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pm272
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Hi. There is a problem that I have been working on and I seem to be getting somewhat unrealistic results. Can anyone critique my modeling method?
Problem: Heated air enters a duct of length L at temp T_h. The outside of the thin walled duct will have convection and radiation both being important. I am assuming duct wall thickness is infinitely conductive. Find the exiting air temp.
My logic is as follows: Model this in "n" thin slices, dx, along the duct. Where n = L/dx. For the first slice simply use T_entering = T_h and set up two energy balances: First at the air: m_dot*c*(T_ent-T_exit) = h_in*A_in*(T_fluid-T_wall) and second at the wall: h_in*A_in*(T_fluid-T_wall) + q_solar*A_out = h_out*A_out*(T_wall-T_amb) + sigma*epsilon*(T_wall^4-T_amb^4).
T_fluid = (T_ent + T_exit)/2
q_solar is only applicable for outdoor conditions. I have assumed T_amb = T_surr for thermal radiation.
With these equations I should be able to begin at n = 1 by guessing a T_exit, then solving for T_wall. Then using the sum of the two energy balance equations above as follows, just for simplicity: m_dot*c*(T_ent-T_exit) + q_solar*A_out = h_out*A_out*(T_wall-T_amb) + sigma*epsilon*(T_wall^4-T_amb^4).
and rearranging to:
m_dot*c*(T_ent-T_exit) + q_solar*A_out - h_out*A_out*(T_wall-T_amb) - sigma*epsilon*(T_wall^4-T_amb^4) = 0
finding the residual: r = m_dot*c*(T_ent-T_exit) + q_solar*A_out - h_out*A_out*(T_wall-T_amb) - sigma*epsilon*(T_wall^4-T_amb^4)
Then guessing a new T_exit and repeat again to get a new r. Use the T_exit value that gives r closest to 0.
Then , n = n + 1 and the new T_ent = the previous T_exit.
When I set all this up in a script, my result seems to indicate that the fluid temp drops extreme amounts in the first meter (When L = 200m for instance and entering temp of 600 K). I have compared this to a quick and dirty autodesk CFD model that leads me to believe that my script does indeed appear unrealistic. On a side note, the autodesk CFD doesn't allow me to include a solar heat flux value in addition to the convection and thermal radiation - which is a bit limiting.
Does this set-up appear complete? Am I omitting anything here?
Thank you for your time.
-D
Problem: Heated air enters a duct of length L at temp T_h. The outside of the thin walled duct will have convection and radiation both being important. I am assuming duct wall thickness is infinitely conductive. Find the exiting air temp.
My logic is as follows: Model this in "n" thin slices, dx, along the duct. Where n = L/dx. For the first slice simply use T_entering = T_h and set up two energy balances: First at the air: m_dot*c*(T_ent-T_exit) = h_in*A_in*(T_fluid-T_wall) and second at the wall: h_in*A_in*(T_fluid-T_wall) + q_solar*A_out = h_out*A_out*(T_wall-T_amb) + sigma*epsilon*(T_wall^4-T_amb^4).
T_fluid = (T_ent + T_exit)/2
q_solar is only applicable for outdoor conditions. I have assumed T_amb = T_surr for thermal radiation.
With these equations I should be able to begin at n = 1 by guessing a T_exit, then solving for T_wall. Then using the sum of the two energy balance equations above as follows, just for simplicity: m_dot*c*(T_ent-T_exit) + q_solar*A_out = h_out*A_out*(T_wall-T_amb) + sigma*epsilon*(T_wall^4-T_amb^4).
and rearranging to:
m_dot*c*(T_ent-T_exit) + q_solar*A_out - h_out*A_out*(T_wall-T_amb) - sigma*epsilon*(T_wall^4-T_amb^4) = 0
finding the residual: r = m_dot*c*(T_ent-T_exit) + q_solar*A_out - h_out*A_out*(T_wall-T_amb) - sigma*epsilon*(T_wall^4-T_amb^4)
Then guessing a new T_exit and repeat again to get a new r. Use the T_exit value that gives r closest to 0.
Then , n = n + 1 and the new T_ent = the previous T_exit.
When I set all this up in a script, my result seems to indicate that the fluid temp drops extreme amounts in the first meter (When L = 200m for instance and entering temp of 600 K). I have compared this to a quick and dirty autodesk CFD model that leads me to believe that my script does indeed appear unrealistic. On a side note, the autodesk CFD doesn't allow me to include a solar heat flux value in addition to the convection and thermal radiation - which is a bit limiting.
Does this set-up appear complete? Am I omitting anything here?
Thank you for your time.
-D