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u(x, 0) = ÷(1 -), 0 0 Eq. 2 Uz = a?uxx, 0 < x < L, t > 0 Eq. 3

u(x, 0) = ÷(1 -), 0 0 Eq. 2 Uz = a?uxx, 0 < x < L, t > 0 Eq. 3

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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Let u = (x,t) represent the temperature of a steelhose with length L. The temperature with t= 0 is (E.q 1 in picture) 

Temperature at the tips of the hose is constnat at (E.q 2)
Temperature inside the hose differs by the heattransferequation (E.q 3) where            α = constant

use method seperation of variables to determine u = u(x,t) when t>0

u(x, 0) = ÷(1 -), 0 <x< L Eq. 1 u(0, t) %3D и(L,t) %3D 0, t > 0 Eq. 2 Uz = a?uxx, 0 < x < L, t > 0 Eq. 3
Transcribed Image Text:u(x, 0) = ÷(1 -), 0 <x< L Eq. 1 u(0, t) %3D и(L,t) %3D 0, t > 0 Eq. 2 Uz = a?uxx, 0 < x < L, t > 0 Eq. 3
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Follow up question. We are given   α2 = 0.1[cm2/s] and a hoselength of 1m. What is the temperature in the middle of the hose after 1000 seconds. Give a series solution and an approximate solution

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