Average heat transfer coefficient (forced convection)

In summary: The mass flow rate is for steam, but I still don't understand how to solve the question. You say that the hydraulic diameter is equal to tube diameter no matter how many tubes I have. Obviously the hydraulic diameter is always the same, but h (convection heat transfer coefficient), is a function of hydraulic diameter. So if we have 10 tubes, or 1 tube, the heat transfer coefficient should change. You can't have same heat transfer coefficient for 1 tube and 10 tubes. Makes no sense.There are 10 tubes, so the heat transfer coefficient should change.
  • #1
bardia sepehrnia
28
4
Homework Statement
Cooling water available at 10C is used to condense steam at 30C in the condenser of a power plant at a rate of 0.15kg/s by circulating the cooling water through a bank of 5-m-long 1.2cm-internal-diameter thin copper tubes. Water enters the tubes at a mean velocity of 4m/s, and leaves at a temperature of 24C. The tubes are nearly isothermal at 30 C. Determine the average heat transfer coefficient between the water and the tubes and the number of tubes needed to achieve the indicated heat transfer rate in the condenser.
Relevant Equations
Q=mcdeltaT, , Q=h*As*deltaTln, Re=(Vmean*Dh)/kinematic viscocity
Nu=0.023(Re^0.8)*(Pr^0.4), Nu=(h*Dh)/k
So firstly, I don't understand if the mass flow rate is for steam or for water. If it is for water, I know I can find the heat transfer rate using equation:Q=mcdeltaT.
But then I don't know how to find h (the average heat transfer coefficient) because I don't know the surface area (As). I can find the log mean temperature difference but there are still 2 unknowns in the equation: Q=h*As*deltaTln. Surface area and average heat transfer coefficient.

I also can calculate the Reynold number and ultimately calculate the Nusselt's number, but I still can't find out h because h=(Nu*Dh/k) which means h is function of diameter, and the diameter of 1 tube is known but since we don't know how many tubes is required, then the Dh is also unknown.

Any help will be appreciated.

My attempt with the solution and trying to use Nusselt number to find h.
1621541158411.png
 
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  • #2
Hi,
bardia sepehrnia said:
if the mass flow rate is for steam or for water
If it's for water, you know the number of pipes from the velocity, isn't it ?

And if it's for steam, you have ##Q## and you also have the number of pipes.

Could it be the exercise is a lot easier than you think ? I remember something like $${1\over U} = {1\over h_{\text{w}} + {1\over \lambda} + {1\over h_{\text{st}}$$and the 'The tubes are nearly isothermal at 30 C' means the last two terms are negligible ?

@Chestermiller, am I making sense ?

##\ ##
 
  • #3
You know the Nussult number and you know the tube diameter, so you know the heat transfer coefficient. Simple as that. The hydraulic diameter is equal to the tube diameter no matter how many tubes you have.

Incidentally, you indicate that for a Re of 50000, the flow is laminar. That is not correct. It is turbulent.
 
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  • #4
Chestermiller said:
You know the Nussult number and you know the tube diameter, so you know the heat transfer coefficient. Simple as that. The hydraulic diameter is equal to the tube diameter no matter how many tubes you have.

Incidentally, you indicate that for a Re of 50000, the flow is laminar. That is not correct. It is turbulent.
The mass flow rate is for steam, but I still don't understand how to solve the question. You say that the hydraulic diameter is equal to tube diameter no matter how many tubes I have. Obviously the hydraulic diameter is always the same, but h (convection heat transfer coefficient), is a function of hydraulic diameter. So if we have 10 tubes, or 1 tube, the heat transfer coefficient should change. You can't have same heat transfer coefficient for 1 tube and 10 tubes. Makes no sense.
 
  • #5
I asked my professor and he said it's for the steam, but I still don't know how to solve this question and what you said didn't help at all.
 
  • #6
bardia sepehrnia said:
The mass flow rate is for steam, but I still don't understand how to solve the question. You say that the hydraulic diameter is equal to tube diameter no matter how many tubes I have. Obviously the hydraulic diameter is always the same, but h (convection heat transfer coefficient), is a function of hydraulic diameter. So if we have 10 tubes, or 1 tube, the heat transfer coefficient should change. You can't have same heat transfer coefficient for 1 tube and 10 tubes. Makes no sense.
Wrong! The hydraulic diameter is a geometric parameter equal to 4 times volume of tubes divided by the wetted heat transfer area: $$D_h=\frac{4\left(\frac{\pi D^2}{4}L\right)n}{(\pi D L)n}=D$$So, $$h=\frac{(287)k}{D}$$

1. Based on the steam condensing in the condenser, what is the heat load of the condenser?

2. What water flow rate do you need to match this heat load with the water entering at 10 C and exiting at 24 C?

3. Based on the tube cross sectional area and water velocity, what is the water flow rate per tube?

4. How many tubes are there?
 
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  • #7
bardia sepehrnia said:
I asked my professor and he said it's for the steam, but I still don't know how to solve this question and what you said didn't help at all.
Please don't insult me by implying that I don't know how to solve heat transfer problems, even a simple one like this. When I said that the hydraulic diameter is equal, in this case, to the tube diameter, I wasn't guessing. Now if that didn't help at all, then I don't know what will!
 

Related to Average heat transfer coefficient (forced convection)

1. What is the definition of average heat transfer coefficient?

The average heat transfer coefficient is a measure of the rate at which heat is transferred between a solid surface and a fluid in forced convection. It is a combination of the convective heat transfer coefficient and the surface area of the object.

2. How is the average heat transfer coefficient calculated?

The average heat transfer coefficient can be calculated by dividing the convective heat transfer rate by the product of the surface area of the object and the temperature difference between the solid surface and the fluid.

3. What factors affect the average heat transfer coefficient?

The average heat transfer coefficient is affected by several factors, including the fluid properties (such as viscosity and thermal conductivity), the flow velocity, the surface roughness of the object, and the geometry of the object.

4. How does the average heat transfer coefficient differ from the overall heat transfer coefficient?

The average heat transfer coefficient is specific to forced convection, while the overall heat transfer coefficient takes into account all modes of heat transfer (convection, conduction, and radiation). The overall heat transfer coefficient is typically lower than the average heat transfer coefficient.

5. Why is the average heat transfer coefficient important in engineering and design?

The average heat transfer coefficient is an important parameter in engineering and design as it helps in determining the rate of heat transfer in a system. It is crucial in designing efficient heat exchangers and predicting the performance of cooling or heating systems.

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