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August 25th, 2017, 11:31 AM   #1
Joined: Jul 2017
From: Iraq

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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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