What is Heat loss from pipes?
The heat that escapes through the pipe wall and insulation while a fluid hotter than its surroundings flows along the pipe. The fluid cools by that much.
On long pipes it decides whether the fluid still arrives hot enough and how much insulation is needed; cooling too far can also cause condensation or deposits.
Tea stays hot in a vacuum flask because the path for heat to escape has a high thermal resistance; pipe insulation does the same job.
Choose the pipe block's heat transfer: adiabatic, automatic, a given heat loss, or a given outlet temperature. Automatic is either a simple model with an overall coefficient U, or a detailed one that adds inside convection, wall, insulation, and outside convection and radiation. With a given outlet temperature, the required heat transfer is solved for (it cannot be given together with a heat loss).
In the simple model, each segment loses:
\delta\dot{Q} = U\,\pi D_o\,\delta x\,(T - T_\infty)
The detailed model adds thermal resistances per unit length in series and iterates the outer surface temperature:
R = \frac{1}{h_i \pi D_i} + \frac{\ln(D_o/D_i)}{2\pi k_w} + \frac{\ln(D_s/D_o)}{2\pi k_{ins}}
Inside: Gnielinski (Nu = 3.66 when laminar). Outside: Churchill–Chu for still air (natural convection), Churchill–Bernstein with wind (forced convection), and radiation \varepsilon\sigma(T_s^4 - T_\infty^4). Properties are updated segment by segment with temperature and pressure.
Every calculation checks the heat balance: heat in or out equals the change in enthalpy, kinetic and potential energy.