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

Mass flow rate of fluid (kg/s).
Outer diameter of tank or vessel surrounded by jacket (m).
Inner diameter of jacket surrounding a vessel or tank (m).
Height of the vessel or tank (m).
Inner diameter of inlet into the jacket (m).
Density of the fluid at Tm (kg/m^3).
Heat capacity of fluid at Tm (J/kg/K).
Thermal conductivity of fluid at Tm (W/m/K).
Viscosity of fluid at Tm (Pa*s).
Viscosity of fluid at Tw (Pa*s).
Density of the fluid at Tw (kg/m^3).
Inlet type (tangential or radial).
Inlet location (top, bottom, or auto).
Roughness of the tank walls (m).