A test was conducted to determine the temperature distribution of a one meter iron reinforcement bar under fire. The initial temperature of the reinforcement bar is given by U(x,0) = Sin 2 nx for 0 < x < 1. The U(1, t) = 0 for 0 < x < 0.01. Given boundary conditions U(0, t) ди? du the heat equation is by taking Ax = 0.25 and At = 0.01 and %3D at C2 = 0.23:
A test was conducted to determine the temperature distribution of a one meter iron reinforcement bar under fire. The initial temperature of the reinforcement bar is given by U(x,0) = Sin 2 nx for 0 < x < 1. The U(1, t) = 0 for 0 < x < 0.01. Given boundary conditions U(0, t) ди? du the heat equation is by taking Ax = 0.25 and At = 0.01 and %3D at C2 = 0.23:
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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Transcribed Image Text:(i)
Examine the system of linear equation of the temperature distribution
by using the most stable finite difference method.
(ii)
Justify why the chosen finite difference method in Q4 (a)(i) is the
most stable method.
Transcribed Image Text:A test was conducted to determine the temperature distribution of a one
meter iron reinforcement bar under fire. The initial temperature of the
reinforcement bar is given by U(x,0) = Sin 2 x for 0 < x < 1. The
boundary conditions U(0, t)
the heat equation is
(b)
U(1,t)
= 0 for 0 < x< 0.01. Given
%3D
du?
by taking Ax = 0.25 and At = 0.01 and
ди
%3D
at
C2 = 0.23:
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