EFF_NTU_METHOD

This function solves a heat exchanger state using the effectiveness-NTU framework from stream flow rates, heat capacities, exchanger subtype, and a valid temperature/UA input combination. It returns exchanger duty and derived thermodynamic properties as an Excel data type.

Core relations include \mathrm{NTU}=\frac{UA}{C_{min}} and Q=\varepsilon C_{min}(T_{h,i}-T_{c,i}).

Excel Usage

=EFF_NTU_METHOD(mh, mc, Cph, Cpc, eff_subtype, Thi, Tho, Tci, Tco, UA, n_shell_tube)

• mh (float, required): Mass flow rate of hot stream (kg/s).
• mc (float, required): Mass flow rate of cold stream (kg/s).
• Cph (float, required): Heat capacity of hot stream (J/kg/K).
• Cpc (float, required): Heat capacity of cold stream (J/kg/K).
• eff_subtype (str, optional, default: “counterflow”): Exchanger configuration subtype (-).
• Thi (float, optional, default: null): Hot inlet temperature (K).
• Tho (float, optional, default: null): Hot outlet temperature (K).
• Tci (float, optional, default: null): Cold inlet temperature (K).
• Tco (float, optional, default: null): Cold outlet temperature (K).
• UA (float, optional, default: null): Area heat transfer coefficient product (W/K).
• n_shell_tube (int, optional, default: null): Number of shell and tube exchangers in series (-).

Returns (float): Heat exchanged, with additional properties for temperatures and ratios.

Example 1: Effectiveness-NTU with known cold outlet

Inputs:

mh	mc	Cph	Cpc	eff_subtype	Tci	Tco	Thi
5.2	1.45	1860	1900	crossflow, mixed Cmax	15	85	130

Excel formula:

=EFF_NTU_METHOD(5.2, 1.45, 1860, 1900, "crossflow, mixed Cmax", 15, 85, 130)

Expected output:

{"type":"Double","basicValue":192850,"properties":{"Q":{"type":"Double","basicValue":192850},"UA":{"type":"Double","basicValue":3041.75},"Cr":{"type":"Double","basicValue":0.284843},"Cmin":{"type":"Double","basicValue":2755},"Cmax":{"type":"Double","basicValue":9672},"effectiveness":{"type":"Double","basicValue":0.608696},"NTU":{"type":"Double","basicValue":1.10408},"Thi":{"type":"Double","basicValue":130},"Tho":{"type":"Double","basicValue":110.061},"Tci":{"type":"Double","basicValue":15},"Tco":{"type":"Double","basicValue":85}}}

Example 2: Effectiveness-NTU with known UA and inlets

Inputs:

mh	mc	Cph	Cpc	eff_subtype	Tci	Thi	UA
5.2	1.45	1860	1900	crossflow, mixed Cmax	15	130	3041.75

Excel formula:

=EFF_NTU_METHOD(5.2, 1.45, 1860, 1900, "crossflow, mixed Cmax", 15, 130, 3041.75)

Expected output:

{"type":"Double","basicValue":192850,"properties":{"Q":{"type":"Double","basicValue":192850},"UA":{"type":"Double","basicValue":3041.75},"Cr":{"type":"Double","basicValue":0.284843},"Cmin":{"type":"Double","basicValue":2755},"Cmax":{"type":"Double","basicValue":9672},"effectiveness":{"type":"Double","basicValue":0.608696},"NTU":{"type":"Double","basicValue":1.10408},"Thi":{"type":"Double","basicValue":130},"Tho":{"type":"Double","basicValue":110.061},"Tci":{"type":"Double","basicValue":15},"Tco":{"type":"Double","basicValue":85}}}

Example 3: Effectiveness-NTU for counterflow

Inputs:

mh	mc	Cph	Cpc	eff_subtype	Tci	Thi	UA
4	2	2000	1800	counterflow	300	420	1500

Excel formula:

=EFF_NTU_METHOD(4, 2, 2000, 1800, "counterflow", 300, 420, 1500)

Expected output:

{"type":"Double","basicValue":137777,"properties":{"Q":{"type":"Double","basicValue":137777},"UA":{"type":"Double","basicValue":1500},"Cr":{"type":"Double","basicValue":0.45},"Cmin":{"type":"Double","basicValue":3600},"Cmax":{"type":"Double","basicValue":8000},"effectiveness":{"type":"Double","basicValue":0.318929},"NTU":{"type":"Double","basicValue":0.416667},"Thi":{"type":"Double","basicValue":420},"Tho":{"type":"Double","basicValue":402.778},"Tci":{"type":"Double","basicValue":300},"Tco":{"type":"Double","basicValue":338.271}}}

