A particular solution of the two and three dimensional transient diffusion equations

Abstract EN

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,×,y)=ᶿ0 erfc (x+y)/√8ct and (t,x,y,z)=ᶿ0 erfc ((x+y+z)/√12ct)