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Ex. The temperature u(x,t) in a strip of metal of width L is governed by the heat equation au =u, for 00. Use separation of variables method to find the unsteady state temperature distribution in the strip given that the initial condition is u(x,0) =x and the boundary conditions u (0,t)=u (L,t)=0 for t>0. The condition u (0,t) = 0 expresses mathematically the constraint that no heat flows through the left boundary (insulated end condition).

Ex. The temperature u(x,t) in a strip of metal of width L is governed by the heat equation au =u, for 00. Use separation of variables method to find the unsteady state temperature distribution in the strip given that the initial condition is u(x,0) =x and the boundary conditions u (0,t)=u (L,t)=0 for t>0. The condition u (0,t) = 0 expresses mathematically the constraint that no heat flows through the left boundary (insulated end condition).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
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Ex. The temperature u(x,t) in a strip of metal of width L is governed by the heat equation au =u, for 0<x<L and t>0. Use separation of variables method to find the unsteady state temperature distribution in the strip given that the initial condition is u(x,0) =x and the boundary conditions u (0,t)=u (L,t)=0 for t>0. The condition u, (0,t) = 0 expresses mathematically the constraint that no heat flows through the left boundary (insulated end condition). -H.W. Problems P.327 "wylie" Q.5,7,8
Transcribed Image Text:Ex. The temperature u(x,t) in a strip of metal of width L is governed by the heat equation au =u, for 0<x<L and t>0. Use separation of variables method to find the unsteady state temperature distribution in the strip given that the initial condition is u(x,0) =x and the boundary conditions u (0,t)=u (L,t)=0 for t>0. The condition u, (0,t) = 0 expresses mathematically the constraint that no heat flows through the left boundary (insulated end condition). -H.W. Problems P.327 "wylie" Q.5,7,8
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