Steady-State Heat Conduction in a Region Indicates an Equilibrium Temperature: Partial Differential Equations Assignment, SMU, Singapore

Assignment Details:

Steady-state heat conduction in a region indicates an equilibrium temperature within that region.

1. Consider the steady-state heat equation

2. Show that the steady-state heat equation (PE1) with nonhomogenous boundary conditions

u(0)=∝, u(L)=β

has, using (L1g), solution

3. Consider a rectangular region Ω = [0, L] × [0, H]: the equilibrium temperature u(x, y) satisfies Laplace’s equation

Find a solution u(x, y) to (LE) under (LER). (10)

4. Consider a rectangular region Ω: the equilibrium temperature satisfies Poisson’s equation