Question

Temperature distribution in an infinite metal satisfies diffusion equation
k ∂
^2u
/∂x^2 =
∂u
/∂t .

The bar has an initial temperature distribution u(x, 0) = exp(−x
^2/a^2) along its length

where −∞ < x < ∞. Find the temperature distribution at a later time t. The

boundary conditions are u(x, t) → 0 and ∂u/∂x → 0 as |x| → ∞.solve using Fourier transformation​

Answer 1

Answer:

Temperature distribution in an infinite metal satisfies diffusion equation

k ∂

^2u

/∂x^2 =

∂u

/∂t .

The bar has an initial temperature distribution u(x, 0) = exp(−x

^2/a^2) along its length

where −∞ < x < ∞. Find the temperature distribution at a later time t. The

boundary conditions are u(x, t) → 0 and ∂u/∂x → 0 as |x| → ∞.solve using Fourier transformation