Forced convection over a pipe. 1

[ULoXer]

Hi there,

First post!

I am trying to design a very simple cooling system.

I need to know what the heat transfer rate is for a hot water pipe surrounded flowing by cold water is.
Essentially we have forced convection over a pipe containing flow.

I know the flowrate within the pipe, the inlet temp, the pipe dimensions and the free-stream velocity and temperature of the remote fluid.

I get stuck because I don't think it's right to assume constant surface temp along the pipe as the fluid exiting the pipe will be at a lower temperature. I may be wrong, however.

How do i solve this problem?

It's been a few years since i did any thermodynamics so any help would greatly appreciated!

ULoXer

 

[ione]

You have a pattern with three thermal resistances in series as you have forced convention inside the tube, conduction through the wall pipe and forced convection outside the tube. The total thermal resistance is the sum of the three thermal resistances.
In the attachment you will find some useful correlations to calculate Nusselt number for forced convection (inside the tube and outside the tube). When you got Nu and geometry and fluid conductivity at film temperature you can calculate the convective heat transfer coefficients.

 

[ULoXer]

How do i know when the problem needs to be aproached as a constant wall heat flux problem and not as a constant wall temp one?

 

[ione]

Please take a look at the attached paper.

Ts indicates the surface wall temperature
Tb indicates the bulk fluid temperature inside the tube.

In the case of constant surface heat flux the driving force of the process (temperature difference ?T) is constant over the length of the tube (fully developed region) and consequently both the wall temperature and the fluid temperature increase.

In the case of constant wall temperature the temperature of the fluid asymptotically tends to the wall temperature reducing the driving force of the heat transfer process, that is the temperature difference ?T.

 

[zekeman]

Yes,but the OP has to solve the problem as a function of distance along the pipe, assuming steady state.
If the external fluid temperature is assumed constant, then you have to solve the ODE

M'*c*dT/dx=U(T0-T)

M' internal flow rate
C specific heat
U overall conductance

T0 external fluid Temp
T Temperature inside fluid as function of x

The solution is
T-T0=(Ti-T0)*e^-(U*x/M'c)

 

[ione]

Zekeman,

I concur the exponential decaying equation you've indicated gives the profile of the temperature, but I have interpreted the second post of ULoXer as an inquiry on how to approach his/her scenario (constant heat flux or constant wall temperature) in order to better define which correlation to use in order to calculate Nu for forced convection inside the pipe.

 

[ULoXer]

Thanks so much! I have made some progress with the fundamental calculations.

Getting a little stuck in the final calcs.

I know my mass properties aren't evaluated at the film temp which may be causing problems.

To use the fresh water mass properties calculator you will need to install the Excel addon I will attach in the next post.

To complicate matters, the remote fluid is seawater.

Attached is what I have so far.

It's good to get back into the thermodynamics!

Cheers!

 

[ULoXer]

Excel properties addon: