A PARTICULAR SOLUTION OF THE TWO AND THREE DIMENSIONAL TRANSIENT DIFFUSION EQUATIONS

Abstract

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 equationsrespectively. 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)