NUMERICAL STABILITY OF FICK’S SECOND LAW TO HEAT FLOW

Abstract

In this paper we shall discuss the stability of Fick’s second law to the study of heat flow using Forward Time, Centered Space or FTCS Approximation. We shall derive one dimensional heat equation from the Fick’s law second with the constant of proportionality called the diffusion constant given and which represent the energy density and temperature respectively at the point  meters along a thin rod at time  (in seconds) having known substances namely a constant density  and specific heat . The Fick’s law is a general diffusion equation.

However, diffusion is the transport of a material or chemical by molecular motion from a region of high concentration to a region of low concentration until they are eventually uniformly distributed. We shall replace the diffusion constant  with an exponential  such that  and a constant  

Numerically, we shall use table to illustrate the effect of (a fixed value) on the stability of the heat Fick’s equation with the help of a working Matlab.