E-NTU Heat Transfer

A detailed model of heat transfer between two main heat transfer fluids.

blockType: EngeeFluids.HeatExchangers.EffectivenessNTU.Interfaces.HeatTransfer

Path in the library:

/Physical Modeling/Fluids/Heat Exchangers/Fundamental Components/E-NTU Heat Transfer

Description

The unit E-NTU Heat Transfer simulates the heat transfer between two heat transfer fluids based on the standard Efficiency-Number of Heat Transfer Units (E-NTU) method. The thermal properties of the fluid are specified explicitly using scalars.

A selection of common heat exchanger configurations is provided in the unit parameters Flow arrangement. These include:

Parallel or counter flow - tube-in-tube with direct flow and counterflow;
Shell and tube - shell-and-tube heat exchanger with one or more passages in the shell;
Cross flow - cross current with mixed and/or unmixed flows;
Generic - effectiveness table - general configuration allows modelling of other heat exchangers based on tabulated efficiency data.

e ntu heat transfer 1 en

Heat flux

The E-NTU model defines the heat flow between heat transfer fluids 1 and 2 in terms of the efficiency parameters :

where

and are the heat fluxes in coolants 1 and 2;
- maximum possible heat flux between heat carriers 1 and 2 under a given set of operating conditions;
- efficiency parameters.

The maximum possible heat flux between the two heat carriers is:

where

- is the minimum value of the flow heat capacity:
and - inlet temperatures of heat transfer fluids 1 and 2;
and - mass flow rates of heat carriers 1 and 2 in the volume at the inlet to the heat exchanger;
and - specific heat capacities at constant pressure of heat carriers 1 and 2.

The Minimum fluid-wall heat transfer coefficient parameter sets the lower limit of allowable values of heat transfer coefficients.

The fluid properties that the block uses in heat transfer calculations are the average value between the value at the inlet and the value in the fluid volume.

Heat exchanger efficiency

Heat exchanger efficiency calculations depend on the heat transfer fluid flow pattern selected in the parameters Flow arrangement. For all types except Generic - effectiveness table, the unit calculates the heat transfer efficiency using analytical expressions written in terms of number of transfer units (NTU) and heat capacity factor. The number of transfer units is defined as:

where

- is the total heat transfer coefficient between heat carriers 1 and 2;
- is the total thermal resistance between heat carriers 1 and 2;
- the total area of the primary and secondary, or finned, heat transfer surfaces.

The heat transfer coefficient is defined as:

The total heat transfer coefficient and thermal resistance used in the calculation , are functions of the heat transfer mechanisms in operation. These mechanisms include convective heat transfer between the heat transfer fluids and the heat exchanger surface and heat conduction through the separating wall [2]:

Where

and are heat transfer coefficients between heat transfer medium 1 and separating wall and between heat transfer medium 2 and separating wall;
and - areas of heat transfer surfaces on the side of heat carriers 1 and 2;
and - thermal resistance of deposits on the side of heat carriers 1 and 2. The thermal resistance of the deposit is defined as the ratio of the deposit coefficient and the area of the heat transfer surface;
- thermal resistance of the separating wall.

e ntu heat transfer 2 en

Below are some analytical expressions used to calculate the heat transfer efficiency [1], depending on the heat exchanger configuration.

Tube-in-tube heat exchanger

For countercurrents, the efficiency parameter is calculated as:

For rectifiers, the efficiency parameter is calculated as:

Shell-and-tube heat exchanger

For a shell and tube heat exchanger with one shell stroke and two, four or six tube strokes, the efficiency parameter for one shell stroke is calculated as:

For shell and tube heat exchanger with shell strokes and , or tube strokes, the efficiency parameter is calculated as:

Cross-flow heat exchanger

For the case of unmixed flows for both heat transfer fluids, the efficiency parameters are calculated as:

For the case of mixed flows for both heat carriers, the efficiency parameter is calculated as:

For the case when the flow c is mixed and c is unmixed, the efficiency parameter is calculated as:

Assumptions and limitations

The flows are single phase flows. Heat transfer is solely due to physical heat. Transfer is limited to the interior of the heat exchanger, with no heat transfer to the environment - the heat exchanger is an adiabatic component.

Ports

Conserving

# H1 — inlet temperature of heat transfer fluid 1
`heat

Details

Non-directional port related to the inlet temperature of the heat transfer medium 1.

