An insulated composite rod is formed of two parts arranged end te equal length. Part a has thermal conductivity ka, for 0 Srs1/2, and conductivity kb, for 1/2
An insulated composite rod is formed of two parts arranged end te equal length. Part a has thermal conductivity ka, for 0 Srs1/2, and conductivity kb, for 1/2
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:An insulated composite rod is formed of two parts arranged end to end, and both halves are of
equal length. Part a has thermal conductivity ka, for 0 srs1/2, and part b has thermal
conductivity kb, for 1/2 sxs1. The nondimensional transient heat conduction equations that
describe the temperature u over the length x of the composite rod are:
du
0sxs1/2
at
1/2 <x< 1
at
where u-temperature, x= axial coordinate, t = time, and r =ka kb. The boundary and initial
conditions are
Boundary conditions
40, 1) = 1
1, 1 -1
x- 1/2
Initial conditions
dx, O) - 0
O<x< 1
Solve this set of equations for the temperature distribution as a function of time.
PLEASE DO IN EXPLICIT METHOD
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