Project 3: Heating of Water in an L-Shaped Pipe

Internal forced convection and plug-flow energy balance

1 Problem Statement

Water flows through an L-shaped pipe. The outer wall temperature is maintained at (100^). The water enters colder and is heated along the pipe.

2 Plug-Flow Model

[ c_p = G’(T_w-T_b) ]

Analytical solution:

[ T_b(s)=T_w-(T_w-T_{in}) (-) ]

3 Julia Example

using Plots

Twall = 100.0
Tin = 20.0
mdot = 0.02
cp = 4180.0
Gprime = 16.0
Ltot = 1.08

s = range(0, Ltot, length=200)

T = Twall .- (Twall - Tin).*exp.(-Gprime .* s ./ (mdot*cp))

plot(s, T,
     xlabel="Distance along pipe [m]",
     ylabel="Bulk temperature [°C]",
     label="Water temperature",
     linewidth=2)

4 Student Tasks

  1. Compute (Re), (Nu), and (h_i).
  2. Compute (G’).
  3. Predict outlet temperature.
  4. Compare numerical and analytical solutions.
  5. Build an ML surrogate for (T_{out}).
  6. Optional: implement a PINN for (T(s)).