Insulated pipe outlet temperature

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

• pipe properties
• insulation properties
• fluid flow rate
• inlet fluid temperature
• ambient temperature
• Should not explicitly listed a priori effort in questions match the expected elaboration effort in answers ? – Poutnik May 9 '19 at 6:50
• 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. – Poutnik May 9 '19 at 6:58
• 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. – Poutnik May 9 '19 at 7:00
• Dear @Poutnik, thanks for the answer. Yes, i know also the fluid properties and the flow regime is turbolent. Can you suggest any link? – Davide DC May 9 '19 at 7:15

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.