SUN_MISHIMA

This function estimates saturated flow-boiling heat transfer using the Sun-Mishima correlation, which is often applied to mini-channel conditions. The model requires either heat flux or excess wall temperature.

A representative relation is:

h_{tp} = \frac{6\,Re_{lo}^{1.05}Bg^{0.54}}{We_l^{0.191}(\rho_l/\rho_g)^{0.142}}\frac{k_l}{D}

It combines liquid-only Reynolds effects with boiling and Weber-number scaling for empirical prediction.

Excel Usage

=SUN_MISHIMA(m, D, rhol, rhog, mul, kl, Hvap, sigma, q, Te)

m (float, required): Mass flow rate (kg/s).
D (float, required): Tube diameter (m).
rhol (float, required): Liquid density (kg/m^3).
rhog (float, required): Gas density (kg/m^3).
mul (float, required): Liquid viscosity (Pa*s).
kl (float, required): Liquid thermal conductivity (W/m/K).
Hvap (float, required): Heat of vaporization (J/kg).
sigma (float, required): Surface tension (N/m).
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	rhol	rhog	kl	mul	sigma	Hvap	Te
1	0.3	567	18.09	0.086	0.000156	0.02	900000	10

Excel formula:

=SUN_MISHIMA(1, 0.3, 567, 18.09, 0.086, 0.000156, 0.02, 900000, 10)

Expected output:

507.671

Example 2: Using heat flux input

Inputs:

m	D	rhol	rhog	kl	mul	sigma	Hvap	q
0.8	0.02	900	12	0.12	0.0002	0.025	180000	70000

Excel formula:

=SUN_MISHIMA(0.8, 0.02, 900, 12, 0.12, 0.0002, 0.025, 180000, 70000)

Expected output:

15391.5

Example 3: Small diameter with higher heat flux

Inputs:

m	D	rhol	rhog	kl	mul	sigma	Hvap	q
0.6	0.01	850	9	0.11	0.00018	0.03	200000	90000

Excel formula:

=SUN_MISHIMA(0.6, 0.01, 850, 9, 0.11, 0.00018, 0.03, 200000, 90000)

Expected output:

21451

Example 4: Mid-range properties with Te

Inputs:

m	D	rhol	rhog	kl	mul	sigma	Hvap	Te
1.2	0.04	700	15	0.09	0.00022	0.018	160000	6

Excel formula:

=SUN_MISHIMA(1.2, 0.04, 700, 15, 0.09, 0.00022, 0.018, 160000, 6)

Expected output:

5898.6

Python Code

Show Code

from ht.boiling_flow import Sun_Mishima as ht_Sun_Mishima

def Sun_Mishima(m, D, rhol, rhog, mul, kl, Hvap, sigma, q=None, Te=None):
    """
    Compute the Sun-Mishima 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): Tube diameter (m).
        rhol (float): Liquid density (kg/m^3).
        rhog (float): Gas density (kg/m^3).
        mul (float): Liquid viscosity (Pa*s).
        kl (float): Liquid thermal conductivity (W/m/K).
        Hvap (float): Heat of vaporization (J/kg).
        sigma (float): Surface tension (N/m).
        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_Sun_Mishima(m=m, D=D, rhol=rhol, rhog=rhog, mul=mul, kl=kl,
            Hvap=Hvap, sigma=sigma, q=q, Te=Te)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

m *

Mass flow rate (kg/s).

D *

Tube diameter (m).

rhol *

Liquid density (kg/m^3).

rhog *

Gas density (kg/m^3).

mul *

Liquid viscosity (Pa*s).

kl *

Liquid thermal conductivity (W/m/K).

Hvap *

Heat of vaporization (J/kg).

sigma *

Surface tension (N/m).

Heat flux (W/m^2).

Excess wall temperature (K).