Brinkman boundary stress condition at inlet and outlet of porous pipe

I am trying to simulate flow through porous pipe, for which i have selected Brinkman equation. This porous pipe is nothing but a honycomb which has small tubes with hydraulic diameter of ~1.5 mm & it is connected between two pipes. velocity of air at the inlet of main pipe is 25 m/s and temperature is 500 °C.

The problem I am facing is I want to give boundary condition for this porous pipe for which I believe that boundary stress at inlet and outlet is suitable.

so can you please help me how to derive the formula for general stresses for boundary stress condition?