Thermodynamically consistent thermal energy equation for an adsorbent/fluid system

We show that thermodynamically inconsistent results are obtained if a thermal energy equation is used that includes the heat of adsorption in modelling heat and mass transfer of adsorption processes as a surface phenomenon. However, if the heat of adsorption is included in the boundary conditions and not in the thermal energy equation, then the results are thermodynamically consistent. For a simple example, we found significant differences in temperature changes and heat flux for low Lewis numbers.