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Question 12. The temperature u(x, t) of a narrow metal rod of length L = 1 with a heat source is modelled by the following non-homogeneous heat equation: Ut = Urr +1-x. Solve the equation if the initial temperature u(x,0) = 4+ x, and the boundary conditions are: и(0, t) %3D 3, и(1, t) 3 5, t> 0. Hint: Transform the non-homogeneous boundary conditions into homogeneous ones for w 3D и — C1х — С2.

Question 12. The temperature u(x, t) of a narrow metal rod of length L = 1 with a heat source is modelled by the following non-homogeneous heat equation: Ut = Urr +1-x. Solve the equation if the initial temperature u(x,0) = 4+ x, and the boundary conditions are: и(0, t) %3D 3, и(1, t) 3 5, t> 0. Hint: Transform the non-homogeneous boundary conditions into homogeneous ones for w 3D и — C1х — С2.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question 12. The temperature u(x, t) of a narrow metal rod of length L = 1 with a heat source is modelled by the following non-homogeneous heat equation: Ut = Urr +1– x. Solve the equation if the initial temperature u(x, 0) = 4+ x, and the boundary conditions are: u(0, t) = 3, u(1, t) = 5, t> 0. Hint: Transform the non-homogeneous boundary conditions into homogeneous ones for w — и — Сіх — C2.
Transcribed Image Text:Question 12. The temperature u(x, t) of a narrow metal rod of length L = 1 with a heat source is modelled by the following non-homogeneous heat equation: Ut = Urr +1– x. Solve the equation if the initial temperature u(x, 0) = 4+ x, and the boundary conditions are: u(0, t) = 3, u(1, t) = 5, t> 0. Hint: Transform the non-homogeneous boundary conditions into homogeneous ones for w — и — Сіх — C2.
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