A thin bar composed of aluminum is 20 cm long. It is initially at a uniform temperature of 30° C. At time t = 0, the left end of the bar (x = 0) is placed in a bath at a constant temperature of 20° C. The right end of the bar (x = 20 cm) is placed in a bath kept at a constant 40° C. (a) Derive the temperature function of the bar for any point in the bar at any time. How does the temperature at the center of the bar change with time?
A thin bar composed of aluminum is 20 cm long. It is initially at a uniform temperature of 30° C. At time t = 0, the left end of the bar (x = 0) is placed in a bath at a constant temperature of 20° C. The right end of the bar (x = 20 cm) is placed in a bath kept at a constant 40° C. (a) Derive the temperature function of the bar for any point in the bar at any time. How does the temperature at the center of the bar change with time?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A thin bar composed of aluminum is 20 cm long. It is initially at a uniform temperature of
30° C. At time t = 0, the left end of the bar (x = 0) is placed in a bath at a constant
temperature of 20° C. The right end of the bar (x :
constant 40° C.
20 cm) is placed in a bath kept at a
(a) Derive the temperature function of the bar for any point in the bar at any time. How
does the temperature at the center of the bar change with time?
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