(Zero temparature ends ) Suppose that a copper rod of lenght 50 cm was placed into a reservoir with hot water at 50° C so that half of it is in the air at 20°C.At t=Q, the rod is taken out and its ends are kept at constant ambient temparature of 20° c. Let us denote the difference between the rod's temparature and the ambient temparature by U(x,t), where x is the distance from the left end of the rod , x=0. The U(x,t) is a solution of the initial boundary value problem: = C Uxx Ut x = 1.14 With boundary conditions as U(0, t) = U(50,t) = 0 30, 0

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