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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
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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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: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.
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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