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.
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Transcribed Image Text: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 2
(1 - o-2*).
й (а, t).
Then derive that solution u
e-c²a?t
200
и (х, t) — 100 —
sin axda.
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