Heat and mass exchange in immobile EPRs

The immobile easily penetrable roughness, EPR, is the heuristic model of a forest or some engineering devices like compact heat exchangers. For such applications, it is necessary to extend the model for including the heat or mass exchange of the EPR with the flow. 

Fluxes from individual obstructions (3.50) are all radiated into a unit volume of the flowing medium (air), so that they need to be multiplied by the obstacle concentration n to estimate the substance income rate, like it was done for forces by (1.6)  

These sources act within the EPR but vanish outside it. This means that discontinuous terms like (1.7) labelled by a star should be used to write the equations uniquely for the internal and external flows  

Note also the difference between the specific frontal area used in (1.8) and the specific full surface area s0 = lim m2/m3 appeared for mass and heat exchange provided 

The further transportation of heat energy and the evaporated substance over the whole flow domain takes place due to the convective motion of the surrounding medium, being thus governed by the equations 

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