Heat Exchanger Interface (TL)
The thermal boundary between a thermally conductive liquid and the environment.
blockType: EngeeFluids.HeatExchangers.EffectivenessNTU.Interfaces.ThermalLiquid
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Path in the library: |
Description
Block Heat Exchanger Interface (TL) It represents a boundary in the network of a heat-conducting liquid for heat exchange between liquids. The unit simulates the pressure drop and temperature change between the inlet and outlet of a thermally conductive liquid and in combination with the unit E-NTU Heat Transfer simulates the heat flow through the interface of two liquids.
Conservation of mass
The form of the mass conservation equation depends on the dynamic compressibility settings. If the checkbox is unchecked Thermal Liquid 1 dynamic compressibility, then the mass conservation equation will have the following form:
where — mass consumption. Subscripts indicate ports A and B.
If the check box is selected Thermal Liquid 1 dynamic compressibility, then the mass conservation equation will have the following form:
where
-
— pressure of the heat-conducting liquid;
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— temperature of the heat-conducting liquid;
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— coefficient of isobaric thermal expansion of a thermally conductive liquid;
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— isothermal modulus of elasticity of a thermally conductive liquid;
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— mass density of a thermally conductive liquid;
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— the volume of heat-conducting liquid at the boundary of the heat exchanger.
Conservation of momentum
The conservation of momentum at the boundary of the heat exchanger depends on the settings of the dynamic compressibility of the liquid. If the check box is selected Thermal Liquid 1 dynamic compressibility, the conservation of momentum depends explicitly on the internal pressure at the boundary of the heat exchanger. The momentum conservation equation for half the volume in port A has the form:
the momentum conservation equation for half the volume in port B has the form:
where
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and — pressure in ports A and B;
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— pressure in the inner node;
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and — pressure loss between port A and the internal node and between port B and the internal node.
If the checkbox is unchecked Thermal Liquid 1 dynamic compressibility, then the conservation of momentum is calculated directly between ports A and B:
Calculation of pressure losses
The calculation of pressure losses depends on the value of the parameter Pressure loss model. If for the parameter Pressure loss model the value is set Pressure loss coefficient, then the pressure loss in half of the volume adjacent to port A is:
and the pressure loss in half of the volume adjacent to port B is:
where
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and — dynamic viscosity of the liquid in ports A and B;
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— parameter value Pressure loss coefficient;
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— the upper limit of the Reynolds number for laminar flow;
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— the lower limit of the Reynolds number for turbulent flow;
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— hydraulic diameter for pressure loss calculations;
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and — liquid density at ports A and B;
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— the total minimum free flow area.
If for the parameter Pressure loss model the value is set Correlation for flow inside tubes, then the pressure loss in half of the volume adjacent to port A is:
and the pressure loss in half of the volume adjacent to port B is:
where
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— the length of the flow path from the entrance to the exit;
-
— pipe length for calculating equivalent losses;
-
and — Darcy friction coefficients in turbulent mode at ports A and B.
The Darcy coefficient of friction in half of the volume adjacent to port A is equal to:
and the Darcy coefficient of friction in half of the volume adjacent to port B is equal to:
where — absolute roughness of the inner surface.
If for the parameter Pressure loss model the value is set Tabulated data - Darcy friction factor vs. Reynolds number, then the pressure loss in half of the volume adjacent to port A is:
and the pressure loss in half of the volume adjacent to port B is:
where
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— shape coefficient for viscous friction of laminar flow;
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and — the Darcy friction coefficients in ports A and B. The block obtains the coefficients of friction from the tabular data specified relative to the Reynolds number.
If for the parameter Pressure loss model the value is set Tabulated data - Euler number vs. Reynolds number, then the pressure loss in half of the volume adjacent to port A is:
and the pressure loss in half of the volume adjacent to port B is:
where
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— the Euler number at the upper limit of the Reynolds number for laminar flows;
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and — the Euler numbers on ports A and B. The block gets the Euler numbers from the tabular data specified relative to the Reynolds number.
