SHAH

This function calculates internal-flow condensation heat transfer using the Shah correlation. It combines a liquid-only convective baseline with a quality- and reduced-pressure-dependent enhancement term.

The two-phase coefficient is estimated as:

h_{TP} = h_L\left[(1-x)^{0.8} + \frac{3.8x^{0.76}(1-x)^{0.04}}{P_r^{0.38}}\right]

where P_r = P/P_c is reduced pressure and h_L is a liquid-only turbulent correlation value. The output is a scalar heat transfer coefficient in W/m^2/K.

Excel Usage

=SHAH(m, x, D, rhol, mul, kl, Cpl, P, Pc)

• m (float, required): Mass flow rate (kg/s).
• x (float, required): Quality at the specific interval (-).
• D (float, required): Channel diameter (m).
• rhol (float, required): Liquid density (kg/m^3).
• mul (float, required): Liquid viscosity (Pa*s).
• kl (float, required): Liquid thermal conductivity (W/m/K).
• Cpl (float, required): Liquid heat capacity at constant pressure (J/kg/K).
• P (float, required): Pressure (Pa).
• Pc (float, required): Critical pressure (Pa).

Returns (float): Heat transfer coefficient (W/m^2/K).

Example 1: Example values from reference

Inputs:

m	x	D	rhol	mul	kl	Cpl	P	Pc
1	0.4	0.3	800	0.00001	0.6	2300	1000000	20000000

Excel formula:

=SHAH(1, 0.4, 0.3, 800, 0.00001, 0.6, 2300, 1000000, 20000000)

Expected output:

2561.26

Example 2: Low quality vapor fraction

Inputs:

m	x	D	rhol	mul	kl	Cpl	P	Pc
0.6	0.1	0.05	900	0.0002	0.12	2000	800000	22000000

Excel formula:

=SHAH(0.6, 0.1, 0.05, 900, 0.0002, 0.12, 2000, 800000, 22000000)

Expected output:

2331.05

Example 3: Mid quality vapor fraction

Inputs:

m	x	D	rhol	mul	kl	Cpl	P	Pc
0.9	0.6	0.08	700	0.00015	0.1	2400	1500000	25000000

Excel formula:

=SHAH(0.9, 0.6, 0.08, 700, 0.00015, 0.1, 2400, 1500000, 25000000)

Expected output:

3569.56

Example 4: Higher mass flow rate

Inputs:

m	x	D	rhol	mul	kl	Cpl	P	Pc
2	0.7	0.12	650	0.00018	0.11	2100	2000000	30000000

Excel formula:

=SHAH(2, 0.7, 0.12, 650, 0.00018, 0.11, 2100, 2000000, 30000000)

Expected output:

3195.67

Python Code

Show Code

from ht.condensation import Shah as ht_Shah

def Shah(m, x, D, rhol, mul, kl, Cpl, P, Pc):
    """
    Calculate condensation heat transfer coefficient using the Shah correlation.

    See: https://ht.readthedocs.io/en/latest/ht.condensation.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 specific interval (-).
        D (float): Channel diameter (m).
        rhol (float): Liquid density (kg/m^3).
        mul (float): Liquid viscosity (Pa*s).
        kl (float): Liquid thermal conductivity (W/m/K).
        Cpl (float): Liquid heat capacity at constant pressure (J/kg/K).
        P (float): Pressure (Pa).
        Pc (float): Critical pressure (Pa).

    Returns:
        float: Heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_Shah(m=m, x=x, D=D, rhol=rhol, mul=mul, kl=kl, Cpl=Cpl, P=P, Pc=Pc)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

m *

Mass flow rate (kg/s).

x *

Quality at the specific interval (-).

D *

Channel diameter (m).

rhol *

Liquid density (kg/m^3).

mul *

Liquid viscosity (Pa*s).

kl *

Liquid thermal conductivity (W/m/K).

Cpl *

Liquid heat capacity at constant pressure (J/kg/K).

P *

Pressure (Pa).

Pc *

Critical pressure (Pa).