Heat equation: Arbitrary temperatures at ends. If the ends x =
0 and x = L...
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Heat equation: Arbitrary temperatures at ends. If the ends x =0 and x = L of the bar in the text are kept at constanttemperatures U1 and U2, respectively. The initial temp distributionis given by u(x, 0) = f (x).
(a) What is the temperature u1(x) in the bar after a long time(theoretically, as t → ∞)? First guess, then calculate.
(b) What is the temperature at any t. Use the heat equationgiven by ut = c^2uxx
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a Ux U1 xU2U1LThe edges are placed at temperatures U1 and U2 respectively Soafter a
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