August 28th, 2017, 10:51 AM  #1 
Newbie Joined: Jul 2017 From: Iraq Posts: 18 Thanks: 0  solving heat PDE using FFCT
solving heat PDE using FFCT the problem is solve the following heat problem using FFCT: A metal bar of length L, is at constant temperature of $ U_0 $ , at $t=0$ the end $x=L$ is suddenly given the constant temperature of $U_1$ 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 $k=1$ Equations used: heat eq. $$ \frac {\partial^2 u} {\partial x^2} = \frac 1 k \frac {\partial u} {\partial t} $$ with the following additional equations: my attempt: my attempt goes like this: $$ \frac {\partial^2 u} {\partial x^2} = \frac 1 k \frac {\partial u} {\partial t} $$ $$ \mathcal{F}_{fc} \left[ \frac {\partial u} {\partial t} \right] = \mathcal{F}_{fc} \frac {\partial^2 u} {\partial x^2} $$ $$ \frac {dU} {dt} = {\left( \frac {{n} {\pi}} L \right)}ˆ{2} * F(x,t) + \left( {1} \right)ˆn \frac {\partial{f(L,t)}} {\partial x}  \frac {\partial{f(0,t)}} {\partial x} $$ $$ \frac {dU} {dt} =  \left( \frac {{n} {\pi}} L \right)ˆ(2) * F(x,t) + \left( {1} \right)ˆn \frac {\partial{f(L,t)}} {\partial x} $$ and i dont know how to continue... Last edited by aows61; August 28th, 2017 at 10:55 AM. Reason: correcting some syntaxes 

Tags 
ffct, heat, pde, solving 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
solving heat PDE using FFCT  aows61  Differential Equations  0  August 28th, 2017 09:44 AM 
Solving the heat equation using FFCT (Finite Fourier Cosine Trans)  aows61  Differential Equations  0  August 25th, 2017 11:31 AM 
heat equation  mona123  Differential Equations  0  February 13th, 2016 08:35 AM 
Heat transfer .. Could please help !  rsoy  Physics  2  October 14th, 2013 04:03 AM 