# Heat Exchanger using the NTU Method¶

The HeatExchangerNTU model can be imported from idaes.generic_models.unit_models, and models a heat exchanger using the effectiveness-NTU method.

## Degrees of Freedom¶

Aside from the inlet conditions, an NTU heat exchanger model has three degrees of freedom which must be fixed for it to be fully specified. Additionally, users may include a pressure change in the unit which adds two additional degrees of freedom.

Standard design variables are:

• heat transfer area,

• heat transfer coefficient, and

• effectiveness.

If pressure change is included, additional degrees of freedom are:

• hot and cold side pressure changes.

## Model Structure¶

The HeatExchanger model contains two ControlVolume0DBlock blocks named hot_side and the cold side. The sign convention is that duty is positive for heat flowing from the hot side to the cold side. Aside from the sign convention there is no requirement that the hot side be hotter than the cold side.

The HeatExchanger has two inlet ports and two outlet ports, named hot_inlet, cold_inlet, hot_outlet, and cold_outlet.

## Variables¶

Variable

Symbol

Index Sets

Doc

heat_duty

$$Q$$

t

Heat transferred from hot side to the cold side

area

$$A$$

None

Heat transfer area

heat_transfer_coefficient

$$U$$

t

Heat transfer coefficient

effectiveness

$$\epsilon$$

t

Effectiveness factor

## Expressions¶

The following Expressions are constructed by the model and can be used in correlations to determine the effectiveness factor.

Minimum heat capacitance:

$C_{min} = min((F_{mol, hot} \times c_{p, mol, hot}), (F_{mol, hot} \times c_{p, mol, hot}))$

Maximum heat capacitance:

$C_{max} = max((F_{mol, hot} \times c_{p, mol, hot}), (F_{mol, hot} \times c_{p, mol, hot}))$

Min and max operators are implemented using smooth approximation using the $$\epsilon_{cmin}$$ parameter.

Heat capacitance ratio:

$C_{ratio} = \frac{C_{min}}{C_{max}}$

Number of theoretical heat transfer units:

$NTU = \frac{U \times A}{C_{min}}$

## Constraints¶

The effectiveness-NTU method is a method to approximate the heat transferred in a heat exchanger using the following calculation:

$Q_{cold} = \epsilon \times C_{min} \times (T_{hot} - T_{cold})$

where $$Q_{cold}$$ is the heat transferred from the hot side to the cold side, $$\epsilon$$ is the effectiveness factor for the heat exchanger, $$C_{min}$$ is the minimum heat capacitance between the hot and cold inlet streams and $$T_{hot}$$ and $$T_{cold}$$ are the temperatures of the hot and cold inlet streams respectively.

Additionally, and overall energy balance constraint is written:

$Q_{hot} = -Q_{cold}$

## Class Documentation¶

class idaes.generic_models.unit_models.heat_exchanger_ntu.HeatExchangerNTU(*args, **kwds)
Parameters
• rule (function) – A rule function or None. Default rule calls build().

• concrete (bool) – If True, make this a toplevel model. Default - False.

• ctype (class) – Pyomo ctype of the block. Default - pyomo.environ.Block

• default (dict) –

Default ProcessBlockData config

Keys
dynamic

Indicates whether this model will be dynamic or not, default = useDefault. Valid values: { useDefault - get flag from parent (default = False), True - set as a dynamic model, False - set as a steady-state model.}

has_holdup

Indicates whether holdup terms should be constructed or not. Must be True if dynamic = True, default - False. Valid values: { useDefault - get flag from parent (default = False), True - construct holdup terms, False - do not construct holdup terms}

hot_side

Hot fluid config arguments

material_balance_type

Indicates what type of mass balance should be constructed, default - MaterialBalanceType.useDefault. Valid values: { MaterialBalanceType.useDefault - refer to property package for default balance type **MaterialBalanceType.none - exclude material balances, MaterialBalanceType.componentPhase - use phase component balances, MaterialBalanceType.componentTotal - use total component balances, MaterialBalanceType.elementTotal - use total element balances, MaterialBalanceType.total - use total material balance.}

energy_balance_type

Indicates what type of energy balance should be constructed, default - EnergyBalanceType.useDefault. Valid values: { EnergyBalanceType.useDefault - refer to property package for default balance type **EnergyBalanceType.none - exclude energy balances, EnergyBalanceType.enthalpyTotal - single enthalpy balance for material, EnergyBalanceType.enthalpyPhase - enthalpy balances for each phase, EnergyBalanceType.energyTotal - single energy balance for material, EnergyBalanceType.energyPhase - energy balances for each phase.}

