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2. Consider the conduction of heat in a rod of length 80cm whose thermal diffusivity constant is 1/18 cm²/s. Suppose the rods initial temperature distribution is u(x, 0) = 80 - x, 0 ≤ x ≤ 80 and that both ends are insulated: Ut = Uxx¹ 18 U₂ ux (0, t) = u =ux (80, t) = 0, 0 < x < 80, t> 0 t> 0 u(x,0) = 80 - x, Find the formal solution to the given initial-boundary value problem 0 < x < 80

2. Consider the conduction of heat in a rod of length 80cm whose thermal diffusivity constant is 1/18 cm²/s. Suppose the rods initial temperature distribution is u(x, 0) = 80 - x, 0 ≤ x ≤ 80 and that both ends are insulated: Ut = Uxx¹ 18 U₂ ux (0, t) = u =ux (80, t) = 0, 0 < x < 80, t> 0 t> 0 u(x,0) = 80 - x, Find the formal solution to the given initial-boundary value problem 0 < x < 80

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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2. Consider the conduction of heat in a rod of length 80cm whose thermal diffusivity constant is 1/18 cm²/s. Suppose the rods initial temperature distribution is u(x,0) = 80-x, 0≤x≤ 80 and that both ends are insulated: Ut = U xx 0 < x < 80, t> 0 18 ux (0, t) = ux (80, t) = 0, u(x, 0) = 80 — x, Find the formal solution to the given initial-boundary value problem t> 0 0 < x < 80
Transcribed Image Text:2. Consider the conduction of heat in a rod of length 80cm whose thermal diffusivity constant is 1/18 cm²/s. Suppose the rods initial temperature distribution is u(x,0) = 80-x, 0≤x≤ 80 and that both ends are insulated: Ut = U xx 0 < x < 80, t> 0 18 ux (0, t) = ux (80, t) = 0, u(x, 0) = 80 — x, Find the formal solution to the given initial-boundary value problem t> 0 0 < x < 80
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