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. = auxx, 0 < x 0, и, 3 аиҳх, which satisfies the initial and boundary conditions u(0, t) = 0, и(п,t) %3D 0, t> 0, t> 0, and u(x, 0) = sin 2x, 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 = t/4, and timet = 2 s. 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. = auxx, 0 < x 0, и, 3 аиҳх, which satisfies the initial and boundary conditions u(0, t) = 0, и(п,t) %3D 0, t> 0, t> 0, and u(x, 0) = sin 2x, 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 = t/4, and timet = 2 s. 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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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.
= auxx,
0 < x <n,t > 0,
и, 3 аиҳх,
which satisfies the initial and boundary conditions
u(0, t) = 0,
и(п,t) %3D 0,
t> 0,
t> 0,
and
u(x, 0) = sin 2x,
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 = t/4, and timet = 2 s.
0 <x < n,
%3D

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