r"""
Dittus and Boelter: turbulent pipe convection (1930)
====================================================

At Berkeley in 1930 Frank Dittus and Llewellyn Boelter correlated tests on
automobile radiator tubes with a power law in the Reynolds and Prandtl
numbers. In McAdams's rounded form,
:math:`Nu = 0.023\,Re^{0.8}Pr^{n}` with :math:`n = 0.4` for heating and
0.3 for cooling (:func:`~engineeringkit.heat_transfer.dittus_boelter_nusselt`),
it became the most quoted equation in convection. This example sizes the
coefficient for water in a tube, shows that the Colburn analogy between
friction and heat transfer reproduces the 0.023, and measures the scatter
against Gnielinski's modern correlation.
"""

# %%
import matplotlib.pyplot as plt
import numpy as np

from engineeringkit.heat_transfer import dittus_boelter_nusselt

# %%
# Water in a radiator tube
# ------------------------
#
# Water at about 300 K (:math:`\nu = 8.57\times10^{-7}` m²/s,
# :math:`k = 0.613` W/(m K), :math:`Pr = 5.83`) flows at 1 m/s in a 20 mm
# tube.

V, D, nu, k, Pr = 1.0, 0.02, 8.57e-7, 0.613, 5.83
Re = V * D / nu
h_heat = dittus_boelter_nusselt(Re, Pr) * k / D
h_cool = dittus_boelter_nusselt(Re, Pr, heating=False) * k / D
print(f"Re = {Re:.0f}: h = {h_heat:.0f} W/(m² K) heating, {h_cool:.0f} W/(m² K) cooling")

# %%
# The Colburn analogy
# -------------------
#
# Colburn (1933) argued that momentum and heat diffuse alike in turbulent
# flow, :math:`St\,Pr^{2/3} = f/8`. With the smooth-pipe friction factor
# :math:`f = 0.184\,Re^{-0.2}` this gives
# :math:`Nu = (f/8)\,Re\,Pr^{1/3} = 0.023\,Re^{0.8}Pr^{1/3}`, the
# Dittus-Boelter form with the exponent 1/3; at :math:`Pr = 1` the two are
# identical.

Re_range = np.geomspace(1e4, 1e6, 60)
f = 0.184 * Re_range**-0.2
colburn = f / 8 * Re_range
assert np.allclose(colburn, dittus_boelter_nusselt(Re_range, 1.0))
print("Colburn's analogy at Pr = 1 reproduces 0.023 Re^0.8 exactly")

# %%
# Against Gnielinski (1976)
# -------------------------
#
# Gnielinski's correlation, built on Petukhov's friction factor, fits modern
# data to about 10%. Dittus-Boelter stays within 30% of it from air to
# water.

fig, ax = plt.subplots(figsize=(6, 4))
for Pr_i in [0.7, 7.0]:
    f = (0.790 * np.log(Re_range) - 1.64) ** -2
    gnielinski = (f / 8) * (Re_range - 1000) * Pr_i / (1 + 12.7 * np.sqrt(f / 8) * (Pr_i ** (2 / 3) - 1))
    db = dittus_boelter_nusselt(Re_range, Pr_i)
    spread = np.max(np.abs(db / gnielinski - 1))
    print(f"Pr = {Pr_i}: largest difference from Gnielinski {spread:.0%}")
    assert spread < 0.30
    line = ax.loglog(Re_range, db, label=f"Dittus-Boelter, Pr = {Pr_i}")[0]
    ax.loglog(Re_range, gnielinski, "--", color=line.get_color(), label=f"Gnielinski, Pr = {Pr_i}")
ax.set(xlabel="Reynolds number", ylabel="Nusselt number", title="Turbulent flow in a smooth tube")
ax.legend()
fig.tight_layout()

plt.show()