A PARTICULAR SOLUTION OF THE TWO AND THREE DIMENSIONAL TRANSIENT DIFFUSION EQUATIONS - Al-Hemiri, Adel (Iraqi Journal of Chemical and Petroleum Engineering, 2011)
A particular solution of the two and three dimensional unsteady state thermal or mass diffusion equation is obtained by introducing a combination of variables of the form, η = (x+y) / √ct , and η = (x+y+z) / √ct, for two and three dimensional equations respectively. And the corresponding solutions are, θ (t,x,y) = θ0 erfc (x+y)/√8ct and θ( t,x,y,z) =θ0 erfc (x+y+z/√12ct)