Example 4: Effectiveness-NTU for shell and tube series

Inputs:

mh	mc	Cph	Cpc	eff_subtype	Tci	Thi	UA	n_shell_tube
3.5	2.2	2100	1900	S&T	310	430	1800	3

Excel formula:

=EFF_NTU_METHOD(3.5, 2.2, 2100, 1900, "S&T", 310, 430, 1800, 3)

Expected output:

{"type":"Double","basicValue":160884,"properties":{"Q":{"type":"Double","basicValue":160884},"UA":{"type":"Double","basicValue":1800},"Cr":{"type":"Double","basicValue":0.568707},"Cmin":{"type":"Double","basicValue":4180},"Cmax":{"type":"Double","basicValue":7350},"effectiveness":{"type":"Double","basicValue":0.320742},"NTU":{"type":"Double","basicValue":0.430622},"Thi":{"type":"Double","basicValue":430},"Tho":{"type":"Double","basicValue":408.111},"Tci":{"type":"Double","basicValue":310},"Tco":{"type":"Double","basicValue":348.489}}}

Python Code

Show Code

from ht.hx import effectiveness_NTU_method as hx_effectiveness_NTU_method

def eff_NTU_method(mh, mc, Cph, Cpc, eff_subtype='counterflow', Thi=None, Tho=None, Tci=None, Tco=None, UA=None, n_shell_tube=None):
    """
    Solve a heat exchanger with the effectiveness-NTU method.

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

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

    Args:
        mh (float): Mass flow rate of hot stream (kg/s).
        mc (float): Mass flow rate of cold stream (kg/s).
        Cph (float): Heat capacity of hot stream (J/kg/K).
        Cpc (float): Heat capacity of cold stream (J/kg/K).
        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'.
        Thi (float, optional): Hot inlet temperature (K). Default is None.
        Tho (float, optional): Hot outlet temperature (K). Default is None.
        Tci (float, optional): Cold inlet temperature (K). Default is None.
        Tco (float, optional): Cold outlet temperature (K). Default is None.
        UA (float, optional): Area heat transfer coefficient product (W/K). Default is None.
        n_shell_tube (int, optional): Number of shell and tube exchangers in series (-). Default is None.

    Returns:
        float: Heat exchanged, with additional properties for temperatures and ratios.
    """
    try:
        results = hx_effectiveness_NTU_method(mh=mh, mc=mc, Cph=Cph, Cpc=Cpc, subtype=eff_subtype, Thi=Thi, Tho=Tho, Tci=Tci, Tco=Tco, UA=UA, n_shell_tube=n_shell_tube)
        if not isinstance(results, dict):
            return "Error: Expected a result dictionary"

        def to_prop(value):
            return {"type": "Double", "basicValue": value}

        return {
            "type": "Double",
            "basicValue": results.get("Q"),
            "properties": {
                "Q": to_prop(results.get("Q")),
                "UA": to_prop(results.get("UA")),
                "Cr": to_prop(results.get("Cr")),
                "Cmin": to_prop(results.get("Cmin")),
                "Cmax": to_prop(results.get("Cmax")),
                "effectiveness": to_prop(results.get("effectiveness")),
                "NTU": to_prop(results.get("NTU")),
                "Thi": to_prop(results.get("Thi")),
                "Tho": to_prop(results.get("Tho")),
                "Tci": to_prop(results.get("Tci")),
                "Tco": to_prop(results.get("Tco"))
            }
        }
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

mh *

Mass flow rate of hot stream (kg/s).

mc *

Mass flow rate of cold stream (kg/s).

Cph *

Heat capacity of hot stream (J/kg/K).

Cpc *

Heat capacity of cold stream (J/kg/K).

eff_subtype Optional Counterflow Parallel Crossflow Crossflow Approximate Crossflow Mixed Cmin Crossflow Mixed Cmax Boiler Condenser Shell and Tube

Exchanger configuration subtype (-).

Thi

Hot inlet temperature (K).

Tho

Hot outlet temperature (K).

Tci

Cold inlet temperature (K).

Tco

Cold outlet temperature (K).

UA

Area heat transfer coefficient product (W/K).

n_shell_tube

Number of shell and tube exchangers in series (-).