My Math Forum  

Go Back   My Math Forum > College Math Forum > Differential Equations

Differential Equations Ordinary and Partial Differential Equations Math Forum

LinkBack Thread Tools Display Modes
August 28th, 2017, 09:44 AM   #1
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.
aows61 is offline  

  My Math Forum > College Math Forum > Differential Equations

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 aaron-math Physics 0 February 9th, 2012 05:16 PM

Copyright © 2018 My Math Forum. All rights reserved.