β Scribed by E. Ruckenstein
No coin nor oath required. For personal study only.
Methods are proposed and illustrated for solving time dependent convective diffusion equations having the form ~+l((~,l)dC_aUyac=~?$ ax ax ay They consist in two types of contraction of Eq. ( 1). Introducing a variable X = X(x, t), satisfying the equation Eq. ( 1) is contracted to Introducing a variable T = 7'( t, x), satisfying the equation $+u(x.r)g= 0, Eq. ( 1) is contracted to Equations ( 9) and ( 36) are solved by means of similarity transformations. The solution of Eq. ( 9) is not able to satisfy the boundary condition for x = 0, and that of Eq. ( 36) the one for t = 0. Both solutions (each of them being valid in a certain range) provide however a complete solution satisfying all the boundary and initial conditions. A number of cases are presented for illustration.
π SIMILAR VOLUMES
A statistical theory for mass transfer near fluid-Γluid and solid-Γluid planar intedaces is developed using the method of projection operators applied to the convective-diffusion equation. A first order smoothing approximation gives a closed integro-differential equation for the mean concentration;