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rogramming for MSE: Final Project

In a nuclear reactor, heat is generated through the fission of uranium atoms. This is typically converted to electricity using steam turbines. Maximizing heat transfer between the fissile material (typically a uranium alloy) and the coolant is an important design consideration in reactor development. At the same time, care needs to be taken such that the fissile material is

contained and does not leak into the coolant or the rest of the reactor. Thus, the fissile material is typically encased in a cladding that functions as a barrier to fission product release. The encased fissile material is referred to as a fuel rod.

You have started working for a nuclear reactor company and for your first assignment, your boss has asked you to model the steady-state temperature profile within several fuel rod designs the

company is considering. These designs have been provided to you in the form of .json files

containing information such as the number of cladding layers, the thicknesses of those layers,

and the material properties of those layers. Your boss estimates that the fissile material will have an average temperature of 1500 K during operation.

Build a python script that, given a json file encoding system parameters, calculates the

steady-state temperature profile in the material system, determines the temperature of the coolant (water) that is to be expected from the system, and creates a visualization (plot) of the temperature profile. Perform these calculations for each of the configuration files included with the project file. Prepare a typed memo where you show and discuss the temperature profile of

each fuel rod configuration. Validate your calculations by comparing one of the calculated profiles with the experimental data provided by plotting them on top of each other - comment on the similarities and differences between your calculations and the experimental data. Next, propose a new fuel rod configuration that achieves a coolant temperature between 500-600 K, using a real material not included in the previous designs, with a cladding thickness less than 2mm thick. Plot the temperature profile of your proposed configuration and briefly explain how you came up with it. Write a few short conclusions from your investigation of heat transfer in fuel rods. Finally, write a paragraph on something you struggled with on this project and how you overcame it.

Your plots should be aesthetically pleasing, adhere to best practices, and informative. Spend time considering the best way to show this information such that someone unfamiliar with the project could quickly understand the plot. Also, remember that you are dealing with real quantities.

There is no length requirement for the memo, it need only be sufficient to convey the necessary information clearly and effectively. Write something that you will be proud of.

Supplementary Information

For this problem, you are calculating the temperature profile in a cylindrical object, which means that the cross-sectional area of the material changes with the radius. To make things easier, you only need to consider heat transfer in the radial direction; that is, along the r-direction.

A system at steady-state conditions is one that does not change with time, only position. Thus, the differential equations that typically describe dynamic systems can be reduced to algebraic relations. These can be found online or in a standard heat transfer textbook. We recommend

“Heat Transfer: A Practical Approach” by Cengel. A pdf version of the steady state heat transfer chapter has been included at the end of this document. At a minimum, you should probably skim sections 1-4.

Visualizing the problem and noting boundary conditions is an essential step in solving heat transfer calculations. An example fuel rod configuration is shown below.

This particular system can be thought of as a series of thermal resistances where each layer imposes some sort of resistance to the transport of heat. The thermal resistance equation for heat transfer by conduction in a cylinder along the r-direction is given by:

𝑅

𝑐𝑜𝑛𝑑

𝑙𝑛(𝑟2/𝑟1) 2π𝐿 * 𝑘

refer to pages 146-147 of included pdf

The heat transfer rate for a given cylindrical layer can be found by the following equation:

𝑇 − 𝑇

𝑄 =

𝑐𝑜𝑛𝑑

1 2

𝑅

𝑐𝑜𝑛𝑑

refer to pages 146-147 of included pdf

Thus, the temperature profile as a function of r within an internal layer can be calculated by rearranging the terms of the previous equations to yield the following equation:

𝑇(𝑟) = 𝑇 −

𝑜

𝑙𝑛(𝑟/𝑟1) 2π𝐿 * 𝑘

𝑐𝑜𝑛𝑑

A few assumptins should be made to simplify this problem. First, assume that conduction is the only mode of heat transport in this system. Second, assume that the fluid in contact with the

surface of the fuel rod is moving slow enough that it forms an essentially stagnant film that heat can conduct through. This layer will be assumed to be 0.5 mm thick. The temperature at the edge of this film is the temperature you will calculate.

Since the fuel is at a single temperature, you need not include it in your calculations; simply set the starting temperature to your fuel temperature. However, it should be represented within your plots.

Final Project Checklist (Bare Minimum)

Plotted temperature profiles for each fuel rod configuration file

Steady-state coolant temperatures for each fuel rod configuration file Comparison plot of fuel rod temperature profile with experimental data

Temperature profile and configuration information of proposed fuel rod design

Turn in your written memo, python code, and proposed configuration file in json format

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