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The temperature distribution u(x,t) of the one-dimensional gold rod is governed by the heat equation as follows. a²u ди = 0.25- əx² at Given the boundary conditions u(0, t) = 2t², u(1,t) = 5t, for 0

The temperature distribution u(x,t) of the one-dimensional gold rod is governed by the heat equation as follows. a²u ди = 0.25- əx² at Given the boundary conditions u(0, t) = 2t², u(1,t) = 5t, for 0

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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(а) The temperature distribution u(x, t) of the one-dimensional gold rod is governed by the heat equation as follows. Q4 a²u ди -= 0.25 at Given the boundary conditions u(0, t) = 2t², u(1, t) = 5t, for 0 <t < 0.04 s and the initial condition u(x, 0) = x(1 – x) for 0<x < 1.0 mm, analyze the temperature distribution of the rod with Ax = 0.25 mm and At = 0.02 s in 4 decimal places.
Transcribed Image Text:(а) The temperature distribution u(x, t) of the one-dimensional gold rod is governed by the heat equation as follows. Q4 a²u ди -= 0.25 at Given the boundary conditions u(0, t) = 2t², u(1, t) = 5t, for 0 <t < 0.04 s and the initial condition u(x, 0) = x(1 – x) for 0<x < 1.0 mm, analyze the temperature distribution of the rod with Ax = 0.25 mm and At = 0.02 s in 4 decimal places.
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