NU_PACKED_BED_GN

This function computes packed-bed Nusselt number using the Gnielinski approach, which scales single-particle heat transfer by an enhancement factor for packed arrangements. Inputs include particle diameter, void fraction, superficial velocity, fluid properties, and optionally a user-specified enhancement factor.

The model uses:

Nu = f_a\,Nu_{sphere}

with Reynolds number defined as:

Re = \frac{\rho v_s d_p}{\mu \epsilon}

where d_p is particle diameter, v_s is superficial velocity, \rho is fluid density, \mu is dynamic viscosity, and \epsilon is voidage.

Excel Usage

=NU_PACKED_BED_GN(dp, voidage, vs, rho, mu, Pr, fa)

dp (float, required): Equivalent spherical particle diameter of packing (m).
voidage (float, required): Void fraction of bed packing (-).
vs (float, required): Superficial velocity of the fluid (m/s).
rho (float, required): Density of the fluid (kg/m^3).
mu (float, required): Dynamic viscosity of the fluid (Pa*s).
Pr (float, required): Prandtl number of the fluid (-).
fa (float, optional, default: null): Heat transfer enhancement factor (-).

Returns (float): Nusselt number for heat transfer to the packed bed.

Example 1: Example packed bed case

Inputs:

dp	voidage	vs	rho	mu	Pr
0.0008	0.4	1	1000	0.001	0.7

Excel formula:

=NU_PACKED_BED_GN(0.0008, 0.4, 1, 1000, 0.001, 0.7)

Expected output:

61.3782

Example 2: Packed bed case with enhancement factor

Inputs:

dp	voidage	vs	rho	mu	Pr	fa
0.0012	0.45	0.8	998	0.0011	4	1.6

Excel formula:

=NU_PACKED_BED_GN(0.0012, 0.45, 0.8, 998, 0.0011, 4, 1.6)

Expected output:

86.0162

Example 3: Lower velocity case

Inputs:

dp	voidage	vs	rho	mu	Pr
0.001	0.38	0.2	950	0.002	10

Excel formula:

=NU_PACKED_BED_GN(0.001, 0.38, 0.2, 950, 0.002, 10)

Expected output:

48.5717

Example 4: Higher Prandtl number case

Inputs:

dp	voidage	vs	rho	mu	Pr
0.0006	0.42	2	1050	0.0009	25

Excel formula:

=NU_PACKED_BED_GN(0.0006, 0.42, 2, 1050, 0.0009, 25)

Expected output:

247.185

Python Code

Show Code

from ht.conv_packed_bed import Nu_packed_bed_Gnielinski as ht_Nu_packed_bed_Gnielinski

def Nu_packed_bed_Gn(dp, voidage, vs, rho, mu, Pr, fa=None):
    """
    Calculate Nusselt number for a packed bed using the Gnielinski correlation.

    See: https://ht.readthedocs.io/en/latest/ht.conv_packed_bed.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        dp (float): Equivalent spherical particle diameter of packing (m).
        voidage (float): Void fraction of bed packing (-).
        vs (float): Superficial velocity of the fluid (m/s).
        rho (float): Density of the fluid (kg/m^3).
        mu (float): Dynamic viscosity of the fluid (Pa*s).
        Pr (float): Prandtl number of the fluid (-).
        fa (float, optional): Heat transfer enhancement factor (-). Default is None.

    Returns:
        float: Nusselt number for heat transfer to the packed bed.
    """
    try:
        dp = float(dp)
        voidage = float(voidage)
        vs = float(vs)
        rho = float(rho)
        mu = float(mu)
        Pr = float(Pr)
        fa_value = None if fa is None else float(fa)
        return ht_Nu_packed_bed_Gnielinski(
            dp=dp,
            voidage=voidage,
            vs=vs,
            rho=rho,
            mu=mu,
            Pr=Pr,
            fa=fa_value,
        )
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

dp *

Equivalent spherical particle diameter of packing (m).

voidage *

Void fraction of bed packing (-).

vs *

Superficial velocity of the fluid (m/s).

rho *

Density of the fluid (kg/m^3).

mu *

Dynamic viscosity of the fluid (Pa*s).

Pr *

Prandtl number of the fluid (-).

Heat transfer enhancement factor (-).