LAZAREK_BLACK

This function estimates flow-boiling heat transfer with the Lazarek-Black correlation for small channels. The method is commonly applied when either wall heat flux or excess wall temperature is known.

The correlation is commonly written as:

h_{tp} = 30\,Re_{lo}^{0.857} Bg^{0.714}\frac{k_l}{D}

where Re_{lo} is a liquid-only Reynolds number and Bg is a boiling group containing heat flux and latent heat effects.

Excel Usage

=LAZAREK_BLACK(m, D, mul, kl, Hvap, q, Te)

m (float, required): Mass flow rate (kg/s).
D (float, required): Channel diameter (m).
mul (float, required): Liquid viscosity (Pa*s).
kl (float, required): Liquid thermal conductivity (W/m/K).
Hvap (float, required): Heat of vaporization (J/kg).
q (float, optional, default: null): Heat flux (W/m^2).
Te (float, optional, default: null): Excess wall temperature (K).

Returns (float): Heat transfer coefficient (W/m^2/K), or an error message if invalid.

Example 1: Example with excess temperature

Inputs:

m	D	mul	kl	Hvap	Te
10	0.3	0.001	0.6	2000000	100

Excel formula:

=LAZAREK_BLACK(10, 0.3, 0.001, 0.6, 2000000, 100)

Expected output:

9501.93

Example 2: Using heat flux input

Inputs:

m	D	mul	kl	Hvap	q
5	0.02	0.0002	0.12	180000	80000

Excel formula:

=LAZAREK_BLACK(5, 0.02, 0.0002, 0.12, 180000, 80000)

Expected output:

20829.3

Example 3: Small channel with low temperature rise

Inputs:

m	D	mul	kl	Hvap	Te
2	0.01	0.00015	0.1	200000	8

Excel formula:

=LAZAREK_BLACK(2, 0.01, 0.00015, 0.1, 200000, 8)

Expected output:

223929

Example 4: Higher heat flux at larger diameter

Inputs:

m	D	mul	kl	Hvap	q
8	0.04	0.00025	0.15	220000	120000

Excel formula:

=LAZAREK_BLACK(8, 0.04, 0.00025, 0.15, 220000, 120000)

Expected output:

19773.5

Python Code

Show Code

from ht.boiling_flow import Lazarek_Black as ht_Lazarek_Black

def Lazarek_Black(m, D, mul, kl, Hvap, q=None, Te=None):
    """
    Compute the Lazarek-Black boiling heat transfer coefficient.

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

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

    Args:
        m (float): Mass flow rate (kg/s).
        D (float): Channel diameter (m).
        mul (float): Liquid viscosity (Pa*s).
        kl (float): Liquid thermal conductivity (W/m/K).
        Hvap (float): Heat of vaporization (J/kg).
        q (float, optional): Heat flux (W/m^2). Default is None.
        Te (float, optional): Excess wall temperature (K). Default is None.

    Returns:
        float: Heat transfer coefficient (W/m^2/K), or an error message if invalid.
    """
    try:
        if Te is None and q is None:
            return "Error: Te or q must be provided"
        return ht_Lazarek_Black(m=m, D=D, mul=mul, kl=kl, Hvap=Hvap, q=q, Te=Te)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

m *

Mass flow rate (kg/s).

D *

Channel diameter (m).

mul *

Liquid viscosity (Pa*s).

kl *

Liquid thermal conductivity (W/m/K).

Hvap *

Heat of vaporization (J/kg).

Heat flux (W/m^2).

Excess wall temperature (K).