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 (R) 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.