STEIN_SCHMIDT

This function calculates the average jacket-side heat transfer coefficient for a vessel using the Stein-Schmidt correlation. It models combined forced and natural convection effects through an equivalent Reynolds number and then evaluates a composite Nusselt-number expression.

The equivalent Reynolds-number form used in the model is:

Re_{eq} = \left[Re^2 \pm \left(\frac{|Gr|\,H/d_{ch}}{50}\right)\right]^{1/2}

The resulting Nusselt number is converted to heat transfer coefficient with:

h = \frac{Nu\,k}{d_{ch}}

Excel Usage

=STEIN_SCHMIDT(m, Dtank, Djacket, H, Dinlet, rho, Cp, k, mu, muw, rhow, inlettype, inletlocation, roughness)

m (float, required): Mass flow rate of fluid (kg/s).
Dtank (float, required): Outer diameter of tank or vessel surrounded by jacket (m).
Djacket (float, required): Inner diameter of jacket surrounding a vessel or tank (m).
H (float, required): Height of the vessel or tank (m).
Dinlet (float, required): Inner diameter of inlet into the jacket (m).
rho (float, required): Density of the fluid at Tm (kg/m^3).
Cp (float, required): Heat capacity of fluid at Tm (J/kg/K).
k (float, required): Thermal conductivity of fluid at Tm (W/m/K).
mu (float, required): Viscosity of fluid at Tm (Pa*s).
muw (float, optional, default: null): Viscosity of fluid at Tw (Pa*s).
rhow (float, optional, default: null): Density of the fluid at Tw (kg/m^3).
inlettype (str, optional, default: “tangential”): Inlet type (tangential or radial).
inletlocation (str, optional, default: “auto”): Inlet location (top, bottom, or auto).
roughness (float, optional, default: 0): Roughness of the tank walls (m).

Returns (float): Average heat transfer coefficient inside the jacket (W/m^2/K).

Example 1: Example from docs

Inputs:

m	Dtank	Djacket	H	Dinlet	rho	Cp	k	mu	muw	rhow
2.5	0.6	0.65	0.6	0.025	995.7	4178.1	0.615	0.000798	0.000355	971.8

Excel formula:

=STEIN_SCHMIDT(2.5, 0.6, 0.65, 0.6, 0.025, 995.7, 4178.1, 0.615, 0.000798, 0.000355, 971.8)

Expected output:

5695.2

Example 2: Tangential inlet with defaults

Inputs:

m	Dtank	Djacket	H	Dinlet	rho	Cp	k	mu	muw	rhow
1.6	0.5	0.56	0.7	0.03	980	4100	0.62	0.0009	0.0006	970

Excel formula:

=STEIN_SCHMIDT(1.6, 0.5, 0.56, 0.7, 0.03, 980, 4100, 0.62, 0.0009, 0.0006, 970)

Expected output:

2779.33

Example 3: Radial inlet at top

Inputs:

m	Dtank	Djacket	H	Dinlet	rho	Cp	k	mu	muw	rhow	inlettype	inletlocation
2.2	0.7	0.75	0.8	0.04	990	4000	0.6	0.0011	0.0008	980	radial	top

Excel formula:

=STEIN_SCHMIDT(2.2, 0.7, 0.75, 0.8, 0.04, 990, 4000, 0.6, 0.0011, 0.0008, 980, "radial", "top")

Expected output:

488.491

Example 4: Nonzero roughness

Inputs:

m	Dtank	Djacket	H	Dinlet	rho	Cp	k	mu	muw	rhow	roughness
3	0.8	0.86	0.9	0.05	995	4200	0.63	0.00085	0.00055	980	0.0001

Excel formula:

=STEIN_SCHMIDT(3, 0.8, 0.86, 0.9, 0.05, 995, 4200, 0.63, 0.00085, 0.00055, 980, 0.0001)

Expected output:

2135.15

Python Code

Show Code

from ht.conv_jacket import Stein_Schmidt as ht_stein_schmidt

def Stein_Schmidt(m, Dtank, Djacket, H, Dinlet, rho, Cp, k, mu, muw=None, rhow=None, inlettype='tangential', inletlocation='auto', roughness=0):
    """
    Calculate the average heat transfer coefficient for a jacket around a vessel.

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

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

    Args:
        m (float): Mass flow rate of fluid (kg/s).
        Dtank (float): Outer diameter of tank or vessel surrounded by jacket (m).
        Djacket (float): Inner diameter of jacket surrounding a vessel or tank (m).
        H (float): Height of the vessel or tank (m).
        Dinlet (float): Inner diameter of inlet into the jacket (m).
        rho (float): Density of the fluid at Tm (kg/m^3).
        Cp (float): Heat capacity of fluid at Tm (J/kg/K).
        k (float): Thermal conductivity of fluid at Tm (W/m/K).
        mu (float): Viscosity of fluid at Tm (Pa*s).
        muw (float, optional): Viscosity of fluid at Tw (Pa*s). Default is None.
        rhow (float, optional): Density of the fluid at Tw (kg/m^3). Default is None.
        inlettype (str, optional): Inlet type (tangential or radial). Valid options: Tangential, Radial. Default is 'tangential'.
        inletlocation (str, optional): Inlet location (top, bottom, or auto). Valid options: Auto, Top, Bottom. Default is 'auto'.
        roughness (float, optional): Roughness of the tank walls (m). Default is 0.

    Returns:
        float: Average heat transfer coefficient inside the jacket (W/m^2/K).
    """
    try:
        return ht_stein_schmidt(
            m=m,
            Dtank=Dtank,
            Djacket=Djacket,
            H=H,
            Dinlet=Dinlet,
            rho=rho,
            Cp=Cp,
            k=k,
            mu=mu,
            muw=muw,
            rhow=rhow,
            inlettype=inlettype,
            inletlocation=inletlocation,
            roughness=roughness,
        )
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

m *

Mass flow rate of fluid (kg/s).

Dtank *

Outer diameter of tank or vessel surrounded by jacket (m).

Djacket *

Inner diameter of jacket surrounding a vessel or tank (m).

H *

Height of the vessel or tank (m).

Dinlet *

Inner diameter of inlet into the jacket (m).

rho *

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

Cp *

Heat capacity of fluid at Tm (J/kg/K).

k *

Thermal conductivity of fluid at Tm (W/m/K).

mu *

Viscosity of fluid at Tm (Pa*s).

muw

Viscosity of fluid at Tw (Pa*s).

rhow

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

inlettype

Inlet type (tangential or radial).

inletlocation

Inlet location (top, bottom, or auto).

roughness

Roughness of the tank walls (m).