# Which temperature to evaluate fluid properties in pipe?

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.

• I figured I could use the inlet temperature to find the inlet density and viscosity which would allow me to find the mass flow rate which I know is constant. I would then use the average temperature between inlet and outlet to find the nusselt number. I could then account for property variation from temperature change using $$Nu = Nu_{m}(\frac{\mu_{m}}{\mu_{s}})^{n}$$ Does this sound like a reasonable approach? Or do you think I should evaluate the inlet density at the average of the inlet and the surface temp? Commented Mar 31, 2014 at 21:51
Changes are huge, I would recommend to re-derive the pipe flow rate with a (linear) temperature dependent formula for viscosity and density. You'll get $Q(T)$, from this can get the heat flux and thus will have a nonlinear differential equation for $T(x)$, which you can integrate numerically. Then find the intercept of $T(x)$ with desired outlet temperature.