Calculating Change in Temp. with Steam & Cold Water Flow

[brobertson89]

Homework Statement

Steam is passing a pipe that has cold water flowing through. I need to find the change in temperature from when the water enters the pipe to when it leaves the pipe.

Homework Equations

First i found the total thermal resistance using:
R_total=R_in+R_(f,in)+R_conduction+R_out

Where R_in and h_in is:
R_in=1/(h_in pi D_in L_pipe )
h_in=k_w/D_H Nu

R_(f,in) = 0 due to negligble build up on the pipe

R_conduction is:
R_cond=ln⁡(D_out/D_in )/(2k_m πL_pipe )

R_out is:
R_out=1/(h_out A_(total,out) )

I then put R_total into this formula:
Q=UA= 1/R_total =m ̇Cp(T_out- T_in )_cold

and rearranged for:

(T_out- T_in )_cold=Q/(m ̇C_p )=1/(R_total m ̇Cp)

The Attempt at a Solution

These are the values that I have either been given or calculated from the above equations. I'm more worried about my method as opposed to the correct value.

Constant / Variable Value Units
D_in 0.032 m
L_pipe 3.68 m
k_w 0.58 -
D_H 0.032 m
μ 855e-06 Ns/m^2
ρ 1000 Kg/m^3
V 20 m/s
Re 60000 -
c_p 4.1818 J/(kgK)
Pr 7.21 -
Nu 8.91 -
n 0.4 -
h_in 161.5 W/(m^2K)
R_in 0.0167 °C/W
D_out 0.035 m
k_m 16 -
R_cond 2.42e-04 °C/W
A_(total,out) 0.002959 m^2
h_out 4455 W/(m^2K)
R_out 0.07586 °C/W
R_total 0.0928 °C/W
Q 10.77 W
m ̇ 0.2 kg/s


THIS GAVE ME A TEMPERATURE DIFFERENCE OF ABOUT 12 DEGREES CELCIUS WHICH SEEMS WAY TOO BIG.

Any help at all would be good, and I'm wide open to criticism. I would really appreciate your help with this as it is going in my undergrad thesis.

Thank you very much,

Brandon

 

[KataKoniK]

Dear Brandon,

Thank you for sharing your work with us. Your approach seems to be generally correct, but there are a few things that could be improved upon.

Firstly, I would recommend double checking your values for the thermal conductivity of water (k_w) and the dynamic viscosity (μ). The value for k_w that you have used seems to be too high, and the value for μ seems to be too low. This could be contributing to your large temperature difference.

Additionally, I would suggest using the more accurate Nusselt number correlation for turbulent flow in a circular pipe, which takes into account the Prandtl number (Pr) as well as the Reynolds number (Re). This will give you a more accurate value for the heat transfer coefficient (h_in) and subsequently the total thermal resistance (R_total).

Lastly, I would recommend checking your units and conversions carefully. Make sure that all of your values are in consistent units (e.g. all lengths in meters, all temperatures in Kelvin, etc.) and that you are using the correct conversion factors when necessary.

I hope this helps and wish you the best of luck with your thesis.