Now, compute the solution to the 2D heat equation on a circular disk in Matlab. Recall that the heat equation is given by:
ut = α^2*∇^2*u.
For this problem, we will solve the heat equation using a finite difference scheme on a Cartesian grid, as in class. We will use a grid of 300×300 with the circular disk in the center. The radius of the circle is r = 1, α = 1, and the domain is [−1.5, 1.5] in x and [−1.5, 1.5] in y.
You can impose the boundary conditions by enforcing the temperature at points that are outside of the disk at the beginning of each new time-step. It should be easy to find points that are outside the disk, because they satisfy x 2 + y 2 > 1.
Simulate the unsteady heat equation for the following boundary conditions:
• The left half of the boundary of the disk is fixed at a temperature of u = 1 and the right half of the boundary is fixed at u = 2. Try simulating this with zero initial conditions first. Next, try initial conditions inside the disk where the top half is u = −1 and the bottom half is u = 1.
• The temperature at the boundary of the disk is fixed at u(θ) = cos(θ).
Include your Matlab code and show some plots of your solutions to the heat equation. Plot the temperature distribution for each case 1) early on in the diffusion process, 2) near steady state, and 3) somewhere in the middle.
Plagiarism Free Papers
All our papers are original and written from scratch. We will email you a plagiarism report alongside your completed paper once done.
All papers are submitted ahead of time. We do this to allow you time to point out any area you would need revision on, and help you for free.
A title page preceeds all your paper content. Here, you put all your personal information and this we give out for free.
Without a reference/bibliography page, any academic paper is incomplete and doesnt qualify for grading. We also offer this for free.
Originality & Security
At Homework Valley, we take confidentiality seriously and all your personal information is stored safely and do not share it with third parties for any reasons whatsoever. Our work is original and we send plagiarism reports alongside every paper.
24/7 Customer Support
Our agents are online 24/7. Feel free to contact us through email or talk to our live agents.
Try it now!
How it works?
Follow these simple steps to get your paper done
Place your order
Fill in the order form and provide all details of your assignment.
Proceed with the payment
Choose the payment system that suits you most.
Receive the final file
Once your paper is ready, we will email it to you.
We work around the clock to see best customer experience.
Our prices are pocket friendly and you can do partial payments. When that is not enough, we have a free enquiry service.
Admission help & Client-Writer Contact
When you need to elaborate something further to your writer, we provide that button.
We take deadlines seriously and our papers are submitted ahead of time. We are happy to assist you in case of any adjustments needed.
Your feedback, good or bad is of great concern to us and we take it very seriously. We are, therefore, constantly adjusting our policies to ensure best customer/writer experience.