I am designing an underfloor heating system and I would like some clarification concerning the flow rate or velocity of water in tubes for the underfloor heating system.
Flow rate can be determined by an energy balance: heat loss of water = heat convected to air in heated rooms.
The velocity is limited by the possible noise generation due to turbulences ( if it is a space where human beings work or live). since water has a high convection coefficient low velocity is not a problem.
If I suppose that the heat load (Q) is known and is constant then a preliminary estimation of the water flow rate can be made by simple energy balance i.e. m_dot=Q/(cp*dT). But in actual system the flow rate may be different from the estimated value(generally higher). For that you may need to evaluate the conduction and convection resistances of the system (if system geometry is known). For air side average Nusselt's number calculation assume flow over a flat plate (the floor). The wall resistance calculation is straight forward. Now with the estimated water flow rate calculate water side average heat transfer coefficient using any suitable model of flow inside horizontal tubes and hence find UA (floor area is known). let Q1= UAdT
now compare Q with Q1 and iterate for Q1 with different water flow rates till you get Q=Q1. This may give you the final water flow rate required.