Thermodynamics Change in Gas Temperature along pipe

In summary: The outside diameter is $$D_0=D_i+t$$where t is the wall thickness, and $k$ can be taken as the value provided in the engineering handbook. With a pipe inside diameter of 0.00457 m, a wall thickness of 0.00089 m, and a thermal conductivity of 15 W/(m K), the overall heat transfer coefficient is $$U=\frac{(2)(15)}{(0.00457)((0.00546)/0.00457)}=653\ W/(m^2 K)$$The differential equation for the temperature profile along the pipe is $$2.64\times 10^{-5}\times (1.04)\frac{dT}{dx}
  • #1
daz18983
5
0

Homework Statement



Nitrogen beginning at 50oC is pumped along a 30m length of Stainless Steel pipe at a flow rate of 1.5 litres per minute. The Pipeline is at ambient temperature 20oC. Find the temperature of the Nitrogen upon it leaving the end of the pipeline.

Pipe OD - 0.00635m
Pipe ID - 0.00457m
Pressure - 1bar

The following data is taken from a copy of 'An Engineering Data Book' -

Cp - Nitrogen at 20oC and 1 bar is 1.04 kJ/(kgK)

Homework Equations



From 'An Engineering Data Book' and 'Thermodynamics an Engineering Approach 4th Edition' i believed that i could work at the figures from the following equations -

Qdot /l = 2Pi.k.(T2-T1)/In(r2/r1)

Qdot = Heat Loss l = Length k = Thermal Conductivity T = Temperatures r = Radius

Wdot - Qdot = mdot.Cp.(T2-T1)

Wdot = Work Energy In Qdot = Heat Loss mdot = mass flow rate Cp = Specific Heat T = Temperatures

The Attempt at a Solution



using k = 15 (Which is the k of Stainless Steel)

I used Qdot /l = 2Pi.k.(T2-T1)/In(r2/r1)

which gave me a figure of 8.653 x 103 for Qdot

Then to calculate mdot i used the following -

mdot = Vdot / v

where Vdot = Volume flow rate and v = specific volume

Vdot = V / delta t

where V = Volume which is 1.5 litres and delta t = 60 seconds (take from flow rate)

therefore Vdot = 0.025 l/s = 25 x 10-5 m3/s

v = R.T1 / P

where R = Gas Constant which is 0.294 kJ/(kg.K) T1 is temperate 1 which is 323K and P is pressure which is 1 bar (1 x 105Pa)

this gives v to be 9.4962 x 10-4 m3/kg

using these mdot becomes 26.32632 x 10-3 kg/s

Now using Wdot - Qdot = mdot.Cp.(T2-T1)
I rearrage to get T2 on its own

therefore T2 = (-Qdot / mdot.Cp) + T1
note that Wdot = 0 and so has been removed

Therefore i get an answer of 50.3oC which is obviously WAY wrong? Can someone please help me with this. Even just a point in the right direction of the correct equations. This is not a homework or coursework question this an engineering question at work and I'm not too sure where to go with it.
 
Physics news on Phys.org
  • #2
This problem should be solved using the following differential heat balance equation: $$\dot{m}C_p\frac{dT}{dx}=-U\pi D_i(T-T_0)$$ where U is the overall heat transfer coefficient, x is distance along the pipe, and Di is the inside dimeter of the pipe. The overall heat transfer coefficient U should include the thermal boundary layer resistance inside the pipe, the conductive resistance of the pipe wall, and the thermal boundary layer resistance outside the pipe. Your analysis only includes the pipe wall conductive resistance, so it can only provide a lower bound to the outlet temperature. The initial condition for the about equation is T = 50 at x = 0, and a boundary condition ##T_0=20##.

Your calculation of the mass flow rate is incorrect. The density of nitrogen at 50 C and 1 atm. is $$\rho=\frac{PM}{RT}=\frac{(1)(28)}{(0.08215)(323)}=1.057 \ gm/l$$So the mass flow rate is $$\dot{m}=\frac{(1.5)(1.057)}{60}=0.0264\ gm/s=2.64\times 10^{-5}\ kg/s$$

For the bounding approximation you are using, in which the inner and outer thermal resistances are neglected, the overall heat transfer coefficient is given by $$U=\frac{2k}{D_i\ln{(D_0/D_i)}}$$where k is the thermal conductivity of the metal wall.
 

1. What is thermodynamics?

Thermodynamics is the branch of physics that deals with the relationships between heat, energy, and work. It studies how these factors affect the behavior of matter and the changes it undergoes.

2. How does gas temperature change along a pipe?

The change in gas temperature along a pipe is determined by the laws of thermodynamics, specifically the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In this case, the gas temperature can increase or decrease depending on the amount of heat added or removed from the system, as well as the work done by the gas as it moves through the pipe.

3. What factors affect the change in gas temperature along a pipe?

The change in gas temperature along a pipe is affected by various factors such as the initial temperature of the gas, the amount of heat added or removed, the type of gas, the properties of the pipe, and the rate of flow of the gas. These factors can influence the efficiency and effectiveness of the system in maintaining a consistent gas temperature along the pipe.

4. How is the change in gas temperature measured along a pipe?

The change in gas temperature along a pipe can be measured using a thermometer or a temperature sensor placed at different points along the pipe. The temperature readings can then be recorded and compared to determine the change in temperature. Other methods such as thermal imaging or infrared cameras can also be used to visualize the temperature distribution along the pipe.

5. What are the practical applications of understanding the change in gas temperature along a pipe?

Understanding the change in gas temperature along a pipe is crucial in many industrial and scientific processes. It can help in designing and optimizing systems that involve the transfer of heat, such as in refrigeration and air conditioning systems, chemical and thermal reactions, and power generation. It also plays a significant role in the transportation and distribution of gases through pipelines, ensuring that the gas remains at the desired temperature for its intended use.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
3
Views
4K
  • Engineering and Comp Sci Homework Help
Replies
14
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
870
  • Engineering and Comp Sci Homework Help
Replies
1
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
10
Views
1K
  • Mechanical Engineering
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
33
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
6
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
9
Views
10K
  • Engineering and Comp Sci Homework Help
Replies
3
Views
3K
Back
Top