heat_exchanger_ntu.rst

Heat Exchanger using the NTU Method

pair: idaes.models.unit_models.heat_exchanger_ntu;HeatExchangerNTU

idaes.models.unit_models.heat_exchanger_ntu

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

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. These names are configurable using the hot_side_name and cold_side_name configuration arguments, in which case aliases are assigned to the control volumes and associated Ports using the names provided (note that hot_side and cold_side will always work). 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. By default these are hot_side_inlet, cold_side_inlet, hot_side_outlet, and cold_side_outlet. If the user supplies different hot and cold side names the inlet and outlets are named accordingly.

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	ϵ	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 × c_{p, mol, hot}), (F_mol, hot × c_{p, mol, hot}))

Maximum heat capacitance:

C_max = max((F_mol, hot × c_{p, mol, hot}), (F_mol, hot × c_{p, mol, hot}))

Min and max operators are implemented using smooth approximation using the ϵ_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 = ϵ × C_min × (T_hot − T_cold)

where Q_cold is the heat transferred from the hot side to the cold side, ϵ 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

HeatExchangerNTU

HeatExchangerNTUData