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

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

Advanced Engineering Mathematics
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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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 < n,t > 0, Uz = auxx, which satisfies the initial and boundary conditions u(0, t) = 0, и(п,t) 3D 0, t > 0, t > 0, and 0 < x < n, 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 = n/4, and time t = 2 s. u(x, 0) = sin 2x , I|
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 < n,t > 0, Uz = auxx, which satisfies the initial and boundary conditions u(0, t) = 0, и(п,t) 3D 0, t > 0, t > 0, and 0 < x < n, 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 = n/4, and time t = 2 s. u(x, 0) = sin 2x , I|
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