Consider the heat distribution u (x, t) in a semi-infinite rod. Assume that the finite end is kept in contact with ice at 0°C and if initially the rod is submerged in hot water at 100°C. Establish that 100 й (а, t) (1-c-d*). Then derive that solution u roop-c²a?t 200 и (х, t) — 100. sin axda.

Consider the heat distribution u (x, t) in a semi-infinite rod. Assume that the finite end is kept in contact with ice at 0°C and if initially the rod is submerged in hot water at 100°C. Establish that 100 й (а, t) (1-c-d*). Then derive that solution u roop-c²a?t 200 и (х, t) — 100. sin axda.