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The general solution for the one dimensional heat equation for a thin laterally insulated bar of finite length Lis u(x, t) = Σ An cos (7x) e-X²², n=1 assuming that the ends of the bar, at x = 0 and x = L, are kept insulated. Here X = n and c² = K, where K is the thermal conductivity, o is the specific heat and p is the 4 cos (¹). density. Assume the initial temperature profile is f(x) = O Then 3πT u(x, t) = 4 cos (₂) e- e-(²)²t L Then u(x, t) = 3 cos Then s(17₂) e- Then u(x, t) = 4 cos s(172)e-(29²4 L e-()²t u(x, t) = 4 cos (72) e-(49²1

The general solution for the one dimensional heat equation for a thin laterally insulated bar of finite length Lis u(x, t) = Σ An cos (7x) e-X²², n=1 assuming that the ends of the bar, at x = 0 and x = L, are kept insulated. Here X = n and c² = K, where K is the thermal conductivity, o is the specific heat and p is the 4 cos (¹). density. Assume the initial temperature profile is f(x) = O Then 3πT u(x, t) = 4 cos (₂) e- e-(²)²t L Then u(x, t) = 3 cos Then s(17₂) e- Then u(x, t) = 4 cos s(172)e-(29²4 L e-()²t u(x, t) = 4 cos (72) e-(49²1

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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The general solution for the one dimensional heat equation for a thin laterally insulated bar of finite length Lis u(x, t) = A, cos (77) e-Xx²², n=1 assuming that the ends of the bar, at x =0 and x = L, are kept insulated. Here X = n and c² = K, where K is the thermal conductivity, o is the specific heat and p is the density. Assume the initial temperature profile is f(x) = 4 cos(x). O Then u(x, t) = 4 cos Then u(x, t) = 3 cos Then Then s(17₂) e- u(x, t)= 4 cos 3πT L (₂) e- e-(²)²t ³ (172) e-(79₁ L u(x, t) = 4 cos e-(+)²³t (72) e-(49²1
Transcribed Image Text:The general solution for the one dimensional heat equation for a thin laterally insulated bar of finite length Lis u(x, t) = A, cos (77) e-Xx²², n=1 assuming that the ends of the bar, at x =0 and x = L, are kept insulated. Here X = n and c² = K, where K is the thermal conductivity, o is the specific heat and p is the density. Assume the initial temperature profile is f(x) = 4 cos(x). O Then u(x, t) = 4 cos Then u(x, t) = 3 cos Then Then s(17₂) e- u(x, t)= 4 cos 3πT L (₂) e- e-(²)²t ³ (172) e-(79₁ L u(x, t) = 4 cos e-(+)²³t (72) e-(49²1
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