THOME

This function computes flow-boiling heat transfer using the Thome microchannel model, a detailed slug/film-based approach for saturated evaporation in small channels. It accepts either heat flux directly or excess wall temperature for an implicit solution.

The model forms a weighted average of regime-specific contributions:

h(z) = \frac{t_l}{\tau}h_l(z) + \frac{t_{film}}{\tau}h_{film}(z) + \frac{t_{dry}}{\tau}h_g(z)

where time fractions and local film behavior are estimated from flow properties, boiling intensity, and fluid thermophysical data.

Excel Usage

=THOME(m, x, D, rhol, rhog, mul, mug, kl, kg, Cpl, Cpg, Hvap, sigma, Psat, Pc, q, Te)

m (float, required): Mass flow rate (kg/s).
x (float, required): Quality at the tube interval (dimensionless).
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).
mug (float, required): Gas viscosity (Pa*s).
kl (float, required): Liquid thermal conductivity (W/m/K).
kg (float, required): Gas thermal conductivity (W/m/K).
Cpl (float, required): Liquid heat capacity (J/kg/K).
Cpg (float, required): Gas heat capacity (J/kg/K).
Hvap (float, required): Heat of vaporization (J/kg).
sigma (float, required): Surface tension (N/m).
Psat (float, required): Saturation pressure (Pa).
Pc (float, required): Critical pressure (Pa).
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 heat flux

Inputs:

m	x	D	rhol	rhog	kl	kg	mul	mug	Cpl	Cpg	sigma	Hvap	Psat	Pc	q
1	0.4	0.3	567	18.09	0.086	0.2	0.000156	0.00001	2300	1400	0.02	900000	100000	22000000	100000

Excel formula:

=THOME(1, 0.4, 0.3, 567, 18.09, 0.086, 0.2, 0.000156, 0.00001, 2300, 1400, 0.02, 900000, 100000, 22000000, 100000)

Expected output:

1633.01

Example 2: Using excess wall temperature

Inputs:

m	x	D	rhol	rhog	kl	kg	mul	mug	Cpl	Cpg	sigma	Hvap	Psat	Pc	Te
0.8	0.3	0.02	850	12	0.12	0.18	0.0002	0.000012	3000	1500	0.025	180000	900000	4000000	6

Excel formula:

=THOME(0.8, 0.3, 0.02, 850, 12, 0.12, 0.18, 0.0002, 0.000012, 3000, 1500, 0.025, 180000, 900000, 4000000, 6)

Expected output:

96633.1

Example 3: Small diameter with higher heat flux

Inputs:

m	x	D	rhol	rhog	kl	kg	mul	mug	Cpl	Cpg	sigma	Hvap	Psat	Pc	q
0.6	0.5	0.01	900	9	0.1	0.16	0.00018	0.000011	2800	1400	0.03	200000	800000	3000000	70000

Excel formula:

=THOME(0.6, 0.5, 0.01, 900, 9, 0.1, 0.16, 0.00018, 0.000011, 2800, 1400, 0.03, 200000, 800000, 3000000, 70000)

Expected output:

20435

Example 4: Mid-range properties with Te

Inputs:

m	x	D	rhol	rhog	kl	kg	mul	mug	Cpl	Cpg	sigma	Hvap	Psat	Pc	Te
1.2	0.35	0.04	700	15	0.09	0.19	0.00022	0.000013	2600	1450	0.018	160000	1200000	6000000	7

Excel formula:

=THOME(1.2, 0.35, 0.04, 700, 15, 0.09, 0.19, 0.00022, 0.000013, 2600, 1450, 0.018, 160000, 1200000, 6000000, 7)

Expected output:

28555.1

Python Code

Show Code

from ht.boiling_flow import Thome as ht_Thome

def Thome(m, x, D, rhol, rhog, mul, mug, kl, kg, Cpl, Cpg, Hvap, sigma, Psat, Pc, q=None, Te=None):
    """
    Compute the Thome microchannel 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).
        x (float): Quality at the tube interval (dimensionless).
        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).
        mug (float): Gas viscosity (Pa*s).
        kl (float): Liquid thermal conductivity (W/m/K).
        kg (float): Gas thermal conductivity (W/m/K).
        Cpl (float): Liquid heat capacity (J/kg/K).
        Cpg (float): Gas heat capacity (J/kg/K).
        Hvap (float): Heat of vaporization (J/kg).
        sigma (float): Surface tension (N/m).
        Psat (float): Saturation pressure (Pa).
        Pc (float): Critical pressure (Pa).
        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_Thome(m=m, x=x, D=D, rhol=rhol, rhog=rhog, mul=mul, mug=mug,
            kl=kl, kg=kg, Cpl=Cpl, Cpg=Cpg, Hvap=Hvap, sigma=sigma, Psat=Psat,
            Pc=Pc, q=q, Te=Te)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

m *

Mass flow rate (kg/s).

x *

Quality at the tube interval (dimensionless).

D *

Tube diameter (m).

rhol *

Liquid density (kg/m^3).

rhog *

Gas density (kg/m^3).

mul *

Liquid viscosity (Pa*s).

mug *

Gas viscosity (Pa*s).

kl *

Liquid thermal conductivity (W/m/K).

kg *

Gas thermal conductivity (W/m/K).

Cpl *

Liquid heat capacity (J/kg/K).

Cpg *

Gas heat capacity (J/kg/K).

Hvap *

Heat of vaporization (J/kg).

sigma *

Surface tension (N/m).

Psat *

Saturation pressure (Pa).

Pc *

Critical pressure (Pa).

Heat flux (W/m^2).

Excess wall temperature (K).