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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=0 , 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 cemparature 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: J; = « U xx = 1.14 I| t Nith boundary conditions as U (0,t) = U (50,t ) = 0 (30, 0 < x < 25 (0, 25 < х < 50 nitial condition : U(x,0)= Find the solution U(x,t) of the given problem.

( 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=0 , 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 cemparature 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: J; = « U xx = 1.14 I| t Nith boundary conditions as U (0,t) = U (50,t ) = 0 (30, 0 < x < 25 (0, 25 < х < 50 nitial condition : U(x,0)= Find the solution U(x,t) of the given problem.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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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=0 , 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 t = x U xx = 1.14 With boundary conditions as U (0,t ) = U(50,t ) = 0 (30, 0 < x < 25 0, 25 < x < 50 Initial condition : U(x,0) = 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=0 , 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 t = x U xx = 1.14 With boundary conditions as U (0,t ) = U(50,t ) = 0 (30, 0 < x < 25 0, 25 < x < 50 Initial condition : U(x,0) = Find the solution U(x,t) of the given problem.
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