A mathematical model of coupled momentum and mass transfer including thermal degradation of trans-resveratrol from grape cane powder was developed. The experimental results, which were used for model validation, were based on a solid-liquid extraction study which was previously conducted using a semi-continuous pressurized low-polarity water (PLPW) column extraction system. During extraction, the system is considered to work under isothermal and steady-state conditions regarding heat and momentum transfer. Verification of those assumptions is also obtained by the simulation of related time-dependent physics. The used mathematical models are based on macroscopic porous medium approach with volume averaged physical properties. The resulting equations were solved using Finite Element Method by COMSOL Multiphysics® version 5.3a. The model enables the prediction of the temperature distribution at pre-heating period, and concentration and degradation of trans-resveratrol in the column. The model can also simulate the changes in temperature and ratio of ethanol in the aqueous extraction solvent.