Question

# 2. Find the steady-state solution of the heat conduction equation

α2uxx = ut,

that satisfies each set

of boundary conditions below.

(a) u(0,t) = 20, u(4,t) = 60, t > 0.

(b) u(0,t) = 20, ux(4,t) = 10, t > 0.

(c) ux(0,t) = −20, ux(4,t) − u(4,t) = 40, t > 0.

(d) ux(0,t) + 2u(0,t) = 0, u(4,t) = 30, t > 0.

(e) ux(0,t) + 2u(0,t) = 0, 2ux(4,t) − u(4,t) = 15, t > 0.

Will the solutions depend on the thermos-diffusivity constant α2?