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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.

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Usually the properties are taken at mean temperature (and pressure) between in- and outlet, often by iteration. If your problem is that sensitive to changes in thermal properties I would calculate the problem sectionwise to account for the non-linearity.

When calculating Nusselt Numbers, often the wall temperature needs to be taken into account as well. Wall temperatures are found by iteration as the heat transfer coefficients are inversely proportional to the T-gradients.

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  • $\begingroup$ 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? $\endgroup$
    – Greg Harrington
    Commented Mar 31, 2014 at 21:51
  • $\begingroup$ A correction as you have it in mind would depend on the actual thermal process and is not always easy to find. So if you devide your tube into sufficiently small sections and calculate them separately you get it right without complicating your model. $\endgroup$
    – Mirc Breitschuh
    Commented Mar 31, 2014 at 22:17
  • $\begingroup$ Usually, when the temperature does not change too much, the Nusselt number is estimated by taking the average properties between inlet and outlet. A correction factor is then applied as you describe to compensate for the temperature gradient at the wall. See for example the Sieder-Tate correlation in en.wikipedia.org/wiki/Nusselt_number $\endgroup$
    – Whelp
    Commented Apr 1, 2014 at 10:07
  • $\begingroup$ @Whelp I would agree on that. But the problem seems to be that temperatures change drastically along the flow path. So just taking mean values between in- and outlet could turn out to be quite inaccurate, depending on the thermal process (which we don't know). This is true independently of the actual correlation (whichever it is) used to obtain Nu. $\endgroup$
    – Mirc Breitschuh
    Commented Apr 1, 2014 at 10:40
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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.

Beforehand check that a linear dependence is accurate enough for the fluid and temperature range you consider.

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