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Use separation of variables to solve the following heat equation in a disk 1 ðu ди = k dt 1 ди r dr 0 0, dr2 и(r, —п, t) — и(r, л, t), ди (r, —л, t) — de ди (r, n, t), u(а, 0, t) —D 0, lu(r, 0, t)| < о, o*, as u(r, 0,0) = sin 20J2 ( =2"r). 3 sin

Use separation of variables to solve the following heat equation in a disk 1 ðu ди = k dt 1 ди r dr 0 0, dr2 и(r, —п, t) — и(r, л, t), ди (r, —л, t) — de ди (r, n, t), u(а, 0, t) —D 0, lu(r, 0, t)| < о, o*, as u(r, 0,0) = sin 20J2 ( =2"r). 3 sin

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 separation of variables to solve the following heat equation in a disk 1 ди 1 du ди = k dt + + 0 <r < a, -n < 0 < n, t > 0, dr2 r dr υ(r, - π, ) = υr , π, ), ди (r, л, t), ди ae ", -n, t) = и(а, ө, t) %—D 0, Ju(r, 0, t)| < ∞, r → 0*, as 2 и(r, 0,0) 3D (). z21 3 sin 20J2
Transcribed Image Text:Use separation of variables to solve the following heat equation in a disk 1 ди 1 du ди = k dt + + 0 <r < a, -n < 0 < n, t > 0, dr2 r dr υ(r, - π, ) = υr , π, ), ди (r, л, t), ди ae ", -n, t) = и(а, ө, t) %—D 0, Ju(r, 0, t)| < ∞, r → 0*, as 2 и(r, 0,0) 3D (). z21 3 sin 20J2
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