Question

In steady state, two dimensional heat flow equation reduces to.

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Answer 1

Answer:

These are the steady state solutions. ... In the 1D case, the heat equation for steady states becomes uxx = 0.

Answer 2

Answer:

The two-dimensional heat equation in steady state is also known as The Laplace equation

A steady state is a state which remains the same over given time period.

In the 2D case, we see that steady states must solve

∇ 2 u = uxx + uyy = 0.

This is Laplace’s equation.

Solutions to Laplace’s equation are called harmonic

functions.

In steady state, two dimensional heat flow equation reduces to

ut = α2(uxx + uyy) −→ u(x, y, t) inside a domain D