \pi L \frac{T_1-T_2}{ln(r_2/r_1)}$$

Which is for conduction, not convection.

I suppose for your first question you are just supposed to rearrange the equation and solve for T2.

For the second question, use Reynold's number (are you using a pipe still?) too see if it is large. According to Wikipedia, 2100 < Re < 4000 is the general transition region for laminar to turbulent flow, so above 4000 and you should expect turbulent flow.

$$\mathrm{Re} = \frac{\rho V L}{\mu} = \frac{V L}{\nu} = \frac{Q L}{\nu A}$$

 

[FChebli]

So for the first question, do I ignore what it says about radiation & convection?

For the second it's a flat plate... I've just asked my instructor via e-mail & he said that Reynold's number has to be above 10^5 to expect turbulet flow.

I appreciate your help, thank you!

 

[Mindscrape]

I don't know, the problem isn't very specific. You may actually want to use a simpler equation such as

$$Q = h A \Delta T$$

where h is a convective heat transfer coefficient for air, A is the area of the pipe (2πrL) and T of course is temperature. I'm not really sure though without a better description of the problem, or the context of what your class has covered recently. Sorry, maybe someone else will know better.