Diffusion equation Definition and 120 Threads

help w/ diffusion equation on semi-infinite domain 0<x<infinity Woo! First post! And I'm trying out/learning the latex code which is really neato! Okay, so... please help! I'm trying to solve \frac{\partial^{2}T}{\partial x^{2}} + \frac{1}{x}\frac{\partial T}{\partial x} =...

Homework Statement The Attempt at a Solution I'm really at a loss on this question, which is why i have achieved so little on it so far. I think i more or less understand what a Fourier transform does (transpose amplitude vs time to amplitude vs frequency, ie the Fourier transform...

Hi, I have seen the solution to the diffusion equation written as C=(N/sqrt(4PiDt))exp(-x^2/4Dt). Hoever, as I understand it, this is for an instant input of N material. I want to express the concentration of substance at a point x away from the source for an arbitrary input signal. Is there...

Homework Statement I need help in solving a problem I was assigned from Numerical Methods for Physics, 2nd Ed., by Garcia. We are asked to create a solution, by hand, for the diffusion equation, using the method of images. In particular, we have a 1-dimensional bar, centered at x = 0, of...

the difference between the Heat and Diffusion equation ?! Please: What is the difference between the Heat and Diffusion equation ?! thank you.

Homework Statement Consider a traveling wave u(x,t) =f(x - at) where f is a given function of one variable. (a) If it is a solution of the wave equation, show that the speed must be a = \pm c (unless f is a linear function). (b) If it is a solution of the diffusion equation, find f and show...

i know that idea would seem a bit weird but, let us suppose we have a surface or volume in d- dimension, here d can be any real number (fractional dimension) the question is that we do not know what value 'd' is \frac{\partial \phi}{\partial t} = D\,\Delta \phi D is a diffusion...

Hey all, I'm wondering if someone can help me understand how to apply the boundary conditions to the diffusion equation in one dimension. Diffusion equation is: \frac{\partial u}{\partial t}=D*\frac{(\partial)^{2}u}{\partial x^{2}} The initial condition is: u(x,0)=0 And the boundary...

Ok, I have been given the steady state diffusion equation in 1d spherical polar coordinates as; D.1/(r^2).'partial'd/dr(r^2.'partial'dc/dr)=0 I know that the solution comes in the form c(r) = A+B/r where A and B are some constants. I just don't know how to get from here to there. I...

Homework Statement The solution to the diffusion equation in 1D may be written as follows: n'(x,t) = N/sqrt(4piDt) * exp(-x^2/4DT) where n'(x,t) is the concentration of the particles at position x at time t, N is the total number of particles and D is the diffusion coefficient. a)...

Hi there, I'm looking for an algorithm which describes the numeric solution to solve the diffusion equation (1D or 2D). I've taken a look on some textbook such as Hamilton and Henry ones but I didn't find a simple solution. anybody knows about it? Where can I find what I'm looking for? Thanks.

Homework Statement Solve: \frac{\partial u}{\partial t} = k\frac{\partial^2 u}{\partial x^2}, 0<x<\pi, t>0 with initial condition u(x,0)=f(x)=\left\{\begin{array}{cc} 1,& 0\leq x< \pi/2 \\ 0, &\pi/2 \leq x < \pi \end{array}\right and with non-homogeneous boundary conditions...

The solution to the diffusion equation in 1D may be written as follows: n'(x,t) = N/sqrt(4piDt) * exp(-x^2/4DT) where n'(x,t) is the concentration of the particles at position x at time t, N is the total number of particles and D is the diffusion coefficient. Write down an expression for the...

Homework Statement I have solved the equation for the neutron density as a function of position and time. I need the boundary conditions to change my infinite number of solutions (the varying separation constant) into one value so that my answer for the critical radius does not contain a...

Hi all, I am stuggling with this question ... http://img86.imageshack.us/img86/2662/picture6fb5.png so far i have only tried part (a), but since i can't see how to do that so far... :( ok so what to do... do we first look at an 'associated problem' ? ... something like...

Hello every body I have previously post my question in this topic: Physics Help and Math Help - Physics Forums > Science Education > Homework & Coursework Questions > Other Sciences > Fick and Cottrell Law And after Goku suggestion I post my question here. So my problem deal with the...

hi i have been trying to solve the diffusion equation using separation of variables. i know the answer should turn out something like the normal probability density function but its just turns into a mess when i try it. i am given the following information: \frac{\partial p}{\partial...

Basically the steady-state diffusion equation can be written in a form \nabla^2\phi\,+\,k^2\phi\,=\,S When S = 0, this is just the Helmholtz equation - http://mathworld.wolfram.com/HelmholtzDifferentialEquation.html See also -...

I have managed to create a simple CFD model to integrate in 3D the heat/diffusion equation, namely dT/dt = k d2T/dx2. This works fine, but I would now like to add the effect of 'less dense rising' assuming the gas is operating in air -- I think I'm right in saying that's called buoyancy (I'm...

Hi, I'm not understanding an example in my book. Can someone please shed some light on it? > Derive the equation satisfied by the temperature u\left( {\mathop r\limits^ \to ,t} \right) at time t for a material of uniform conductivity k, specific heat capacity s and density \rho . Express the...