TO_SOLVE_Q_THOME

This function evaluates the residual equation used to solve for heat flux in the Thome flow-boiling model when excess wall temperature is prescribed. It is primarily an internal numerical helper for implicit root-finding workflows.

Conceptually, it evaluates:

R(q) = T_{e,model}(q,\ldots) - T_{e,target}

A root at R(q)=0 indicates the heat flux that is consistent with the specified operating state and target excess wall temperature.

Excel Usage

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

• q (float, required): Heat flux (W/m^2).
• 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).
• kl (float, required): Liquid thermal conductivity (W/m/K).
• kg (float, required): Gas thermal conductivity (W/m/K).
• mul (float, required): Liquid viscosity (Pa*s).
• mug (float, required): Gas viscosity (Pa*s).
• Cpl (float, required): Liquid heat capacity (J/kg/K).
• Cpg (float, required): Gas heat capacity (J/kg/K).
• sigma (float, required): Surface tension (N/m).
• Hvap (float, required): Heat of vaporization (J/kg).
• Psat (float, required): Saturation pressure (Pa).
• Pc (float, required): Critical pressure (Pa).
• Te (float, required): Excess wall temperature (K).

Returns (float): Heat flux residual value (W/m^2), or an error message if invalid.

Example 1: Baseline residual calculation

Inputs:

q	m	x	D	rhol	rhog	kl	kg	mul	mug	Cpl	Cpg	sigma	Hvap	Psat	Pc	Te
100000	1	0.4	0.3	567	18.09	0.086	0.2	0.000156	0.00001	2300	1400	0.02	900000	100000	22000000	7

Excel formula:

=TO_SOLVE_Q_THOME(100000, 1, 0.4, 0.3, 567, 18.09, 0.086, 0.2, 0.000156, 0.00001, 2300, 1400, 0.02, 900000, 100000, 22000000, 7)

Expected output:

54.2367

Example 2: Lower quality with smaller diameter

Inputs:

q	m	x	D	rhol	rhog	kl	kg	mul	mug	Cpl	Cpg	sigma	Hvap	Psat	Pc	Te
70000	0.8	0.25	0.02	850	12	0.12	0.18	0.0002	0.000012	3000	1500	0.025	180000	900000	4000000	6

Excel formula:

=TO_SOLVE_Q_THOME(70000, 0.8, 0.25, 0.02, 850, 12, 0.12, 0.18, 0.0002, 0.000012, 3000, 1500, 0.025, 180000, 900000, 4000000, 6)

Expected output:

-3.1047

Example 3: Higher quality with higher heat flux

Inputs:

q	m	x	D	rhol	rhog	kl	kg	mul	mug	Cpl	Cpg	sigma	Hvap	Psat	Pc	Te
120000	0.6	0.6	0.01	900	9	0.1	0.16	0.00018	0.000011	2800	1400	0.03	200000	800000	3000000	8

Excel formula:

=TO_SOLVE_Q_THOME(120000, 0.6, 0.6, 0.01, 900, 9, 0.1, 0.16, 0.00018, 0.000011, 2800, 1400, 0.03, 200000, 800000, 3000000, 8)

Expected output:

-3.31727

Example 4: Mid-range properties

Inputs:

q	m	x	D	rhol	rhog	kl	kg	mul	mug	Cpl	Cpg	sigma	Hvap	Psat	Pc	Te
90000	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:

=TO_SOLVE_Q_THOME(90000, 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:

-1.49611

Python Code

Show Code

from ht.boiling_flow import to_solve_q_Thome as ht_to_solve_q_Thome

def to_solve_q_Thome(q, m, x, D, rhol, rhog, kl, kg, mul, mug, Cpl, Cpg, sigma, Hvap, Psat, Pc, Te):
    """
    Compute the Thome heat flux residual for a specified wall temperature.

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

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

    Args:
        q (float): Heat flux (W/m^2).
        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).
        kl (float): Liquid thermal conductivity (W/m/K).
        kg (float): Gas thermal conductivity (W/m/K).
        mul (float): Liquid viscosity (Pa*s).
        mug (float): Gas viscosity (Pa*s).
        Cpl (float): Liquid heat capacity (J/kg/K).
        Cpg (float): Gas heat capacity (J/kg/K).
        sigma (float): Surface tension (N/m).
        Hvap (float): Heat of vaporization (J/kg).
        Psat (float): Saturation pressure (Pa).
        Pc (float): Critical pressure (Pa).
        Te (float): Excess wall temperature (K).

    Returns:
        float: Heat flux residual value (W/m^2), or an error message if invalid.
    """
    try:
        return ht_to_solve_q_Thome(q=q, m=m, x=x, D=D, rhol=rhol, rhog=rhog, kl=kl,
            kg=kg, mul=mul, mug=mug, Cpl=Cpl, Cpg=Cpg, sigma=sigma, Hvap=Hvap,
            Psat=Psat, Pc=Pc, Te=Te)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

q *

Heat flux (W/m^2).

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).

kl *

Liquid thermal conductivity (W/m/K).

kg *

Gas thermal conductivity (W/m/K).

mul *

Liquid viscosity (Pa*s).

mug *

Gas viscosity (Pa*s).

Cpl *

Liquid heat capacity (J/kg/K).

Cpg *

Gas heat capacity (J/kg/K).

sigma *

Surface tension (N/m).

Hvap *

Heat of vaporization (J/kg).

Psat *

Saturation pressure (Pa).

Pc *

Critical pressure (Pa).

Te *

Excess wall temperature (K).