
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 28th, 2017, 09:44 AM  #1 
Newbie Joined: Jul 2017 From: Iraq Posts: 18 Thanks: 0  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 10:04 AM. 

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

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
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 
How much heat energy?  girlbadatmath  Chemistry  2  November 12th, 2014 11:44 AM 
Heat Equation  WWRtelescoping  Differential Equations  0  September 7th, 2014 03:23 PM 
Heat of Fusion  aaronmath  Physics  0  February 9th, 2012 05:16 PM 