Design study: finned tubes or a packed bed?

PyTES models share their outputs, parameters, experiments and energy reference across families (DESIGN D4), so different designs compare like for like. This notebook uses that to answer a practical question:

A heat battery for domestic hot water should store about 2.5 kWh between 10 °C and 70 °C and deliver 3 kW until its outlet falls below 40 °C. Should it be a finned-tube unit or a packed bed of PCM capsules?

The point is the workflow, not a verdict: with other materials, sizes or heat transfer coefficients the answer changes.

import pytes
from pytes import plotting
from pytes.experiments import Experiment, run_experiment
from pytes.experiments import step as s

T_cold, T_hot = 273.15 + 10, 273.15 + 70

Same PCM, same storable energy

The finned-tube unit is the default sharp-front model, with one tube. The packed bed takes the same PCM, fluid and temperatures from it (parameters are layered by prefix, DESIGN D1; see parameter layers), and its cross-section is sized with energy_between so that it stores the same energy between 10 °C and 70 °C.

finned = pytes.SharpFrontModel()
finned_values = finned.default_parameter_values
capacity = pytes.energy_between(finned, T_cold, T_hot, finned_values)

bed = pytes.PackedBedModel()
bed_values = bed.default_parameter_values
shared = (
    "Reference temperature [K]",
    "Initial temperature [K]",
    "Inlet temperature [K]",
)
for name, value in finned_values.items():
    if name.startswith(("PCM ", "Heat transfer fluid ")) or name in shared:
        bed_values[name] = value
bed_values["Bed cross-sectional area [m2]"] = 1
per_area = pytes.energy_between(bed, T_cold, T_hot, bed_values)
bed_values["Bed cross-sectional area [m2]"] = capacity / per_area

print(f"finned tubes: {capacity / 3.6e6:.2f} kWh")
print(
    f"packed bed: {pytes.energy_between(bed, T_cold, T_hot, bed_values) / 3.6e6:.2f} kWh, "
    f"cross-section {capacity / per_area:.3f} m2"
)

finned tubes: 2.45 kWh
packed bed: 2.45 kWh, cross-section 0.047 m2

The same test for both

Both start full (uniform at 70 °C) and deliver 3 kW with water at 10 °C, the flow adjusted to hold the power (see experiments), until the outlet falls below 40 °C.

test = Experiment(
    [
        s.Power(
            3e3,
            inlet_temperature=T_cold,
            termination=[
                s.outlet_temperature_below(273.15 + 40),
                s.mass_flow_rate_above(1.0),
            ],
            period=10,
        )
    ]
)
results = {}
for name, model, values in [
    ("finned tubes", finned, finned_values),
    ("packed bed", bed, bed_values),
]:
    results[name] = run_experiment(model, test, parameter_values=values)
    delivered = results[name]["Discharged energy [J]"].entries[-1]
    minutes = results[name]["Time [min]"].entries[-1]
    print(
        f"{name}: 3 kW for {minutes:.1f} min, delivering {delivered / 3.6e6:.2f} kWh "
        f"({delivered / capacity:.0%} of what it stores)"
    )

fig, axes = plotting.plot_summary(list(results.values()), labels=list(results))

finned tubes: 3 kW for 34.5 min, delivering 1.72 kWh (70% of what it stores)

packed bed: 3 kW for 25.5 min, delivering 1.28 kWh (52% of what it stores)

Both store the same energy, but the finned unit delivers about 70 % of it before the outlet cools, and the bed only about half: heat leaves its large paraffin capsules (55 mm across) slowly, through a low film coefficient and a poorly conducting PCM, so the outlet cools long before the capsules are spent.

What would make the bed competitive?

Smaller capsules at the same porosity store the same energy but expose more surface and conduct over a shorter distance.

for radius in (27.5e-3, 15e-3, 7.5e-3):
    values = bed_values.copy()
    values["Capsule radius [m]"] = radius
    solution = run_experiment(bed, test, parameter_values=values)
    delivered = solution["Discharged energy [J]"].entries[-1]
    print(
        f"capsules of {2e3 * radius:4.0f} mm: 3 kW for "
        f"{solution['Time [min]'].entries[-1]:5.1f} min, {delivered / capacity:.0%} delivered"
    )

capsules of   55 mm: 3 kW for  25.5 min, 52% delivered

capsules of   30 mm: 3 kW for  38.7 min, 79% delivered

capsules of   15 mm: 3 kW for  45.0 min, 92% delivered

The same few lines answer the next question too: a different PCM, a higher film coefficient, more tubes. Every family exposes the same outputs and runs the same experiments, so a comparison is a loop over models and parameter values.