For a heat conduction equation in one dimensional, a parabolic equation can be employed to characterize time-variable problems. This equation requires approximation for the second derivative in space and the first derivative in time for the long and thin copper rod with a length of 54x cm and k = 1.15cm2/s. At t = 0 second, the temperature of the rod is f(x) = 2x and the boundary conditions are fixed for all times at T(0) = 175°C and T(54x) = 75°C. Select one value from each Ax and At from the given range, 0< Ax < 2cm and 0< At < 0.2 second. Evaluate the temperature distribution using THREE (3) numerical methods for 0
For a heat conduction equation in one dimensional, a parabolic equation can be employed to characterize time-variable problems. This equation requires approximation for the second derivative in space and the first derivative in time for the long and thin copper rod with a length of 54x cm and k = 1.15cm2/s. At t = 0 second, the temperature of the rod is f(x) = 2x and the boundary conditions are fixed for all times at T(0) = 175°C and T(54x) = 75°C. Select one value from each Ax and At from the given range, 0< Ax < 2cm and 0< At < 0.2 second. Evaluate the temperature distribution using THREE (3) numerical methods for 0
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:For a heat conduction equation in one dimensional, a parabolic equation can be
employed to characterize time-variable problems. This equation requires
approximation for the second derivative in space and the first derivative in time
for the long and thin copper rod with a length of 54x cm and k = 1.15cm2/s. At
t = 0 second, the temperature of the rod is f(x) = 2x and the boundary
conditions are fixed for all times at T(0) = 175°C and T(54x) = 75°C. Select one
value from each Ax and At from the given range, 0 < Ax < 2cm and 0< At <
0.2 second. Evaluate the temperature distribution using THREE (3) numerical
methods for 0<x< 54x cm and 0st< 54t seconds. Determine the best
method and justify your answer.
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