Heat transfer -- length of the tube required to heat water....

[Ian Limjap]

Homework Statement

Water flowing at the rate 3.5 kg s−1 through a tube with an inner diameter of 2 cm is to be heated from 20 to 40◦C. If the tube wall temperature is maintained at 90◦C, determine the length of the tube required.

Homework Equations

Q'=Cp*m*(DeltaT)
Q=2*pi*r*L*Q'

The Attempt at a Solution

Q=mass flowrate*Cp(DeltaT)
=3.5*4.18*10^3*(40-20)=292600J/s
L=Q/2*pi*rQ'
However, I'm missing Q and L.
I would like to know if I need the prandlt number for this question or the viscosity of water? Would I need more information to solve this problem?
Any help will be greatly appreciated.
Thanks.

 

[Chestermiller]

Yes. You need to determine the Reynolds number, the Prantdl number, and then the Nussult number. You need to determine the heat transfer coefficient. Also, you sign for the heat load is wrong.

Chet

 

[Ian Limjap]

Thanks for replying.

 

[Ian Limjap]

I ended up with L=(0.023Re^0.8Pr^0.4kA(Tw-T))/q

 

[Chestermiller]

I ended up with L=(0.023Re^0.8Pr^0.4kA(Tw-T))/q

What value did you use for T in this equation? How could the length increase with decreasing q? How could the length increase with increasing heat transfer coefficient? Is A the wetted perimeter, the cross sectional area, or the total surface area? You need to go back and get your algebra correct.

What value do you calculate for the heat load?
What values do you calculate for the Reynolds number and the Prantdl number?
What value do you calculate for the Nussult number?
What value do you calculate for the heat transfer coefficient?
What value do you calculate for the log-mean temperature difference?
What value do you calculate for the required heat transfer area?

Chet

 

[Ian Limjap]

Again, thanks for replying.

 

[Ian Limjap]

Hi, my answer is
L=0.0165m

 

[Ian Limjap]

I used the mean of the bulk inlet and outlet temperatures and used that to find the properties of the fluid.

 

[Ian Limjap]

I apologise for the confusion I wasn't really given an answer for this.

 

[Nidum]

Does the required heat transfer into the fluid stream really take place in just a 16,5 mm length of 20 mm bore pipe ?

 

[Nidum]

Re: your message in which you ask 'what do I mean ?'

Intuitively your answer seems wrong .

In any case all the assumptions and calculation methods usually used to estimate heat transfer in pipes are going to be of very doubtful validity when used on a pipe which is actually shorter than it's diameter .

 

[Chestermiller]

Hi, my answer is
L=0.0165m

Now let's see the answers to the questions I asked in post #5. Nidum and I are both doubtful about what you did.

 

[Ian Limjap]

I got about 100m.

 

[Ian Limjap]

I did my calculations again and I ended up with 100m.

 

[Chestermiller]

I did my calculations again and I ended up with 100m.

I still doubt that you got it right. Until you answer my questions, I won't be responding to any more of your threads. And believe me when I say that your really need help with that other heat transfer thread you started.

Chet