Solve Problem 5 if the ends x = 0 and x = L are held at tem- perature zero.
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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Question
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd49a5070-9d99-4a2f-a144-be47e7ddead5%2Ffc1dee7d-db57-4825-9d0c-e4ff1c23b2b3%2F7hxtufn_processed.png&w=3840&q=75)
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]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd49a5070-9d99-4a2f-a144-be47e7ddead5%2Ffc1dee7d-db57-4825-9d0c-e4ff1c23b2b3%2Fru2c0ce_processed.png&w=3840&q=75)
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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