# Flow inside pipe, heat transfer

## Homework Statement

A 5m long heated pipe is used heat up water from 15°C to 65°C. Water flow through the pipe is 10liter/min. The heating gives a constant heat flow in all parts of the pipes surface. The inner and outer diameter of the pipe is 30 and 50 mm, respectively. Calculate the heat transferred to the water and the inner surface temperature of the pipe at the end (point where water leaves the pipe at temperature of 65oC)

## The Attempt at a Solution

When calculating the heat transferred to the water I used
Q = m,massflow*Cp*dT.

Cp was taken at the "medium" temperature of 40 celsius. My question is: Can you use the heat transferred to the water, i.e. Q, in calculating the wall temperatures at a given point in the pipe? I would then use Q = h*A,i*(Twall-65) and solve for Twall. h is calculated by using the Reynolds/Nusselt number,

Last edited:

Chestermiller
Mentor

## Homework Statement

A pipe with heating is used to heat up water from 5 celsius to 65 celsius. The volume flow through the pipe is 10L/min. The heated pipe gives a constant heat input over the length of the pipe. Find the effect of the heat exchanger and the temperature of the inner pipe wall at the exit.

## The Attempt at a Solution

When calculating the effect of the heat exchanger I used
Q = m,massflow*Cp*dT.

Cp was taken at the "medium" temperature of 40 celsius. My question is: Can you use the effect of the heat exchanger, i.e. Q, in calculating the wall temperatures at a given point in the pipe? I would then use Q = h*A,i*(Twall-65) and solve for Twall. h is calculated by using the Reynolds/Nusselt number,
What is the exact statement of the problem?

What is the exact statement of the problem?
I have now edited my first post with the correct problem statement, as well as how I wanted to solve it, as I mixed it with another question while typing..

Chestermiller
Mentor
A 5m long heated pipe is used heat up water from 15°C to 65°C. Water flow through the pipe is 10liter/min. The heating gives a constant heat flow in all parts of the pipes surface. The inner and outer diameter of the pipe is 30 and 50 mm, respectively. Calculate the heat transferred to the water and the inner surface temperature of the pipe at the end (point where water leaves the pipe at temperature of 65oC)
If the heat flux is constant along the length of the pipe, what is the heat flux at the inner surface of the pipe?

If the heat flux is constant along the length of the pipe, what is the heat flux at the inner surface of the pipe?
It is equal to the heat flux along the length of the pipe?

Chestermiller
Mentor
No. It is equal to the component of heat flux perpendicular to the wall of the pipe. What is the overall heat load of the pipe?

No. It is equal to the component of heat flux perpendicular to the wall of the pipe. What is the overall heat load of the pipe?
That would be 34.6kW.

Chestermiller
Mentor
What is the inside surface area of the pipe? What is the wall heat flux at the inside surface of the pipe?

What is the inside surface area of the pipe? What is the wall heat flux at the inside surface of the pipe?
The inside surface area of the pipe would be 0.47 m2. The wall heat flux is 34.6 kW / 0.47 m2 ?

Chestermiller
Mentor
The inside surface area of the pipe would be 0.47 m2. The wall heat flux is 34.6 kW / 0.47 m2 ?
Can you please actually state that as a single number with units?
Is the flow (a) laminar or (b) turbulent?

Sorry. 73.6 kW / m^2 I would say. The flow is turbulent.

Chestermiller
Mentor
Sorry. 73.6 kW / m^2 I would say. The flow is turbulent.
Based on your heat transfer correlation, what is the heat transfer coefficient for the flow inside the pipe?

Based on your heat transfer correlation, what is the heat transfer coefficient for the flow inside the pipe?
It is 1548 W/m^2*K

Chestermiller
Mentor
Based on the heat flux and this heat transfer coefficient, what is the temperature difference between the bulk fluid and the wall?

That is 47 degrees, and Twall is then 112 celsius. Is this correct?

Is this way of solving the problem only possible because the heating gives a constant heat flow across the length of the pipe? I.e. using the calculated total heat transferred in finding inner wall temperatures at different places across the pipe.