solving diffusion equation
- To: mathgroup at smc.vnet.net
- Subject: [mg42446] solving diffusion equation
- From: "kl" <klimm1290 at yahoo.com>
- Date: Tue, 8 Jul 2003 04:37:26 -0400 (EDT)
- Organization: Purdue University
- Sender: owner-wri-mathgroup at wolfram.com
Hello all hardworking mathematicians! I am trying to solve the diffusion equation given by Fick's law using mathematica. The equation is as follows f = (TAU)*(PHI)*(D12)*(RHOg)*(grad OMEGA) f: mass flux (kg/m2-sec) TAU: Tortuosity - a constant PHI: Porosity - a constant D12: Binary Diffusion Coefficient (m2/sec) RHOg: Density (kg/m3) OMEGA: mass fraction grad: is the gradient operator. As can be seen from the equation, TAU, PHI are physical constants D12: although as time goes and as the gas spreads, this value changes, you can assume it to be constant to start with. OMEGA is the main parameter and at a particular point, it will change as time goes by. Thus this is the single differential equation that governs the diffusion of a gas in porous medium. Can I solve this equation using mathematica? If I release a given amount of gas (say Helium) at a given point in a cylindrical porous structure, can I solve this unsteady problem and find OMEGA values at different points in the cylinder at different time instances? Any ideas, suggestion, directions will be highly appreaciated. If you know anything (any resource) about the kind of problem ( or similar problem )I am trying to solve, please let me know. Regards, KL