I am always confused about which temperature to evaluate fluid properties at. Let's say I have a helical pipe and I know the inlet temperature, outlet temperature, and surface temperature and the inlet Reynold's number. I must determine the length of the pipe needed to satisfy the outlet temperature which means I must know the mass flow rate. I can do this by determining the inlet density and viscosity.
When I use the inlet temperature for these properties, the length is 1.046 m When I use the average between the inlet and the surface, the length is 0.3994 m. When I use the average between the inlet and the outlet, the length is 0.5768 m.
As you can see, the temperature I use drastically changes the pipe length.
Also, I am always confused as to what temperature to evaluate the properties at for the Nusselt number as well.