8. Find the solution of the heat conduction problem = 4ut, 0< x < 2, t> 0 = 0, u(2, t) = 0, t> 0 u(0,t) u(x, 0) = 2 sin (Tx/2) – sin Tx + 4 sin 2rx, 0 0. In each of Problems 9 through 12, find an expression for the temperature u(x, t) if the initial temperature distribution in the rod is the given function. Suppose that a? = 1.

8. Find the solution of the heat conduction problem = 4ut, 0< x < 2, t> 0 = 0, u(2, t) = 0, t> 0 u(0,t) u(x, 0) = 2 sin (Tx/2) – sin Tx + 4 sin 2rx, 0 0. In each of Problems 9 through 12, find an expression for the temperature u(x, t) if the initial temperature distribution in the rod is the given function. Suppose that a? = 1.

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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Question

My question is a heat equation problem, and the question is shown in the first picture. I did not understand how the bn is found on the second picture. I did not understand why b1=1, and how.

8. Find the solution of the heat conduction problem
= 4ut, 0< x < 2, t> 0
= 0, u(2, t) = 0, t> 0
u(0,t)
u(x, 0) = 2 sin (Tx/2) – sin Tx + 4 sin 2rx, 0<x < 2.
Consider the conduction of heat in a rod 40 cm in length whose ends are maintained at 0°C for all t > 0. In each of Problems 9 through 12, find an
expression for the temperature u(x, t) if the initial temperature distribution in the rod is the given function. Suppose that a? = 1.

2.
परक
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4 sin (2x) - Sinfn)
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We

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