Analytical Solution Sample Clauses

Analytical Solution. Central Limit Approximating Ap- proach Taking the Ising Model, we’ll try to draw some conclusions about the relations be- tween variables P∞, P0, J and Nr.

Analytical Solution. ‌ Molecular diffusion in a two-component variable density mixture can be described using Xxxx’x law of diffusion (Bird et al., 1960): J = −cD∇xhe where J is the molar flux, c is the molar concentration, D is the molecular diffusivity coefficient and xhe is the helium molar fraction. The molar concentration and molecular diffusivity coefficient can be assumed to be constant such that for a one-dimensional problem Equation (2.12) leads to the unsteady, one-dimensional diffusion equation: ∂xhe ∂t = ∂2xhe D ∂y2 (2.13) where t is time and y is the vertical coordinate. Equation (2.13) can be solved using the method of separation of variables to obtain (Crank, 1975):  h 2 ∞  nπh   n2π 2   nπy  xhe = xhe,0  l + π ∑ sin l  exp−