Energy conservation
Energy conservation at the boundary of the heat exchanger depends on the settings of the dynamic compressibility of the liquid. If the check box is selected Thermal Liquid 1 dynamic compressibility, then the energy conservation equation has the form:
where
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— the internal energy of the liquid volume at the boundary of the heat exchanger;
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and — energy flows at ports A and B respectively;
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— heat flow through port H, representing the thermal boundary, into the block.
The derivatives of internal energy are defined as:
and
where — the specific internal energy of a thermally conductive liquid, or the internal energy contained in a unit mass of this liquid.
If the checkbox is not checked Thermal Liquid 1 dynamic compressibility, then the density of a thermally conductive liquid will be considered as a constant. Then the volumetric modulus of elasticity is virtually infinite, and the coefficient of thermal expansion is zero. The derivatives of pressure and temperature in the compressible case are not taken into account, and the energy conservation equation is presented as follows:
where — total internal energy of an incompressible heat-conducting liquid:
Heat transfer ratios
This unit calculates and outputs the value of the heat transfer coefficient between the liquid and the wall. The calculation method depends on the parameter value Heat transfer coefficient model.
If for the parameter Heat transfer coefficient model the value is set Constant heat transfer coefficient, then the heat transfer coefficient has a constant value set by the block parameter:
where
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— the coefficient of heat transfer between the liquid and the wall;
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— parameter value Liquid-wall heat transfer coefficient.
For all other parameter values Heat transfer coefficient model The heat transfer coefficient is defined as the arithmetic mean of the heat transfer coefficients of the ports:
where and — coefficients of heat transfer between the liquid and the wall in ports A and B.
The heat transfer coefficient in port A is equal to:
and the heat transfer coefficient in port B is equal to:
where
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and — Nusselt numbers on ports A and B;
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and — thermal conductivity at ports A and B;
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— hydraulic diameter for heat transfer calculations.
The hydraulic diameter used in heat transfer calculations is defined as:
where
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— the length of the flow path used in heat transfer calculations;
-
— the total surface area of the heat transfer.
Calculation of the Nusselt number
The method of calculating the Nusselt number depends on the value of the parameter Heat transfer coefficient model.
If for the parameter Heat transfer coefficient model the value is set Correlation for flow inside tubes, the Nusselt number in port A will be:
and the Nusselt number in port B:
where
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— parameter value Nusselt number for laminar flow heat transfer;
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and — Prandtl numbers on ports A and B.
If for the parameter Heat transfer coefficient model the value is set Tabulated data - Colburn factor vs. Reynolds number, the Nusselt number in port A will be:
and the Nusselt number in port B:
where
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and — the Colburn factor on ports A and B. The block obtains the Colburn factor from tabular data presented as a function of the Reynolds number;
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and — Reynolds numbers based on hydraulic diameters for calculating heat transfer in ports A and B. These values are defined on port A and B as:
and
If for the parameter Heat transfer coefficient model the value is set Tabulated data - Nusselt number vs. Reynolds number and Prandtl number, the Nusselt number in port A will be:
and the Nusselt number in port B:
Calculation of the hydraulic diameter
The hydraulic diameter used in heat transfer calculations differs from the hydraulic diameter used in pressure loss calculations if the heated perimeter and the friction perimeter do not match. For a tube-in-tube heat exchanger with an annular cross section, the hydraulic diameter for heat transfer calculations is:
and the hydraulic diameter for pressure calculations is:
where
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— the outer diameter of the annular shell;
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— the inner diameter of the ring.
The difference between the outer and inner diameter, shown in orange, represents a thermally conductive liquid. The blue area inside the inner diameter is a liquid that exchanges heat with a heat—conducting liquid.
