Analytical Solution of Advection-Diffusion Transport Equation using Change-of-Variable and Integral Transform.

We present a formal exact solution of the linear advection-diffusion transport equation with constant coefficients for both transient and steady-state regimes. A classical mathematical substitution transforms the original advection-diffusion equation problem into an exclusively diffusive equation. The new diffusion problem is solved exactly using the Generalized Integral Transform Technique (GITT), resulting in an explicit solution.  The new solution is shown to converge faster than a hybrid analytical-numerical solution previously obtained by applying the GITT directly to the advection-diffusion transport equation.