NTU_FROM_EFF

This function determines the number of transfer units required to achieve a specified effectiveness at a given heat-capacity ratio and exchanger configuration. It inverts standard effectiveness-NTU relationships.

The inversion is \mathrm{NTU} = f^{-1}(\varepsilon, C_r, \text{subtype}).

Excel Usage

=NTU_FROM_EFF(effectiveness, Cr, eff_subtype, n_shell_tube)
  • effectiveness (float, required): Thermal effectiveness of the exchanger (-).
  • Cr (float, required): Heat capacity rate ratio Cmin/Cmax (-).
  • eff_subtype (str, optional, default: “counterflow”): Exchanger configuration subtype (-).
  • n_shell_tube (int, optional, default: null): Number of shell and tube exchangers in series (-).

Returns (float): Thermal number of transfer units (-).

Example 1: NTU from effectiveness for parallel flow

Inputs:

effectiveness Cr eff_subtype
0.5881156068417585 0.7 parallel

Excel formula:

=NTU_FROM_EFF(0.5881156068417585, 0.7, "parallel")

Expected output:

5

Example 2: NTU from effectiveness for crossflow

Inputs:

effectiveness Cr eff_subtype
0.8444821799748551 0.7 crossflow

Excel formula:

=NTU_FROM_EFF(0.8444821799748551, 0.7, "crossflow")

Expected output:

5

Example 3: NTU from effectiveness for counterflow

Inputs:

effectiveness Cr eff_subtype
0.9206703686051108 0.7 counterflow

Excel formula:

=NTU_FROM_EFF(0.9206703686051108, 0.7, "counterflow")

Expected output:

5

Example 4: NTU from effectiveness for shell and tube series

Inputs:

effectiveness Cr eff_subtype n_shell_tube
0.9205058702789254 0.7 S&T 50

Excel formula:

=NTU_FROM_EFF(0.9205058702789254, 0.7, "S&T", 50)

Expected output:

5

Python Code

Show Code 
from ht.hx import NTU_from_effectiveness as hx_NTU_from_effectiveness

def NTU_from_eff(effectiveness, Cr, eff_subtype='counterflow', n_shell_tube=None):
    """
    Solve NTU from effectiveness, capacity ratio, and configuration.

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

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

    Args:
        effectiveness (float): Thermal effectiveness of the exchanger (-).
        Cr (float): Heat capacity rate ratio Cmin/Cmax (-).
        eff_subtype (str, optional): Exchanger configuration subtype (-). Valid options: Counterflow, Parallel, Crossflow, Crossflow Approximate, Crossflow Mixed Cmin, Crossflow Mixed Cmax, Boiler, Condenser, Shell and Tube. Default is 'counterflow'.
        n_shell_tube (int, optional): Number of shell and tube exchangers in series (-). Default is None.

    Returns:
        float: Thermal number of transfer units (-).
    """
    try:
      result = hx_NTU_from_effectiveness(effectiveness=effectiveness, Cr=Cr, subtype=eff_subtype, n_shell_tube=n_shell_tube)
      return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Thermal effectiveness of the exchanger (-).
Heat capacity rate ratio Cmin/Cmax (-).
Exchanger configuration subtype (-).
Number of shell and tube exchangers in series (-).