momentum_balance_type

Indicates what type of momentum balance should be constructed, default - MomentumBalanceType.pressureTotal. Valid values: { MomentumBalanceType.none - exclude momentum balances, MomentumBalanceType.pressureTotal - single pressure balance for material, MomentumBalanceType.pressurePhase - pressure balances for each phase, MomentumBalanceType.momentumTotal - single momentum balance for material, MomentumBalanceType.momentumPhase - momentum balances for each phase.}

has_pressure_change

Indicates whether terms for pressure change should be constructed, default - False. Valid values: { True - include pressure change terms, False - exclude pressure change terms.}

property_package

Property parameter object used to define property calculations default - useDefault. Valid values: { useDefault - use default package from parent model or flowsheet, PhysicalParameterObject - a PhysicalParameterBlock object.}

property_package_args

A ConfigBlock with arguments to be passed to property block(s) and used when constructing these, default - None. Valid values: { see property package for documentation.}

cold_side

Cold fluid config arguments

material_balance_type

Indicates what type of mass balance should be constructed, default - MaterialBalanceType.useDefault. Valid values: { MaterialBalanceType.useDefault - refer to property package for default balance type **MaterialBalanceType.none - exclude material balances, MaterialBalanceType.componentPhase - use phase component balances, MaterialBalanceType.componentTotal - use total component balances, MaterialBalanceType.elementTotal - use total element balances, MaterialBalanceType.total - use total material balance.}

energy_balance_type

Indicates what type of energy balance should be constructed, default - EnergyBalanceType.useDefault. Valid values: { EnergyBalanceType.useDefault - refer to property package for default balance type **EnergyBalanceType.none - exclude energy balances, EnergyBalanceType.enthalpyTotal - single enthalpy balance for material, EnergyBalanceType.enthalpyPhase - enthalpy balances for each phase, EnergyBalanceType.energyTotal - single energy balance for material, EnergyBalanceType.energyPhase - energy balances for each phase.}

momentum_balance_type

Indicates what type of momentum balance should be constructed, default - MomentumBalanceType.pressureTotal. Valid values: { MomentumBalanceType.none - exclude momentum balances, MomentumBalanceType.pressureTotal - single pressure balance for material, MomentumBalanceType.pressurePhase - pressure balances for each phase, MomentumBalanceType.momentumTotal - single momentum balance for material, MomentumBalanceType.momentumPhase - momentum balances for each phase.}

has_pressure_change

Indicates whether terms for pressure change should be constructed, default - False. Valid values: { True - include pressure change terms, False - exclude pressure change terms.}

property_package

Property parameter object used to define property calculations default - useDefault. Valid values: { useDefault - use default package from parent model or flowsheet, PhysicalParameterObject - a PhysicalParameterBlock object.}

property_package_args

A ConfigBlock with arguments to be passed to property block(s) and used when constructing these, default - None. Valid values: { see property package for documentation.}

• initialize (dict) – ProcessBlockData config for individual elements. Keys are BlockData indexes and values are dictionaries described under the “default” argument above.

• idx_map (function) – Function to take the index of a BlockData element and return the index in the initialize dict from which to read arguments. This can be provided to overide the default behavior of matching the BlockData index exactly to the index in initialize.

Returns

(HeatExchangerNTU) New instance

class idaes.generic_models.unit_models.heat_exchanger_ntu.HeatExchangerNTUData(component)[source]

Heat Exchanger Unit Model using NTU method.

build()[source]

General build method for UnitModelBlockData. This method calls a number of sub-methods which automate the construction of expected attributes of unit models.

Inheriting models should call super().build.

Parameters

None

Returns

None

initialize(hot_side_state_args=None, cold_side_state_args=None, outlvl=0, solver=None, optarg=None, duty=None)[source]

Heat exchanger initialization method.

Parameters
• hot_side_state_args – a dict of arguments to be passed to the property initialization for the hot side (see documentation of the specific property package) (default = None).

• cold_side_state_args – a dict of arguments to be passed to the property initialization for the cold side (see documentation of the specific property package) (default = None).

• outlvl – sets output level of initialization routine

• optarg – solver options dictionary object (default=None, use default solver options)

• solver – str indicating which solver to use during initialization (default = None, use default solver)

• duty – an initial guess for the amount of heat transfered. This should be a tuple in the form (value, units), (default = (1000 J/s))

Returns

None