Question

Consider the conduction of heat in a rod 60 cm in length whose ends are maintained...

Consider the conduction of heat in a rod

60 cm

in length whose ends are maintained at 0°C for all

t > 0.

Find an expression for the temperature

u(x, t)

if the initial temperature distribution in the rod is the given function. Suppose that

α2 = 1.

u(x, 0) =
0,      0 ≤ x < 15,
90,      15 ≤ x ≤ 45,
0,      45 < x ≤ 60
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