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how can i calculate the outlet pipe temperature knowing the following data:

  • pipe properties
  • insulation properties
  • fluid flow rate
  • inlet fluid temperature
  • ambient temperature
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  • $\begingroup$ Should not explicitly listed a priori effort in questions match the expected elaboration effort in answers ? $\endgroup$ – Poutnik May 9 '19 at 6:50
  • $\begingroup$ You have forgotten temperature dependent fluid properties. But I predict that a general solution does not exist,there are only approximations, applicable for some specific, often idealized or simplified scenarios. Big difference is laminar or turbulent or transient flow mode. $\endgroup$ – Poutnik May 9 '19 at 6:58
  • $\begingroup$ I guess the best approach is to search for empirical formulas used in the domain of industrial hot water providers, e.g in a firm of a book of tabelized values. $\endgroup$ – Poutnik May 9 '19 at 7:00
  • $\begingroup$ Dear @Poutnik, thanks for the answer. Yes, i know also the fluid properties and the flow regime is turbolent. Can you suggest any link? $\endgroup$ – Davide DC May 9 '19 at 7:15
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This is definitely a very do-able calculation. The starting equation is $$(T_{out}-T_{amb})=(T_{in}-T_{amb})\exp{\left(-\frac{U\pi DL}{\dot{M}C_p}\right)}$$where $\dot{M}$ is the mass flow rate and U is the overall heat transfer coefficient. U is related to the heat transfer resistances situated between the fluid and the ambient atmosphere by the equation: $$U=\frac{1}{r_f+r_w+r_i+r_a}$$where $r_f$ is the forced convective resistance on the fluid side of the pipe wall, $r_w$ is the conductive resistance of the pipe wall, $r_i$ is the conductive resistance of the insulation, and $r_a$ is the convective resistance of the outside air.

The two conductive resistances are easy to obtain based on 1D radial conduction through a cylinder. The convective resistance of the outside air is obtainable from correlations of natural convection to cylinders (see Chapter 14 of Transport Phenomena by Bird, Stewart, and Lightfoot).

The forced convective resistance on the fluid side of the boundary is a function of the flow Reynolds number and the fluid Prantdl number, and can be estimated for turbulent flow using Seider-Tate correlation, also presented in Chapter 14 of Bird et al (Fig. 14.3-2).

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