The governing equation for the temperature distribution with time on a 2D square plate measuring 1 unit by1 unit is
engineering
Description
ME 3291 Homework Assignment
(1)
The governing equation
for the temperature distribution with time on a 2D square plate measuring 1
unit by1 unit is
∂T/∂t = ∂2T/∂x2
+ ∂2T/∂y2 ,
subjected to the
Dirichlet boundary conditions for T
provided in Fig.1. You are to
obtain the following:
(a) The temperature contour plot on the square
plate with time, say at t=0.01, 0.1 and at steady state. (You can provide
contours at other times too to depict the convergence of the results at steady
state.) Take the initial condition at t=0 as T=0.0 for the whole domain.
(b) Separately,
program and compute for the Laplace Equation
∂2T/∂x2
+ ∂2T/∂y2 = 0
and obtain the solution for comparison to the
steady state solution in (a).
For the above, you
have to show clearly how you treat the Dirichlet boundary conditions, provide a
listing of your program, and other pertinent workings. The various contour plots
can be carried out using the Techp1ot or any other suitable software. (On
matrix inversion, you have the choice to use the direct method like Gauss
Elimination or indirect iterative methods.)
