# why m=1, and why n=pi/2, 3pi/2, ............ The problem of unsteady heat conduction in a metal...

why m=1, and why n=pi/2, 3pi/2, ............   The problem of unsteady heat conduction in a metal plate of length 1 meter is described by the equation: where u is the temperature, with initial/boundary conditions: a(2,0) = 1 (0,t) = 1 Ou #### Earn Coin

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• ### Problem 3 Solve the unsteady heat conduction problem: subject to the boundary conditions: u(0,t)0, (1,t)1; and... Problem 3 Solve the unsteady heat conduction problem: subject to the boundary conditions: u(0,t)0, (1,t)1; and the initial condition ua, 0) and sketch the form of the complete solution.

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• ### 3. In class we discussed the heat conduction problem with the boundary conditions a(0, t) 0, t4(1... 3. In class we discussed the heat conduction problem with the boundary conditions a(0, t) 0, t4(1,t)-0, t > 0 and the initial condition u(r,0) f(a) We found the solution to be of the form where (2n-1)n 1,2,3,. TL 20 Now consider the heat conduction problem with the boundary conditions u(0, t) 1,u(T, t)0, t>0 and the initial condition ur,0) 0. Find u(r,t). Hint: First you must find the steady state. 3. In class we discussed the heat conduction problem...

• ### Consider a 2 m long metal rod. The temperature u(z,t) at a point along the rod at any time t is found by solving the heat equation k where k is the material property. The left end of the rod ( 0) is... Consider a 2 m long metal rod. The temperature u(z,t) at a point along the rod at any time t is found by solving the heat equation k where k is the material property. The left end of the rod ( 0) is maintained at 20°C and the right end is suddenly dipped into snow (0°C). The initial temperature distribution in the rod is given by u(x,0)- (i) Use the substitution u(z,t) ta,t)+20-10z to reduce the above problem to a...

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• ### (a) Consider the one-dimensional heat equation for the temperature u(x, t), Ou,02u where c is the... (a) Consider the one-dimensional heat equation for the temperature u(x, t), Ou,02u where c is the diffusivity (i) Show that a solution of the form u(x,t)-F )G(t) satisfies the heat equation, provided that 护F and where p is a real constant (ii) Show that u(x,t) has a solution of the form (,t)A cos(pr)+ Bsin(p)le -P2e2 where A and B are constants (b) Consider heat flow in a metal rod of length L = π. The ends of the rod, at...

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• ### Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where ?(?,?)... 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...

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• ### Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,... 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.: 4x(0,t) = 0; uz (6,t) = 0; t> 0; 1. C.: u(x,0) = 12 + 5cos (6x) – 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...