4. The solution to a heat conduction problem with homogeneous boundary conditions is: u(x, t) = > (-1)n+18 ,-1.71n²n²t/16 sin n=1 (a) What is the length of the rod (in centimeters)? (b) Use Table 1 to determine which material was used to make the rod. (c) Write out the first three terms of u(x, t). (d) Use your partial sum from (b) to approximate the temperature at the midpoint when t = 1,5, 10.
4. The solution to a heat conduction problem with homogeneous boundary conditions is: u(x, t) = > (-1)n+18 ,-1.71n²n²t/16 sin n=1 (a) What is the length of the rod (in centimeters)? (b) Use Table 1 to determine which material was used to make the rod. (c) Write out the first three terms of u(x, t). (d) Use your partial sum from (b) to approximate the temperature at the midpoint when t = 1,5, 10.
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
Transcribed Image Text:Material
a (cm²/s)
Silver
1.71
Copper
Aluminum
1.14
0.86
Cast iron
Granite
0.12
0.011
Brick
0.0038
Water
0.00144
Table 1: Thermal Diffusivity Constants for Common Materials
Transcribed Image Text:4.
The solution to a heat conduction problem with homogeneous boundary conditions is:
u(x, t) =
Σ
(-1)n+18
-1.71n²n²t/16 sin
e
n=1
(a) What is the length of the rod (in centimeters)?
(b) Use Table 1 to determine which material was used to make the rod.
(c) Write out the first three terms of u(x, t).
(d) Use your partial sum from (b) to approximate the temperature at the midpoint when t = 1,5, 10.
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