# Heat transfer through pipe penetrating nuclear reactor

• Bakery87
In summary, in order to determine the temperature vs. time of an aqueous nuclear reactor, you will need to use a heat transfer equation such as Newton's Law of Cooling. This will involve knowing the initial temperature of the water in the reactor vessel, the k-value of the material and environment, and the total power output of the reactor. With this information, you can calculate the temperature as a function of time and use this to determine the necessary size of pipes for cooling the reactor.
Bakery87
What I'm trying to figure out is the temperature vs. time of a aqueous nuclear reactor. I'm trying to cool 200kW of energy with metal pipes running through a working reactor. This is just a heat calc, I'm not actually building one.

The reactor runs at 200kW, is liquid filled, and will be cooled with water running through pipes that run through the reactor core. Assuming we have inlet cooling water at 25*C, and we need to constantly remove heat from the reactor, what size pipes do I need?

I already have figured out, by m*Cp*deltaT, I will have somewhere around 2-4 kg water flow per second. I used this to find the approx. flowrate.

200*10^3 = m*cp*deltaT

So what I have is a vessel that's 125L or water solution, being chilled cold water running through pipes that penetrate the vessel. So what is the temperature of the vessels water solution vs. time?

I need to calculate how much heat is transferred to the water inside the pipe. This means I can vary the area of pipes, thickness, and make. I'm thinking I'll use a 2mm wall thickness, and steel as the pipe's material.

Any help is appreciated.

The best way to answer this question is to use a heat transfer equation such as Newton's Law of Cooling. This equation states that the rate of heat transfer (Q) is equal to the difference in temperature between the object and its surroundings (T1-T2) multiplied by a constant (k) which depends on the properties of the material and the properties of the environment. This equation can be written as: Q = k*(T1-T2) You can use this equation to calculate the temperature of the water inside the reactor vessel as a function of time. You will need to know the initial temperature of the water in the vessel, the k-value of the material (steel) and the environment (water), and the total power output of the reactor. You can then solve for the temperature as a function of time using the following equation: T(t) = T0 + (Q/k)*(1 - e^(-kt)) Where T0 is the initial temperature of the water solution, Q is the total amount of heat released from the reactor, k is the heat transfer constant, and t is the time. Once you have the temperature as a function of time, you can then use this to determine the size of pipes that are needed to cool the reactor. You would need to calculate the total amount of heat that needs to be removed from the reactor in order to get the desired cooling effect. You can then use this to calculate the necessary flow rate for the cooling water, and then use this to determine the diameter of the pipe required.

I would approach this problem by first considering the principles of heat transfer. In this case, we are dealing with conduction heat transfer through the metal pipes, convection heat transfer between the water inside the pipes and the reactor, and possibly radiation heat transfer as well.

To determine the temperature vs. time of the aqueous nuclear reactor, we would need to consider the heat balance equation, which takes into account the rate of heat transfer, the heat capacity of the materials involved, and the temperature difference between the reactor and the cooling water. This equation can be solved using numerical methods or by creating a mathematical model.

In terms of determining the size of pipes needed, it will depend on various factors such as the desired cooling rate, the thermal conductivity of the pipes, and the flow rate of the cooling water. A larger pipe diameter and thicker wall thickness may result in better heat transfer, but it may also increase the cost and complexity of the system. Therefore, a trade-off analysis may be necessary to determine the most optimal pipe size.

It is also important to consider the potential for heat loss through the pipes and insulation may be necessary to minimize this. Additionally, the choice of pipe material will also impact the heat transfer rate, as different materials have different thermal conductivities.

Overall, it is essential to carefully consider all the factors involved in heat transfer through the pipes penetrating the nuclear reactor to accurately predict the temperature vs. time of the reactor and ensure efficient cooling.

## 1. How does heat transfer occur through a pipe penetrating a nuclear reactor?

Heat transfer through a pipe penetrating a nuclear reactor occurs through a process called conduction. This is when heat is transferred from a hotter object to a cooler object through direct contact.

## 2. What factors affect the rate of heat transfer through a pipe in a nuclear reactor?

The rate of heat transfer through a pipe in a nuclear reactor is affected by several factors, including the temperature difference between the pipe and the reactor, the material and thickness of the pipe, and the properties of the fluid or gas flowing through the pipe.

## 3. How is the temperature of the pipe regulated in a nuclear reactor?

The temperature of the pipe in a nuclear reactor is regulated through the control of the fluid or gas flowing through the pipe. This is typically done through the use of a coolant, which absorbs heat from the pipe and carries it away to a heat exchanger.

## 4. What safety measures are in place to prevent heat transfer failures in nuclear reactors?

Nuclear reactors have several safety measures in place to prevent heat transfer failures, such as redundant cooling systems and temperature monitoring systems. Additionally, the design and construction of the pipes and reactor components are rigorously tested and regulated to ensure their safety and reliability.

## 5. How is heat transfer through pipes in a nuclear reactor different from other types of heat transfer?

Heat transfer through pipes in a nuclear reactor is different from other types of heat transfer, such as convection or radiation, because it occurs through direct contact between the pipe and the reactor. This makes it more efficient and controllable, but also requires careful management to prevent overheating or other issues.

• Engineering and Comp Sci Homework Help
Replies
15
Views
2K
• Engineering and Comp Sci Homework Help
Replies
1
Views
982
• Engineering and Comp Sci Homework Help
Replies
22
Views
2K
• Engineering and Comp Sci Homework Help
Replies
7
Views
998
• Materials and Chemical Engineering
Replies
17
Views
556
• Engineering and Comp Sci Homework Help
Replies
1
Views
2K
• Mechanical Engineering
Replies
15
Views
2K
• Engineering and Comp Sci Homework Help
Replies
3
Views
2K
• Engineering and Comp Sci Homework Help
Replies
3
Views
1K
• Engineering and Comp Sci Homework Help
Replies
1
Views
2K