Approximate analytical solution for transient heat and mass transfer across an irregular interface

Motivated by practical applications in heat conduction and contaminant transport, we consider mass diffusion across a perturbed interface separating two finite regions of distinct diffusivity. Under the assumption continuity solution diffusive flux at interface, use perturbation theory to develop an asymptotic expansion valid for small perturbations. Each term satisfies initial-boundary value problem on unperturbed domain subject conditions depending previously determined terms expansion. Demonstration is carried out specific, practically-relevant set initial boundary with semi-analytical solutions problems developed using standard Laplace transform eigenfunction techniques. Results several choices confirm good agreement numerical solution.