Ports
Conserving
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A
—
thermal liquid port
thermal liquid
Details
Thermal liquid inlet port.
| Program usage name |
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B
—
thermal liquid port
thermal liquid
Details
Thermal liquid outlet port.
| Program usage name |
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#
H
—
inlet temperatures
`heat
Details
Port related to the inlet temperature of the thermal liquid.
| Program usage name |
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Output
#
C
—
flux heat capacity
scalar
Details
The value of the flow heat capacity of a thermal liquid.
| Data types |
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| Complex numbers support |
No |
#
HC
—
heat transfer coefficient
scalar
Details
The value of the heat transfer coefficient between a thermal liquid flow and a boundary, given as a scalar.
| Data types |
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| Complex numbers support |
No |
Parameters
Parameters
#
Minimum free-flow area —
the cross-sectional area of the hole at its narrowest point
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Details
The total area of the flow, free of obstacles, based on the smallest distance between the pipes or the corrugation step.
| Units |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Hydraulic diameter for pressure loss —
diameter or equivalent channel diameter
m | cm | ft | in | km | mi | mm | um | yd
Details
The hydraulic diameter of the tubes or channels that make up the heat exchange interface. The hydraulic diameter is the ratio of the cross–sectional area of the flow to the perimeter of the channel.
| Units |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Thermal Liquid volume —
total volume of heat-conducting liquid in the channel
l | gal | igal | m^3 | cm^3 | ft^3 | in^3 | km^3 | mi^3 | mm^3 | um^3 | yd^3 | N*m/Pa | N*m/bar | lbf*ft/psi | ft*lbf/psi
Details
The total volume of the heat-conducting liquid contained in the flow channel.
| Units |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Laminar flow upper Reynolds number limit — the beginning of the transition between laminar and turbulent modes
Details
The value of the Reynolds number corresponding to the beginning of the transition from the laminar to the turbulent regime. Above this value, inertial forces begin to dominate, as a result of which the flow passes from laminar to turbulent mode. The default value corresponds to a round tube with a smooth inner surface.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Turbulent flow lower Reynolds number limit — the end of the transition between laminar and turbulent modes
Details
The value of the Reynolds number corresponding to the end of the transition from the laminar to the turbulent regime. Below this value, viscous forces begin to dominate, as a result of which the flow passes from a turbulent to a laminar regime. The default value corresponds to a round tube with a smooth inner surface.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Pressure loss model —
mathematical model for calculating pressure loss due to friction
Pressure loss coefficient | Correlation for flow inside tubes | Tabulated data - Darcy friction factor vs. Reynolds number | Tabulated data - Euler number vs. Reynolds number
Details
A mathematical model for pressure loss due to friction. This parameter determines which expressions to use for calculation and which block parameters to specify as input.
For more information, see Calculation of pressure losses.
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| Default value |
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| Evaluatable |
No |
# Pressure loss coefficient — total loss factor for all flow resistances between ports
Details
The total loss coefficient for all flow resistances in the channel, including wall friction (major losses) and local resistances due to bends, bends and other geometry changes (minor losses).
The loss coefficient is an empirical dimensionless number used to express pressure losses due to friction. It can be calculated based on experimental data or derived from product specifications.
Dependencies
To use this parameter, set for the parameter Pressure loss model meaning Pressure loss coefficient.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Length of flow path from inlet to outlet —
distance traveled from port to port
m | cm | ft | in | km | mi | mm | um | yd
Details
The total distance that the stream must travel between the ports. In multi-pass shell-and-tube heat exchangers, the total distance is the sum of all the passes of the casing. In tube bundles, corrugated plates, and other channels where the flow is divided into parallel branches, this is the distance traveled in one branch. The longer the flow path, the greater the main pressure loss due to wall friction.
Dependencies
To use this parameter, set for the parameter Pressure loss model meaning Correlation for flow inside tubes or Tabulated data - Darcy friction factor vs. Reynolds number.
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Aggregate equivalent length of local resistances —
total local pressure losses, expressed in length
m | cm | ft | in | km | mi | mm | um | yd
Details
Total local pressure losses, expressed in length. The length of the direct channel leads to equivalent losses equal to the sum of the existing local resistances of the bends, tees and joints. The longer the equivalent length, the higher the pressure loss due to local resistances.
