An insulated uniform metal rod, 40 cm long, has the temperature of its ends maintained at 0°C for all t>0. The initial temperature distribution along the rod is defined by х, 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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An insulated uniform metal rod, 40 cm long, has the temperature of its ends maintained
at 0°C for all t>0. The initial temperature distribution along the rod is defined by
х,
f(x) = {40 – x,
0 < x < 20
20 < x < 40,
where x measures the distance of a point from a fixed end. Solve the heat equation
ди
a²u
at
to determine an expression for the temperature u of any point in the rod at time t.
Transcribed Image Text:An insulated uniform metal rod, 40 cm long, has the temperature of its ends maintained at 0°C for all t>0. The initial temperature distribution along the rod is defined by х, f(x) = {40 – x, 0 < x < 20 20 < x < 40, where x measures the distance of a point from a fixed end. Solve the heat equation ди a²u at to determine an expression for the temperature u of any point in the rod at time t.
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