1. A very long cylinder of radius c is split lengthwise into two halves. The surfaces of the halves of the cylinder are kept at temperature of +u 0 and −u 0 , respectively. Find the steady-state...

1. A very long cylinder of radius c is split lengthwise into two halves. The surfaces of the halves of the cylinder are kept at temperature of +u₀
and −u₀, respectively. Find the steady-state temperature everywhere inside the cylinder.

2. Find the steady-state temperature at any point in a spherical shell of inner radius b1 and outer radius b₂
if the temperature distributions u(b₁, θ) = f₁(θ) and u(b₂, θ) = f₂(θ) are maintained over the inner and outer surfaces, respectively.