Dependencies
To use this parameter, set for the parameter Pressure loss model meaning Correlation for flow inside tubes.
| Units |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Internal surface absolute roughness —
the average height of the roughness on the wall surface that leads to friction losses
m | cm | ft | in | km | mi | mm | um | yd
Details
The average height of the roughness on the wall surface, which leads to viscous friction losses. The higher the average height, the rougher the wall and the greater the pressure loss due to viscous friction. The surface roughness value is used to obtain the Darcy coefficient of friction from the Haaland ratio.
Dependencies
To use this parameter, set for the parameter Pressure loss model meaning Correlation for flow inside tubes.
| Units |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Reynolds number vector for Darcy friction factor — the Reynolds number at each reference point of the Darcy coefficient of friction lookup table
Details
The vector of Reynolds numbers for which it is necessary to determine the Darcy coefficient of friction. The block uses this vector to create a Darcy coefficient of friction lookup table.
Dependencies
To use this parameter, set for the parameter Pressure loss model meaning Tabulated data - Darcy friction factor vs. Reynolds number.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Darcy friction factor vector — the Darcy coefficient of friction at each reference point of the Reynolds number lookup table
Details
The vector of the Darcy friction coefficients corresponding to the values specified in the parameter Reynolds number vector for Darcy friction factor. The block uses this vector to create a Darcy coefficient of friction lookup table.
Dependencies
To use this parameter, set for the parameter Pressure loss model meaning Tabulated data - Darcy friction factor vs. Reynolds number.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Laminar friction constant for Darcy friction factor — correction for pressure loss for flow cross-section under laminar flow conditions
Details
Correction for pressure loss for laminar flow. This parameter is called the shape coefficient and can be used to obtain the Darcy coefficient of friction when calculating pressure losses in the laminar regime. The default value corresponds to cylindrical pipes.
Some additional shape coefficients for non-circular sections can be determined from analytical solutions of the Navier-Stokes equations. An air duct with a square section has a shape coefficient of 56, an air duct with a rectangular section with an aspect ratio of 2:1 has a shape coefficient of 62, and a coaxial pipe has a shape coefficient of 96. The thin channel between the parallel plates also has a shape coefficient of 96.
Dependencies
To use this parameter, set for the parameter Pressure loss model meaning Correlation for flow inside tubes.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Reynolds number vector for Euler number — the Reynolds number at each reference point of the Euler number lookup table
Details
The vector of Reynolds numbers for which it is necessary to determine the Euler number. The block uses this vector to create an Euler number lookup table.
Dependencies
To use this parameter, set for the parameter Pressure loss model meaning Tabulated data - Euler number vs. Reynolds number.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Euler number vector — the Euler number at each reference point of the Reynolds number lookup table
Details
The vector of Euler numbers corresponding to the values specified in the parameter Reynolds number vector for Euler number. The block uses this vector to create an Euler number lookup table.
Dependencies
To use this parameter, set for the parameter Pressure loss model meaning Tabulated data - Euler number vs. Reynolds number.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Heat transfer coefficient model —
mathematical model for heat exchange between a heat carrier and a wall
Constant heat transfer coefficient | Correlation for flow inside tubes | Tabulated data - Colburn factor vs. Reynolds number | Tabulated data - Nusselt number vs. Reynolds number and Prandtl number
Details
A mathematical model used to calculate the heat flow between liquids in a heat exchanger. You can assume a constant heat transfer coefficient, use an empirical relationship for the flow inside the pipes, or specify tabular data for the Colburn number or the Nusselt number.
For more information, see Calculation of the Nusselt number.
| Values |
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| Default value |
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| Program usage name |
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| Evaluatable |
No |
#
Liquid-wall heat transfer coefficient —
the coefficient of heat transfer during convection between the coolant and the wall
W/(m^2*K) | Btu_IT/(hr*ft^2*deltadegR)
Details
The heat transfer coefficient for convection between the coolant and the wall.
