Solve for the equilibrium temperature distribution using the 2D Laplace equation on an L x H sized rectangular domain with the following boundary conditions:

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 15E
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Solve for the equilibrium temperature distribution using the 2D Laplace equation on an
L x H sized rectangular domain with the following boundary conditions:
1. Left: u(0,y) = f(y) (fixed temperature)
2. Bottom: u₂(x,0) = 0 (insulating)
3. Top: u₂(x, H) = 0 (insulating)
4. Right: u(L, y) = 0 (zero temperature)
Solve for a general boundary temperature f(y). Also solve for the particular temperature
distribution f(y) = sin(4Ty/H).
u(0,y)-f(y)
U₂, (x,H) = 0
7² - 0
u(L, y) - 0
u₂(x,0) = 0
Without too much extra work, tell me how this solution would change if we also made the
right boundary condition insulating?
Transcribed Image Text:Solve for the equilibrium temperature distribution using the 2D Laplace equation on an L x H sized rectangular domain with the following boundary conditions: 1. Left: u(0,y) = f(y) (fixed temperature) 2. Bottom: u₂(x,0) = 0 (insulating) 3. Top: u₂(x, H) = 0 (insulating) 4. Right: u(L, y) = 0 (zero temperature) Solve for a general boundary temperature f(y). Also solve for the particular temperature distribution f(y) = sin(4Ty/H). u(0,y)-f(y) U₂, (x,H) = 0 7² - 0 u(L, y) - 0 u₂(x,0) = 0 Without too much extra work, tell me how this solution would change if we also made the right boundary condition insulating?
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,