Materiala (cm²/s)Silver1.71CopperAluminum1.140.86Cast ironGranite0.120.011Brick0.0038Water0.00144Table 1: Thermal Diffusivity Constants for Common Materials 4.The solution to a heat conduction problem with homogeneous boundary conditions is:u(x, t) =Σ(-1)n+18-1.71n²n²t/16 sinen=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.

Given that, ux,t=∑n=1∞-1n+18nπe-1.71n2π2t16sinnπx4

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

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

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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