Dependencies
To use this parameter, set for the parameter Heat transfer coefficient model meaning Constant heat transfer coefficient.
| Units |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Heat transfer surface area —
the effective surface area used in heat transfer between the heat carrier and the wall
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Details
The effective surface area used in heat transfer between heat carriers in a heat exchanger.
| Units |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Nusselt number for laminar flow heat transfer — the constant value of the Nusselt number for laminar flow
Details
The constant value of the Nusselt number for laminar flows. This parameter allows you to calculate convective heat fluxes in laminar flows. The value of the Nusselt number depends on the geometry of the component. The default value corresponds to a cylindrical tube.
Dependencies
To use this parameter, set for the parameter Heat transfer coefficient model meaning Correlation for flow inside tubes.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Reynolds number vector for Colburn factor — the Reynolds number at each reference point of the Colburn factor lookup table
Details
The vector of Reynolds numbers for which it is necessary to determine the Colburn factor. The block uses this vector to create a Colburn factor lookup table. The number of values in this vector must be equal to the dimension of the parameter. Colburn factor vector to calculate the reference points of the table.
Dependencies
To use this parameter, set for the parameter Heat transfer coefficient model meaning Tabulated data - Colburn factor vs. Reynolds number.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Colburn factor vector — the Colburn factor at each reference point of the Reynolds number lookup table
Details
Vector of Colburn factors corresponding to the values specified in the parameter Reynolds number vector for Colburn factor. The block uses this vector to create a Colburn factor lookup table.
Dependencies
To use this parameter, set for the parameter Heat transfer coefficient model meaning Tabulated data - Colburn factor vs. Reynolds number.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Reynolds number vector for Nusselt number — the Reynolds number at each reference point of the Nusselt number lookup table
Details
The vector of Reynolds numbers for which it is necessary to determine the Nusselt number. The block uses this vector to create a Nusselt number lookup table.
Dependencies
To use this parameter, set for the parameter Heat transfer coefficient model meaning Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Prandtl number vector for Nusselt number — the Prandtl number at each reference point of the Nusselt number lookup table
Details
The vector of Prandtl numbers for which it is necessary to determine the Nusselt number. The block uses this vector to create a Nusselt number lookup table.
Dependencies
To use this parameter, set for the parameter Heat transfer coefficient model meaning Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Nusselt number table, Nu(Re,Pr) — the Nusselt number at each reference point of the Reynolds-Prandtl number lookup table
Details
The matrix of Nusselt numbers corresponding to the values specified in the parameters Reynolds number vector for Nusselt number and Prandtl number vector for Nusselt number. The block uses this matrix to create a Nusselt number lookup table.
Dependencies
To use this parameter, set for the parameter Heat transfer coefficient model meaning Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Length of flow path for heat transfer —
the characteristic length traveled during heat transfer between the coolant and the wall
m | cm | ft | in | km | mi | mm | um | yd
Details
The characteristic length for heat transfer between the heat carrier and the wall.
Dependencies
To use this parameter, set for the parameter Heat transfer coefficient model meaning Tabulated data - Colburn factor vs. Reynolds number or Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.
| Units |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
Effects and Initial Conditions
# Thermal Liquid 1 dynamic compressibility — compressibility of the liquid in the heat exchanger
Details
An option for simulating pressure changes inside the heat exchanger. If this option is unchecked, then the pressure derivatives are not taken into account in the equations of conservation of energy and mass. The pressure inside the heat exchanger is defined as the average of the two port pressures.
| Default value |
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| Program usage name |
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| Evaluatable |
No |
#
Thermal Liquid initial temperature —
the initial temperature of the heat-conducting liquid
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Details
The temperature of the heat-conducting liquid at the beginning of the simulation.
| Units |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Thermal Liquid initial pressure —
initial pressure of the heat-conducting liquid
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
The pressure of the heat-conducting liquid at the beginning of the simulation.
| Units |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |