[ahmed1]

hi everyone, this is the first topic for me.
i have question regarding insulation thickness calculation for pipe going to flare and having a light HC gas flowing inside.
i used this equation Q=(2π*k*L*(T1-T2))/(ln(r2/r1))
where
Q, heat transfer
k, thermal conductivity
L lenght of pipe
T1, inlet temp
T2, outlet temp
r1, inner dia
r2 outer dia, must be found

k,T1,T2,r1,L are given but to find r2 i have to assume Q/L( heat loss per unit of length)
my question is how to assume of find the heat loss per unit of length

[curiouscat]

T1, inlet temp
T2, outlet temp

Are you sure T1 / T2 are not internal and ambient temperatures? I am suspicious.

What the source of your Equation?

[ahmed1]

http://www.enggcyclopedia.com/2011/09/sample-problem-insulation-thickness-calculation-pipe/
this is the source
and yes T2 is the ambient temp

[curiouscat]

http://www.enggcyclopedia.com/2011/09/sample-problem-insulation-thickness-calculation-pipe/
this is the source
and yes T2 is the ambient temp

Is this a homework problem or a practical one?

[ahmed1]

no,this is only an example of how to find the thickness but in my case i have real one and i explained it above.
my question is on what basis we can make assumption for Q/L in order to r2

[curiouscat]

no,this is only an example of how to find the thickness but in my case i have real one and i explained it above.
my question is on what basis we can make assumption for Q/L in order to r2

I would suspect perhaps based on if a component condenses at a certain Temp. that's one critical limit. Do you have any condensables in your stream?

[ahmed1]

for my case, the fluid  is mainly is C1 and C2 in pipeline going to flare.
T1=308 K,   T2=323 K( in our country, summer),   r1=1.07 m,  k=.033
so in order to avoid the temp of the fluid to increase due to conduction with the ambient, i have to calculate the reqired thickness for the pipe. to do so, i have to find r2 from the equation, then (r2-r1)= thickness.
the problem now how to find Q/L ( heat loss per unit of length), hence the length of the pipe which must be insulated is 20 m but no need for that since we need to find out Q/L (i think)
we assume that the maximum allowable incease in T1 is 3°C (due to heat transfer) not more than this so T1 will reach to 311 K. so from that, how can i calculate or assume the heat loss to use it in the equation.

i tried to use Q=k*A*(dT/dx), conduction heat transfer. but that will not work since i need to have dx which is the thickness.

so how can i calculate of assume Q/L

[curiouscat]

Interesting problem. After a bit of calculations I get

[tex]
T=T_2-(T_2-T_1)\times exp \left (-\frac{\pi k}{\dot{m}C_p} \frac{r_1+r_2}{r_2-r_1} \times y \right)
[/tex]

Notation should be obvious. Ask if not. y is distance from pipe start.

Let's see your actual values to see if this makes any sense.

For you this ought to become:

[tex]
T_1+3=T_2-(T_2-T_1)\times exp \left (-\frac{\pi k}{\dot{m}C_p} \frac{r_1+r_2}{r_2-r_1} \times L \right)
[/tex]

Except r2 you know everything. Solve.

Caveat emptor!

[ahmed1]

from where you got this equation it seems strange. i noticed that the temperatures will cancel each other and we will end up with
3= exp[..]
is it right?

[curiouscat]

i noticed that the temperatures will cancel each other and we will end up with
3= exp[..]
is it right?

Not right. How will they cancel?

it seems strange.

What's strange?

[ahmed1]

you are right i just confused
sorry
i will try it
but is it right to use Cp (specific heat capacity)= 844 j/kg.K since i am using fiber glass as the insulator material?

[curiouscat]

but is it right to use Cp (specific heat capacity)= 844 j/kg.K since i am using fiber glass as the insulator material?

No. I should've clarified. Cp and m_dot for the gas.

[ahmed1]

from where you got this equation?

[curiouscat]

from where you got this equation?

A heat balance and some calculus.

[ahmed1]

last question about this topic
could you show me how you derived this equation from the heat balance equation?
i would like to convence my section head.