代做Mechanical Engineering、代写MATLAB程序设计、代做MATLAB语言

日期：2019-12-07 10:24

Assignment 4: Mechanical Engineering Case Study –

Temperature Distribution Simulation

Available: November 24th

Due: December 7th @ 11:55pm

Programming aspects to get familiarized with:

? MATLAB Metrics

? MATLAB Functions

? MATLAB Animations

? MATLAB Figures

The Task

The temperature distribution in a thin metal plate with constant (isothermal) temperatures on each side

can be modeled using a 2D grid, as shown in the Figure below. Typically, the number of points in the

grid is specified (N number of rows by M number of columns), as are the constant temperatures on the

four sides. The temperatures of the interior points are initialized to zero, but they change according to

the temperatures around them. Assuming that the temperature of an interior point can be computed as

the average of the four adjacent temperatures; the points shaded in the figure below represent the

adjacent temperatures for the pointed labeled x in the grid. Each time that the temperature of an interior

point changes, the temperatures of the points adjacent to it change. These changes continue until a

thermal equilibrium is achieved and all temperatures become constant. A thermal equilibrium is

reached when the difference between the previous and current temperature of every element in the grid

becomes smaller than a specific threshold (entered by the user).

The Software

Develop a software to model this temperature distribution for a grid with N rows (between 50 and 200)

and M columns (between 50 and 200). Allow the user to enter the temperatures for the four sides (initial

conditions). Use a one-dimensional array to store these temperatures (top, bottom, left, and right values

are between 0 and 255). Thus, when a point is updated, its new value is used to update the next point.

Continue updating the points, moving across the rows until the temperature differences (between the

previous temperature and the newly calculated temperature) for all the grid elements are less than a

tolerance value (provided by the user, the threshold is between 0 and 0.05). The software must provide

a visual display (animation) for the temperature distribution. You may use any form of input

mechanism (such as text fields to receive the required data from the user). You may design this program

using multiple functions.

Given test cases:

Test Case 1: Hot edges

Dimensions of grid: 200 x 200

Boundary conditions: 255, 255, 255, 255

Simulation Threshold: 0.02

Test Case 2: Mixed boundary conditions

Dimensions of grid: 200 x 200

Boundary conditions: 255, 0, 255, 0

Simulation Threshold: 0.05

Test Case 3: Zero boundary conditions

Dimensions of grid: 200 x 200

Boundary conditions: 0, 0, 0, 0

Simulation Threshold: 0.01

Write your report using the five steps model for software development (as discussed in class):

a) Step 1: Problem Identification and Statement (5 points)

b) Step 2: Gathering Information (10 points)

c) Step 3: Test Cases and algorithm (35 points)

d) Step 4: Code or implementation (35 points)

e) Step 5: Test and Verification (15 points)