A one-dimensional unsteady state mathematical model of coupled heat and mass transfer equations is accomplished to simulate the convective drying of cylindrical quince slices with axis parallel to the hot air flow. The semi-analytical proposed solution method considers fundamentals of the convective drying process and takes internal resistances to temperature and moisture content into account. Green's function method (GFM) is used due to existence of time dependent boundary conditions. In the present study, unlike classic problems, evaporation term initiate a strong coupling between heat and mass transfer equations and therefore in the present study the basic idea of numerical solutions which is repetition and correction, is used to present a novel analytical solution and correct it. In addition the effects of Biot number and relative humidity on drying kinetics are investigated. The agreement between published experimental results and model predictions is remarkable. (C) 2016 Elsevier Ltd. All rights reserved.