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August 25th, 2017, 11:31 AM  #1 
Newbie Joined: Jul 2017 From: Iraq Posts: 18 Thanks: 0  Solving the heat equation using FFCT (Finite Fourier Cosine Trans)
1. The problem statement: Solve the following heat Eq. using FFCT: A metal bar of length L is at constant temperature of Uo, at t=0 the end x=L is suddenly given the constant temperature U1, and the end x=0 is insulated. Assuming that the surface of the bar is insulated, find the temperature at any point x of the bar at any time t>0, assume thermal diffusivity coefficient (k) =1 2. Relevant equations heat equation: dˆ2U/dxˆ2=(1/k) dU/dt FFCT equation of derivative: F (dˆ2U/dxˆ2)= ( n*pi/b)ˆ2 *F(n,t)+(1)ˆn * (ux(b,t)ux(0,t) 3. The attempt at a solution my attempt has many mistake at the start of transforming. 

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cosine, equation, ffct, finite, fourier, heat, solving, trans 
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