The transient conservation equations for heat and mass transfer in a drying solid were solved using a finite element technique. The material being dried is a discretely non-homogeneous material. It is subjected to a convection boundary condition. The shrinkage of the material surrounding a non-shrinking, low loss factor material is treated numerically by continuously redefining the computational domain of the problem. Results of the numerical prediction of drying rates and temperature distribution within the drying solid were compared with experimental results and found to be in good agreement. Local convection heat transfer boundary conditions were prescribed with the use of a computational fluid dynamic code. Cylindrical pieces of carrot with a coaxial cylindrical insert of Teflon were used as the non-homogeneous models for the experimental and computational study.