


Now we like to
know T_{f,} T_{f, air, }T_{c} and temperature
gradient in term of known quantity.


Since we have
three unknowns and we like to derive dimensionless temperature, we need to
have two energy balance equations.




where h_{r}
and h_{f} are the heat transfer coefficients for radiation (between
ceiling and floor) and convection (between air and floor surface). And is
density of the supply air and V is volumetric flow rate and C_{p} is
the specific heat. Note we linearize
radiation heat transfer, otherwise it is fourth power.




Based on the
equations (1) and (2), we could drive dimensionless temperature,


