Now, compute the solution to the 2D heat equation on a circular disk in Matlab.
Recall that the heat equation is given by:
ut = alpha^2 * grenadian^2 * u:
For this problem, we will solve the heat equation using a fnite 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, alpha = 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 nd 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(theta) = cos(theta).
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.
More details please see the picture.
GET SOLUTION FOR THIS ASSIGNMENT
TO BE RE-WRITTEN FROM THE SCRATCH
- Original and non-plagiarized custom papers. Our writers develop their writing from scratch unless you request them to rewrite, edit or proofread your paper.
- Timely Delivery. capitalessaywriting.com believes in beating the deadlines that our customers have imposed because we understand how important it is.
- Customer satisfaction. Customer satisfaction. We have an outstanding customer care team that is always ready and willing to listen to you, collect your instructions and make sure that your custom writing needs are satisfied
- Privacy and safety. It’s secure to place an order at capitalessaywriting.com We won’t reveal your private information to anyone else.
- Writing services provided by experts. Looking for expert essay writers, thesis and dissertation writers, personal statement writers, or writers to provide any other kind of custom writing service? film dealing with the march on Washington on August 28, 1963
- Enjoy our bonus services. You can make a free inquiry before placing and your order and paying this way, you know just how much you will pay. compute the solution to the 2D heat equation on a circular disk in Matlab
- Premium papers. We provide the highest quality papers in the writing industry. Our company only employs specialized professional writers who take pride in satisfying the needs of our huge client base by offering them premium writing services.