/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.
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.
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:
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.
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.
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.
#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;
С - 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.
#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
K*m^2/W | deltadegR*ft^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^2*K) | Btu_IT/(hr*ft^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.
#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
K*m^2/W | deltadegR*ft^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^2*K) | Btu_IT/(hr*ft^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.