Use the method of separation of variables, find the solution u(x, t) for the following heat conduction equation in a thin metallic rod where both ends are held at the constant temperature of zero. 0 < x < T, t > 0, Ut = auxx, which satisfies the initial and boundary conditions и (0, t) 3D 0, и (п,t) — 0, t > 0, t > 0, and u(x,0) = sin 2x, 0
Use the method of separation of variables, find the solution u(x, t) for the following heat conduction equation in a thin metallic rod where both ends are held at the constant temperature of zero. 0 < x < T, t > 0, Ut = auxx, which satisfies the initial and boundary conditions и (0, t) 3D 0, и (п,t) — 0, t > 0, t > 0, and u(x,0) = sin 2x, 0
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Use the method of separation of variables, find the solution u(x,t) for the following heat conduction equation in a thin metallic rod where both ends are held at the constant temperature of zero.
Transcribed Image Text:Use the method of separation of variables, find the solution u(x, t) for the
following heat conduction equation in a thin metallic rod where both ends are
held at the constant temperature of zero.
0 < x < T, t > 0,
Ut = auxx,
which satisfies the initial and boundary conditions
и (0, t) 3D 0,
и (п,t) — 0,
t > 0,
t > 0,
and
u(x,0)
= sin 2x,
0<x π,
where a is the thermal conductivity of the metallic rod. If a = 0.8 cm2/s, find
the temperature in °C of the rod at the position x = 1/4, and time t = 2 s.
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