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Solve Problem 5 if the ends x = 0 and x = L are held at tem- perature zero.

Solve Problem 5 if the ends x = 0 and x = L are held at tem- perature zero.

Advanced Engineering Mathematics
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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Please solve 6. I attached the solution to question 5 already. 

5. Suppose heat is lost from the lateral surface of a thin rod of length L into a surrounding medium at temperature zero. If the linear law of heat transfer applies, then the heat equation takes on the form a²u k 0<x<L, t> 0, h a constant. Find the temperature u(x, t) if the initial temperature is f(x) throughout and the ends x = 0 and x = L are insulated. See FIGURE 13.3.3. insulated 0 - hu = ди at 0° insulated L x 0° heat transfer from lateral surface of the rod FIGURE 13.3.3 Rod in Problem 5 6. Solve Problem 5 if the ends x = 0 and x = L are held at tem- perature zero.
Transcribed Image Text:5. Suppose heat is lost from the lateral surface of a thin rod of length L into a surrounding medium at temperature zero. If the linear law of heat transfer applies, then the heat equation takes on the form a²u k 0<x<L, t> 0, h a constant. Find the temperature u(x, t) if the initial temperature is f(x) throughout and the ends x = 0 and x = L are insulated. See FIGURE 13.3.3. insulated 0 - hu = ди at 0° insulated L x 0° heat transfer from lateral surface of the rod FIGURE 13.3.3 Rod in Problem 5 6. Solve Problem 5 if the ends x = 0 and x = L are held at tem- perature zero.
e=th | 1 | ²1500) 5. u(x, t) e = f(x) dx + ²/2 ([^f(x) cos 77 x dx ) e ² ² L n=1 -k(n²w²/L²)t COS NTT L x]
Transcribed Image Text:e=th | 1 | ²1500) 5. u(x, t) e = f(x) dx + ²/2 ([^f(x) cos 77 x dx ) e ² ² L n=1 -k(n²w²/L²)t COS NTT L x]
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