Register to reply

Thermo-ish diffusion/wave equation - metal plate and temperature difference

Share this thread:
samee
#1
Jul31-12, 11:33 AM
P: 60
1. The problem statement, all variables and given/known data

The edges of a thin plate are held at the temperature described below. Determine the steady-state temperature distribution in the plate. Assume the large flat surfaces to be insulated.

If the plate is lying along the x-y plane, then one corner would be at the origin. The height of the plate would be 1m along the y-axis and the length would be 2m along the x-axis. The edge along the y-axis is being held at 0 C. The edge along the x-axis is being held at 0 C. The edge parallel to the x-axis is being held at 0 C. The edge parallel to the y-axis is being held at 50sin(pi*y) C.

2. Relevant equations

So I'm assuming this question is actually just a diffusion equation or a wave equation, because that's what the rest of our homework was on. Alpha2uxx=ut
and
u(x,t)=X(x)T(t)=(C1coskx+C2sinkx)e-K2alpha2t+C3+C4x

3. The attempt at a solution

So I tried to solve this like the wave equations and it seems to just be blowing out of proportion and not making sense... Also... I think we need to consider a thrid position variable here, we need x,y AND t. I don';t know how to do this at all :(
Phys.Org News Partner Science news on Phys.org
Scientists discover RNA modifications in some unexpected places
Scientists discover tropical tree microbiome in Panama
'Squid skin' metamaterials project yields vivid color display

Register to reply

Related Discussions
Large wave number region of difference method of diffusion Engineering, Comp Sci, & Technology Homework 0
Solving diffusion equation using finite difference method Nuclear Engineering 0
Solving the diffusion equation finite difference technique Differential Equations 0
The temperature distribution on metal plate is given by... Calculus & Beyond Homework 2
The difference between the Heat and Diffusion equation ? Differential Equations 2