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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 so 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: = C Uxx Ut x = 1.14 With boundary conditions as U(0, t) = U(50,t) = 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° C so 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: = C Uxx Ut x = 1.14 With boundary conditions as U(0, t) = U(50,t) = 0 30, 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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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 so 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: U; = « Uxx x = 1.14 With boundary conditions as U(0, t) = U(50, t) = 0 30, 0<x< 25 Initial condition: U(x,o) = 25 <х < 50 Find the solution U(x,t) of the given problem.
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 so 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: U; = « Uxx x = 1.14 With boundary conditions as U(0, t) = U(50, t) = 0 30, 0<x< 25 Initial condition: U(x,o) = 25 <х < 50 Find the solution U(x,t) of the given problem.
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