( Zero temparature ends ) Suppose that a copper rod of lenght 50 cm was placed into a reservoir with hot water at 50° Cso that half of it is in the air at 20°C. At t=Q, the rod is taken out and its ends are kept at constant ambient temparature of 20° c. Let us denote the difference between the rod's temparature and the ambient temparature by U(x,t) , where x is the distance from the left end of the rod, x=0. The U(x,t) is a solution of the initial boundary value problem: ww = « Uxx x = 1.14 With boundary conditions as U(0, t) = U(50, t) = 0 Initial condition : U(x,0) = 30, 0
( Zero temparature ends ) Suppose that a copper rod of lenght 50 cm was placed into a reservoir with hot water at 50° Cso that half of it is in the air at 20°C. At t=Q, the rod is taken out and its ends are kept at constant ambient temparature of 20° c. Let us denote the difference between the rod's temparature and the ambient temparature by U(x,t) , where x is the distance from the left end of the rod, x=0. The U(x,t) is a solution of the initial boundary value problem: ww = « Uxx x = 1.14 With boundary conditions as U(0, t) = U(50, t) = 0 Initial condition : U(x,0) = 30, 0
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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![( Zero temparature ends ) Suppose that a copper rod of lenght 50 cm was placed into a reservoir with
hot water at 50° C se that half of it is in the air at 20° C. At t=Qthe rod is taken out and its ends are
kept at constant ambient temearature of 20° c. Let us denote the difference between the rots
temparature and the ambient temearature by Uix,t), where x is the distance from the left end of the
rod, x=0. The Ufx,t) is a solution of the initial boundary value problem:
U, = x Ux
x = 1.14
With boundary conditions as U(0, t) = U(50, t) = 0
Initial condition : U(x.o) = { 30, 0< x << 25
lon25 x < 50
Find the solution Uixt) of the given problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd18d0348-cc6f-43f6-b4e3-89536bbcb794%2F79bbceba-b096-4231-ad4e-88dff028b060%2Fway3dqh_processed.png&w=3840&q=75)
Transcribed Image Text:( Zero temparature ends ) Suppose that a copper rod of lenght 50 cm was placed into a reservoir with
hot water at 50° C se that half of it is in the air at 20° C. At t=Qthe rod is taken out and its ends are
kept at constant ambient temearature of 20° c. Let us denote the difference between the rots
temparature and the ambient temearature by Uix,t), where x is the distance from the left end of the
rod, x=0. The Ufx,t) is a solution of the initial boundary value problem:
U, = x Ux
x = 1.14
With boundary conditions as U(0, t) = U(50, t) = 0
Initial condition : U(x.o) = { 30, 0< x << 25
lon25 x < 50
Find the solution Uixt) of the given problem.
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