LEHRER

This function computes the average jacket-side heat transfer coefficient for a vessel jacket using the Lehrer correlation. It combines forced convection behavior in the jacket channel with optional buoyancy effects depending on inlet orientation and thermal conditions.

The Nusselt-number form used by the correlation can be represented as:

Nu = \left[\frac{0.03Re^{0.75}Pr}{1 + \frac{1.74(Pr-1)}{Re^{0.125}}}\right]\left(\frac{\mu}{\mu_w}\right)^{0.14}

The average heat transfer coefficient is then obtained from:

h = \frac{Nu\,k}{d_g}

Excel Usage

=LEHRER(m, Dtank, Djacket, H, Dinlet, rho, Cp, k, mu, muw, isobaric_expansion, dT, inlettype, inletlocation)

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).
isobaric_expansion (float, optional, default: null): Constant pressure expansivity of a fluid (m^3/mol/K).
dT (float, optional, default: null): Temperature difference of fluid in jacket (K).
inlettype (str, optional, default: “tangential”): Inlet type (tangential or radial).
inletlocation (str, optional, default: “auto”): Inlet location (top, bottom, or auto).

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

Example 1: Tangential inlet example from docs

Inputs:

m	Dtank	Djacket	H	Dinlet	dT	rho	Cp	k	mu	muw
2.5	0.6	0.65	0.6	0.025	20	995.7	4178.1	0.615	0.000798	0.000355

Excel formula:

=LEHRER(2.5, 0.6, 0.65, 0.6, 0.025, 20, 995.7, 4178.1, 0.615, 0.000798, 0.000355)

Expected output:

2922.13

Example 2: Radial inlet with expansion term

Inputs:

m	Dtank	Djacket	H	Dinlet	dT	rho	Cp	k	mu	muw	inlettype	isobaric_expansion
2.5	0.6	0.65	0.6	0.025	20	995.7	4178.1	0.615	0.000798	0.000355	radial	0.000303

Excel formula:

=LEHRER(2.5, 0.6, 0.65, 0.6, 0.025, 20, 995.7, 4178.1, 0.615, 0.000798, 0.000355, "radial", 0.000303)

Expected output:

3269.44

Example 3: Automatic inlet location with bottom entry

Inputs:

m	Dtank	Djacket	H	Dinlet	dT	rho	Cp	k	mu	muw	inletlocation
1.8	0.5	0.56	0.7	0.03	15	980	4100	0.62	0.0009	0.0006	bottom

Excel formula:

=LEHRER(1.8, 0.5, 0.56, 0.7, 0.03, 15, 980, 4100, 0.62, 0.0009, 0.0006, "bottom")

Expected output:

1406.42

Example 4: Tangential inlet with defaults

Inputs:

m	Dtank	Djacket	H	Dinlet	dT	rho	Cp	k	mu	muw
3.1	0.8	0.86	0.9	0.04	10	990	4000	0.6	0.0011	0.0008

Excel formula:

=LEHRER(3.1, 0.8, 0.86, 0.9, 0.04, 10, 990, 4000, 0.6, 0.0011, 0.0008)

Expected output:

1303.56

Python Code

Show Code

from ht.conv_jacket import Lehrer as ht_lehrer

def Lehrer(m, Dtank, Djacket, H, Dinlet, rho, Cp, k, mu, muw=None, isobaric_expansion=None, dT=None, inlettype='tangential', inletlocation='auto'):
    """
    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.
        isobaric_expansion (float, optional): Constant pressure expansivity of a fluid (m^3/mol/K). Default is None.
        dT (float, optional): Temperature difference of fluid in jacket (K). 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'.

    Returns:
        float: Average heat transfer coefficient inside the jacket (W/m^2/K).
    """
    try:
        return ht_lehrer(
            m=m,
            Dtank=Dtank,
            Djacket=Djacket,
            H=H,
            Dinlet=Dinlet,
            rho=rho,
            Cp=Cp,
            k=k,
            mu=mu,
            muw=muw,
            isobaric_expansion=isobaric_expansion,
            dT=dT,
            inlettype=inlettype,
            inletlocation=inletlocation,
        )
    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).

isobaric_expansion

Constant pressure expansivity of a fluid (m^3/mol/K).

Temperature difference of fluid in jacket (K).

inlettype

Inlet type (tangential or radial).

inletlocation

Inlet location (top, bottom, or auto).