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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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
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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