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).

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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