polykin.transport.hmt¤
Nu_sphere_free ¤
Nu_sphere_free(Ra: float, Pr: float) -> float
Calculate the Nusselt number for free convection on a sphere.
The average Nusselt number \(\overline{Nu}=\bar{h}D/k\) is estimated by the following expression:
\[ \overline{Nu} = 2 + \frac{0.589 Ra^{1/4}}{[1 + (0.469/Pr)^{9/16}]^{4/9}} \]
\[\begin{bmatrix}
Ra \lesssim 10^{11} \\
Pr \ge 0.7 \\
\end{bmatrix}\]
where \(Ra\) is the Rayleigh number and \(Pr\) is the Prandtl number. The properties are to be evaluated at the film temperature.
References
- Churchill, S.W, "Free convection around immersed bodies", in Heat Exchange Design Handbook, Section 2.5.7, Hemisphere Publishing, New York, 1983.
- Incropera, Frank P., and David P. De Witt. "Fundamentals of heat and mass transfer", 4th edition, 1996, p. 502.
PARAMETER | DESCRIPTION |
---|---|
Ra
|
Rayleigh number based on sphere diameter.
TYPE:
|
Pr
|
Prandtl number.
TYPE:
|
RETURNS | DESCRIPTION |
---|---|
float
|
Nusselt number. |
See also
Nu_sphere
: related method for forced convection.
Examples:
Estimate the external heat transfer coefficient for a 50 mm sphere with a surface temperature of 330 K immersed in water with a bulk temperature of 290 K.
>>> from polykin.transport import Nu_sphere_free
>>> rho = 1.0e3 # kg/m³
>>> mu = 0.70e-3 # Pa.s
>>> cp = 4.2e3 # J/kg/K
>>> k = 0.63 # W/m/K
>>> beta = 362e-6 # 1/K
>>> D = 50e-3 # m
>>> g = 9.81 # m/s²
>>> Pr = cp*mu/k
>>> Gr = g*beta*(330-290)*D**3/(mu/rho)**2
>>> Ra = Gr*Pr
>>> Nu = Nu_sphere_free(Ra, Pr)
>>> h = Nu*k/D
>>> print(f"h={h:.1e} W/m²·K")
h=7.8e+02 W/m²·K
Source code in src/polykin/transport/hmt.py
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