5. Find the solution of the heat conduction problem for each initial condition given: Suxxx =...
Question #5 all parts thanks 5. Find the solution of the heat conduction problem for each initial condition given: 0<x <6, t> 0. (a) ux,0)-x)-4sin(x)-3sin(2x) +7sin(570:). (b) ux, 0)-x)-9t (c) In each of cases (a) and (b), find the limit of u(3,1) as t approaches oo. Are they different? Did you 45 expect them to be different?
7. (a) Find the solution of the heat conduction problem: Suxx = ut, 0<x< 5, u(0, 1) = 20, tu(5, 1) = 80, 1>0 u(x,0) = f(x) = 12x + 20 + 13sin(tor) - 5sin(3 tex). (b) Find lim u(2, t). (c) If the initial condition is, instead, u(x,0) = 10x – 20 + 13sin( Tox) - 5sin(3 7ox), will the limit in (b) be different? What would the difference be?
Find the solution of the heat conduction problem and provide a detailed graph showing the initial, intermediate and final temperature distribution in the bar. 3. ut uxx ux(0, t) 0 ux(1,t) 0 u(x, 0) 1-x Find the solution of the heat conduction problem and provide a detailed graph showing the initial, intermediate and final temperature distribution in the bar. 4. ut = 2uxx u(0,t) 0 u(10,t) 10 u(x, 0) = 10 Find the solution of the heat conduction problem and...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where ?(?,?) represents the temperature. 9??? = ?? ; 0 < ? < 6; ? > 0; B. C. : ?? (0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?, 0) = 12 + 5??? ( ? 6 ?) − 4???(2??); 0 < ? < 6 (a) When ? = 0, what would be the temperature at ? = 3? (Use...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0 < x < 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t>0; I. C.: u(x,0) = 12 + 5cos (6x) – 4cos(21x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.:u,(0,t) = 0; ux(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos ( x) – 4cos(27x); 0<x< 6 (a) Whent 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or mixed...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut 0<x< 6; t> 0; B.C.: 4x(0,t) = 0; uz (6,t) = 0; t> 0; 1.C. : u(x,0) = 12 + scos (x) – 4cos(2x); 0 < x < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Ut; 0<x< 6; t> 0; B.C. : Ux(0,t) = 0; Ux(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos (x) – 4cos(21x); 0 < X < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos (x) – 4cos(27x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or...
please I need solution as soon as possible Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = uti 0<x< 6; t>0; B.C.: uz (0.t) = 0; ux(6,t) = 0; t> 0; 1. C. :U(x,0) = 12 + 5cos (6x) – 4cos(2x); 0<x<6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (6) Determine whether the boundary...