Program usage name

thermal_port1

# H2 — inlet temperature of heat transfer fluid 2
`heat

Details

Non-directional port related to the inlet temperature of the heat transfer fluid 2.

Program usage name

thermal_port2

Input

# C1 — heat capacity of coolant 1
scalar

Details

Input port that receives the value of the flow heat capacity of the heat transfer medium 1. The flow heat capacity is the product of the mass flow rate and the specific heat capacity of the heat transfer medium.

Data types	`Float64`.
Complex numbers support	No

# C2 — heat capacity of coolant 2
scalar

Details

Input port that receives the value of the flow heat capacity of the heat transfer medium 2. The flow heat capacity is the product of the mass flow rate and the specific heat capacity of the heat transfer fluid.

Data types	`Float64`.
Complex numbers support	No

# HC1 — heat transfer coefficient of heat transfer medium 1
scalar

Details

Heat transfer coefficient between heat transfer medium 1 and separating wall.

Data types	`Float64`.
Complex numbers support	No

# HC2 — heat transfer coefficient of coolant 2
scalar

Details

Heat transfer coefficient between the heat transfer medium 2 and the separating wall.

Data types	`Float64`.
Complex numbers support	No

Parameters

Common

# Flow arrangement — method of flow equalisation in the heat exchanger
Parallel or counter flow | Shell and tube | Cross flow | Generic - effectiveness table

Details

Configuration of the heat exchanger.

Select Generic - effectiveness table to model other heat exchanger geometries based on tabulated efficiency data.

In the configuration. Parallel or counter flow the relative flow directions of heat transfer fluids 1 and 2 determine whether the heat exchanger will be based on direct flow or counterflow. The flow directions depend on the rest of the model.

Values	`Parallel or counter flow` \| `Shell and tube` \| `Cross flow` \| `Generic - effectiveness table`
Default value	`Parallel or counter flow`
Program usage name	`flow_arrangement_type`
Evaluatable	No

# Number of shell passes — the number of times the flow passes through the casing before exiting

Details

The number of times the flow passes through the shell in a shell-and-tube heat exchanger.

Dependencies

To use this parameter, set the parameters Flow arrangement to . Shell and tube.

Default value	`1`
Program usage name	`shell_count`
Evaluatable	Yes

# Cross flow type — mixing condition in each channel
Both fluids mixed | Both fluids unmixed | Controlled Fluid 1 mixed & Controlled Fluid 2 unmixed | Controlled Fluid 1 unmixed & Controlled Fluid 2 mixed

Details

Type of flow mixing. The heat transfer fluid flow can be mixed or unmixed. The type of flow mixing is used to determine which empirical heat transfer correlations should be used. Mixed flow means that the heat transfer fluid is free to move transversely along the flow path. Unmixed flow means that the heat transfer fluid is restricted to move only along the flow path. For example, the side with ribs is considered unmixed flow.

Dependencies

To use this parameter, set the parameter Flow arrangement to . Cross flow.

Values	`Both fluids mixed` \| `Both fluids unmixed` \| `Controlled Fluid 1 mixed & Controlled Fluid 2 unmixed` \| `Controlled Fluid 1 unmixed & Controlled Fluid 2 mixed`
Default value	`Both fluids mixed`
Program usage name	`cross_flow_type`
Evaluatable	No

# Number of heat transfer units vector, NTU — the number of heat transfer units at each reference point in the look-up table for heat exchanger efficiency

Details

A vector of values , for which the tabular efficiency data is to be specified. The number of heat transfer units is a dimensionless parameter defined as:

where

- is the area of the heat exchange surface;
- total heat transfer coefficient;
- the smallest of the flow heat capacity values for hot and cold coolant.

Dependencies

To use this parameter, set the parameters Flow arrangement to . Generic - effectiveness table.

Default value	`[0.5, 1.0, 2.0, 3.0, 4.0, 5.0]`
Program usage name	`NTU_vector`
Evaluatable	Yes

# Thermal capacity ratio vector, CR — heat capacity coefficient at each reference point in the look-up table to determine the heat exchanger efficiency

Details

A vector of values of heat capacity coefficients for which to specify tabulated efficiency data. The heat capacity coefficient is defined as:

where and are the minimum and maximum value of the flow heat capacity.

Dependencies

To use this parameter, set the parameters Flow arrangement to . Generic - effectiveness table.

Default value	`[0.0, 0.25, 0.5, 0.75, 1.0]`
Program usage name	`C_ratio_vector`
Evaluatable	Yes

# Effectiveness table, E(NTU,CR) — heat exchanger efficiency at each reference point of the search table by number of transfer units and heat capacity coefficient

Details

Matrix to of heat exchanger efficiency values. The rows of the matrix correspond to the values specified in the parameters Number of heat transfer units vector, NTU. The matrix columns correspond to the values specified in the parameter Thermal capacity ratio vector, CR.

Dependencies

To use this parameter, set the Flow arrangement parameters to the value of Generic - effectiveness table.

Default value	`[0.3 0.3 0.3 0.3 0.3; 0.6 0.55 0.5 0.47 0.43; 0.85 0.76 0.68 0.61 0.55; 0.94 0.83 0.72 0.65 0.58; 0.98 0.86 0.75 0.66 0.58; 0.99 0.86 0.75 0.66 0.58]`
Program usage name	`effectiveness_matrix`
Evaluatable	Yes

# Wall thermal resistance — resistance of the wall to heat flow due to heat conduction
K/W

Details

Thermal resistance of the wall separating two heat carriers.

Units	`K/W`
Default value	`0.00016 K/W`
Program usage name	`R_wall`
Evaluatable	Yes

Controlled Fluid 1

# Heat transfer surface area — total area of heat exchange surfaces on the coolant side 1
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

Total surface area on the heat transfer medium side 1 for the heat exchange between cold and hot heat transfer medium.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.01 m^2`
Program usage name	`heat_transfer_area1`
Evaluatable	Yes

# Fouling factor — fouling factor on the coolant side 1
K*m^2/W | deltadegR*ft^2*hr/Btu_IT

Details

An empirical parameter used to quantify the increase in thermal resistance due to dirt deposits on the heat transfer surface.

Units	`Km^2/W` \| `deltadegRft^2*hr/Btu_IT`
Default value	`1e-4 K*m^2/W`
Program usage name	`fouling_factor1`
Evaluatable	Yes

# Minimum fluid-wall heat transfer coefficient — lower limit for the heat transfer coefficient of the heat transfer medium 1
W/(m^2*K) | Btu_IT/(hr*ft^2*deltadegR)

Details

The lowest permissible value of the heat transfer coefficient. If the heat transfer coefficient at port HC1 is less than Minimum fluid-wall heat transfer coefficient, it is equated to this value.

The unit uses the heat transfer coefficient to calculate the heat flow between the heat carriers as described in Heat Flow.

Units	`W/(m^2K)` \| `Btu_IT/(hrft^2*deltadegR)`
Default value	`5.0 W/(m^2*K)`
Program usage name	`alpha1_min`
Evaluatable	Yes

Controlled Fluid 2

# Heat transfer surface area — total area of heat exchange surfaces on the coolant side 2
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

Total surface area on the heat transfer medium side 2 for the heat exchange between cold and hot heat transfer medium.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.01 m^2`
Program usage name	`heat_transfer_area2`
Evaluatable	Yes

# Fouling factor — fouling factor on the coolant side 2
K*m^2/W | deltadegR*ft^2*hr/Btu_IT

Details

An empirical parameter used to quantify the increase in thermal resistance due to dirt deposits on the heat transfer surface.

Units	`Km^2/W` \| `deltadegRft^2*hr/Btu_IT`
Default value	`1e-4 K*m^2/W`
Program usage name	`fouling_factor2`
Evaluatable	Yes

# Minimum fluid-wall heat transfer coefficient — lower limit for the heat transfer coefficient of the heat transfer medium 2
W/(m^2*K) | Btu_IT/(hr*ft^2*deltadegR)

Details

The lowest permissible value of the heat transfer coefficient. If the heat transfer coefficient at port HC2 is less than Minimum fluid-wall heat transfer coefficient, it is equated to this value.

The unit uses the heat transfer coefficient to calculate the heat flow between the heat transfer media as described in Heat Flow.

Units	`W/(m^2K)` \| `Btu_IT/(hrft^2*deltadegR)`
Default value	`5.0 W/(m^2*K)`
Program usage name	`alpha2_min`
Evaluatable	Yes

Literature

Holman J. P. Heat Transfer. 9th ed. New York, NY: McGraw Hill, 2002.
Shah R. K. and D. P. Sekulic. Fundamentals of Heat Exchanger Design. Hoboken, NJ: John Wiley & Sons, 2003.