Solve for the equilibrium temperature distribution using the 2D Laplace equation on anL 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 temperaturedistribution f(y) = sin(4Ty/H).u(0,y)-f(y)U₂, (x,H) = 07² - 0u(L, y) - 0u₂(x,0) = 0Without too much extra work, tell me how this solution would change if we also made theright boundary condition insulating?

In this question, we solve the Laplace equation by using the variable saperation method and using Fourier series.

Answered: Solve for the equilibrium temperature…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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: