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5. Consider the heat problem that is described by: 0.9urr = Ut; 0 < x < 5, t > 0 и (0, t) — 0, и(5, t) — 0, t>0 u(x, 0) = 5x – x² 0 < x < 5 (a) Identify the heat diffusivity constant a2, the length of the bar L, and the initial temperature distribution f(x). (b) Plug a2 and L into u(x, t) to describe the solutions to this problem. u(x, t) = £ -a²n²n² Cne sin n=1

5. Consider the heat problem that is described by: 0.9urr = Ut; 0 < x < 5, t > 0 и (0, t) — 0, и(5, t) — 0, t>0 u(x, 0) = 5x – x² 0 < x < 5 (a) Identify the heat diffusivity constant a2, the length of the bar L, and the initial temperature distribution f(x). (b) Plug a2 and L into u(x, t) to describe the solutions to this problem. u(x, t) = £ -a²n²n² Cne sin n=1

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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5. Consider the heat problem that is described by: 0.9urr = Ut, 0 < x < 5, t> 0 и (0, t) — 0, и(5, t) — 0, t>0 и(х, 0) — 5х — 1? 0 < x < 5 (a) Identify the heat diffusivity constant a2, the length of the bar L, and the initial temperature distribution f (x). (b) Plug a² and L into u(x, t) to describe the solutions to this problem. -Σ -a²n²n?t/L² Cne u(x, t) = sin n=1 (c) Plug L and f(x) into the following equation to describe the coefficients Cn- f(x) Cn sin n=1 Note: You are not actually calculating anything in this problem. You are just setting up the solution and the Fourier sine series.
Transcribed Image Text:5. Consider the heat problem that is described by: 0.9urr = Ut, 0 < x < 5, t> 0 и (0, t) — 0, и(5, t) — 0, t>0 и(х, 0) — 5х — 1? 0 < x < 5 (a) Identify the heat diffusivity constant a2, the length of the bar L, and the initial temperature distribution f (x). (b) Plug a² and L into u(x, t) to describe the solutions to this problem. -Σ -a²n²n?t/L² Cne u(x, t) = sin n=1 (c) Plug L and f(x) into the following equation to describe the coefficients Cn- f(x) Cn sin n=1 Note: You are not actually calculating anything in this problem. You are just setting up the solution and the Fourier sine series.
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