EAS 230 Programming Project

Project Overview

This project was completed for EAS 230: Engineering Computation at the University at Buffalo in Spring 2024.

Collaborators

• Kashfy Gazi
• Ryan Zgoda

Language

This project is written in MATLAB.

Project Description

This project focuses on numerical solutions to heat transfer problems in one-dimensional plates using finite difference methods. It solves the transient heat conduction equation with various boundary conditions for different radioactive materials.

Key Features

1. TemperatureSolver Function

A core solver that implements both explicit and implicit finite difference methods to compute temperature distributions across a plate:

• Explicit Method: Uses forward-time, central-space (FTCS) scheme
• Implicit Method: Uses backward-time, central-space (BTCS) scheme with matrix solution

2. Material Properties

The project analyzes thermal behavior of three nuclear materials:

• Uranium
• Thorium
• Plutonium

Material properties retrieved include:

• Thermal conductivity (k)
• Thermal diffusivity (α)
• Heat generation rate (gdot)
• Melting point

3. Boundary Conditions

Four different boundary condition types are implemented at the plate boundaries:

1. Prescribed Temperature - Fixed temperature boundary
2. Prescribed Heat Flux - Fixed heat flow boundary
3. Insulated - Zero heat flux (adiabatic)
4. Convective - Heat exchange with surroundings

Case Studies

Case 1: Temperature distribution evolution in a uranium plate (10 cm) over 10 minutes

• Compares explicit method with varying spatial discretizations (51, 101, 201 nodes)
• Compares implicit method with different time stepping strategies
• Generates visualizations at 1, 2.5, 5, and 10 second intervals

Case 2: Material comparison under various boundary conditions

• Analyzes three materials (Uranium, Thorium, Plutonium)
• Applies all four boundary condition types
• Calculates and displays minimum/maximum temperatures after 10 minutes

Case 3: Additional implicit method analysis

Files

• Case1.m, Case2.m, Case3.m - Main case study scripts
• TemperatureSolver.m - Core finite difference solver function
• Properties.m - Material property loader function
• Properties.xlsx - Material property database
• .mat files - Saved results and analysis data

Engineering Applications

This project demonstrates practical applications of:

• Numerical methods for PDEs (Partial Differential Equations)
• Finite difference discretization schemes
• Stability analysis of numerical methods
• Engineering problem-solving with MATLAB