The temperature in a semi-infinite solid is modeled by the boundary-value problem k 02 u 0x2 0u 0t , x . 0, t . 0 u(0, t) u0, lim xSq u(x, t) 0, t . 0 u(x, 0) 0, x . 0 Solve for u(x, t). Use the solution to determine analytically the value of limtSq u(x, t), x . 0.

I c 4tY'=- s-s( n _^i - \11/ /Jl C -.- 9X =t T rr! \N {l' ' t^fl ---T--'-:ral...