The variables and parameters used in this example are as follows: C_A = concentration, J_A = diffusion flux, v = velocity, R_A = source term (mol m⁻³ s⁻¹).

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accumulation: in (diffusion): ACAAX AYAZ; x-direction JA,xlx Ay Az At, y-direction JA, yly Ax Az At, z-direction JA,zlz AX AyAt; x-direction (vx CA)|x Ay Az At, y-direction (₂CA)ly Ax Az At, z-direction (₂CA)z Ax Ayat; Out (diffusion): x-direction JA,xlx+AX AYAZAt, y-direction JA.yly+Ay AX AZ At, z-direction JA,zlz+Az AX AyAt; x-direction (vx CA)x+Ax Ay Az At, y-direction (UCA)ly+AyAX Az At, z-direction (₂CA)|z+az AX AyAt; RAAX AYAZAt. In(flow): Out (flow): Production: Using the balance equation and taking the limit as Ax, Ay, Az, At → 0 yields a(vxCA) a(vyCA) a (vzCA) əJA.X əJA.y AJA.z + RA. (3.1) ax az ay az əx Əy Finally, using Fick's law, JA.X aCA at = - == -DAB (@CA/Ox), we obtain