ECKERT

Overview

The ECKERT function calculates the Eckert number (Ec), a dimensionless quantity used in continuum mechanics and heat transfer analysis. The Eckert number expresses the relationship between a flow’s kinetic energy and the boundary layer enthalpy difference, making it useful for characterizing heat transfer dissipation and viscous heating effects. It is named after Ernst R. G. Eckert, a pioneer in heat transfer research.

This implementation uses the fluids library, an open-source Python package for fluid dynamics calculations. For detailed documentation, see the fluids.core.Eckert documentation.

The Eckert number is defined as the ratio of kinetic energy to enthalpy difference:

\text{Ec} = \frac{V^2}{C_p \Delta T}

where:

• V is the velocity of the fluid (m/s)
• C_p is the specific heat capacity at constant pressure (J/kg/K)
• \Delta T is the temperature difference (K)

Physically, the Eckert number can be interpreted as:

\text{Ec} = \frac{\text{Kinetic energy}}{\text{Enthalpy difference}} = \frac{\text{Advective transport}}{\text{Heat dissipation potential}}

The Eckert number is particularly important in high-speed flow applications where viscous dissipation becomes significant. When Ec is small (Ec << 1), viscous heating effects are negligible and can be ignored in heat transfer calculations. When Ec approaches or exceeds unity, kinetic energy conversion to thermal energy through viscous effects becomes significant, such as in supersonic flows, high-speed bearing lubrication, or polymer processing. According to the fluids documentation, the Eckert number is fairly rare in practice but finds use in specialized heat transfer calculations.

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

Excel Usage

=ECKERT(V, Cp, dT)

• V (float, required): Velocity (m/s)
• Cp (float, required): Specific heat capacity at constant pressure (J/kg/K)
• dT (float, required): Temperature difference (K)

Returns (float): Eckert number (float), or error message string.

Examples

Example 1: Demo case 1

Inputs:

V	Cp	dT
10	2000	25

Excel formula:

=ECKERT(10, 2000, 25)

Expected output:

0.002

Example 2: Demo case 2

Inputs:

V	Cp	dT
20	2000	25

Excel formula:

=ECKERT(20, 2000, 25)

Expected output:

0.008

Example 3: Demo case 3

Inputs:

V	Cp	dT
10	4000	25

Excel formula:

=ECKERT(10, 4000, 25)

Expected output:

0.001

Example 4: Demo case 4

Inputs:

V	Cp	dT
10	2000	50

Excel formula:

=ECKERT(10, 2000, 50)

Expected output:

0.001

Python Code

import micropip
await micropip.install(["fluids"])
from fluids.core import Eckert as fluids_eckert

def eckert(V, Cp, dT):
    """
    Calculate the Eckert number using fluids.core.Eckert.

    See: https://fluids.readthedocs.io/fluids.core.html#fluids.core.Eckert

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

    Args:
        V (float): Velocity (m/s)
        Cp (float): Specific heat capacity at constant pressure (J/kg/K)
        dT (float): Temperature difference (K)

    Returns:
        float: Eckert number (float), or error message string.
    """
    # Convert inputs to float
    try:
        V = float(V)
        Cp = float(Cp)
        dT = float(dT)
    except Exception:
        return "Error: All parameters must be numeric values."

    # Validate inputs
    if Cp == 0 or dT == 0:
        return "Error: Cp and dT must be nonzero."

    # Call the fluids library function
    try:
        result = fluids_eckert(V=V, Cp=Cp, dT=dT)
        return result
    except Exception as e:
        return f"Error: Failed to calculate Eckert number: {str(e)}"

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