# Specific Dissipation Heat Exchanger (TL-TL)

Heat exchanger parameterized by specific dissipation data for systems with two thermal liquid flows

Since R2024a

Libraries:
Simscape / Fluids / Heat Exchangers / Thermal Liquid

## Description

The Specific Dissipation Heat Exchanger (TL-TL) block models the complementary cooling and heating of fluids held briefly in thermal contact across a thin conductive wall. The block uses a simplified model based on the concept of specific dissipation, which is a measure of the heat transfer rate.

### Heat Transfer Model

The block heat transfer model depends on the heat transfer rate defined by the specific dissipation. Specific dissipation is a measure of the heat transfer rate observed when thermal liquid 1 and thermal liquid 2 inlet temperatures differ by one degree. Its product with the inlet temperature difference gives the expected heat transfer rate

`$Q=\xi \left({T}_{\text{In,1}}-{T}_{\text{In,2}}\right),$`

where ξ is specific dissipation and TIn is inlet temperature for thermal liquid 1 (subscript `1`) or thermal liquid 2 (subscript `2`). The specific dissipation is a tabulated function of the mass flow rates into the exchanger through the thermal liquid 1 and thermal liquid 2 inlets:

`$\xi =f\left({\stackrel{˙}{m}}_{\text{1}},{\stackrel{˙}{m}}_{\text{2}}\right)$`

To accommodate reverse flows, the tabulated data can extend over positive and negative flow rates, in which case the inlets can also be thought of as outlets. The data normally derives from measurement of heat transfer rate against temperature in a real prototype:

`$\xi =\frac{Q}{{T}_{\text{In,1}}-{T}_{\text{In,2}}}$`

The heat transfer model, as it relies almost entirely on tabulated data, and as that data normally derives from experiment, requires little detail about the exchanger. Flow arrangement, mixing condition, and number of shell or tube passes, if relevant to the heat exchanger modeled, are assumed to manifest entirely in the tabulated data.

See the Specific Dissipation Heat Transfer block for more detail on the heat transfer calculations.

### Composite Structure

The block is a composite component. A Specific Dissipation Heat Exchanger Interface (TL) block models the thermal liquid flow on side 1 of the heat exchanger. Another models the thermal liquid flow on side 2. A Specific Dissipation Heat Transfer block captures the heat exchanged across the wall between the flows.

## Ports

### Conserving

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Opening for thermal liquid 1 to enter and exit its side of the heat exchanger.

Opening for thermal liquid 1 to enter and exit its side of the heat exchanger.

Opening for thermal liquid 2 to enter and exit its side of the heat exchanger.

Opening for thermal liquid 2 to enter and exit its side of the heat exchanger.

## Parameters

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### Heat Transfer

Mass flow rate of thermal liquid 1 at each breakpoint in the lookup table for the specific heat dissipation table. The block inter- and extrapolates the breakpoints to obtain the specific heat dissipation of the heat exchanger at any mass flow rate. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.

The mass flow rates can be positive, zero, or negative, but they must increase monotonically from left to right. Their number must equal the number of columns in the Specific heat dissipation table parameter. If the table has m rows and n columns, the mass flow rate vector must be n elements long.

Mass flow rate of thermal liquid 2 at each breakpoint in the lookup table for the specific heat dissipation table. The block inter- and extrapolates the breakpoints to obtain the specific heat dissipation of the heat exchanger at any mass flow rate. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.

The mass flow rates can be positive, zero, or negative, but they must increase monotonically from left to right. Their number must equal the number of columns in the Specific heat dissipation table parameter. If the table has m rows and n columns, the mass flow rate vector must be n elements long.

Specific heat dissipation at each breakpoint in its lookup table over the mass flow rates of thermal liquid 1 and thermal liquid 2. The block inter- and extrapolates the breakpoints to obtain the effectiveness at any pair of thermal liquid 1 and thermal liquid 2 mass flow rates. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.

The specific heat dissipation values must be not be negative. They must align from top to bottom in order of increasing mass flow rate in the thermal liquid 1 channel, and from left to right in order of increasing mass flow rate in the thermal liquid 2 channel. The number of rows must equal the size of the Thermal liquid 1 mass flow rate vector parameter, and the number of columns must equal the size of the Thermal liquid 2 mass flow rate vector parameter.

If your heat exchanger data sheet supplies the heat transfer coefficients, multiply the provided heat transfer coefficients by the surface area to calculate the specific dissipation.

Warning condition for specific heat dissipation in excess of minimum heat capacity rate. Heat capacity rate is the product of mass flow rate and specific heat, and its minimum value is the lowest between the flows. This minimum gives the specific dissipation for a heat exchanger with maximum effectiveness and cannot be exceeded. See the Specific Dissipation Heat Transfer block for more detail.

### Thermal Liquid 1|2 Tab

Mass flow rate at each breakpoint in the lookup table for the pressure drop. The block inter- and extrapolates the breakpoints to obtain the pressure drop at any mass flow rate. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.

The mass flow rates can be positive, zero, or negative and they can span across laminar, transient, and turbulent zones. They must, however, increase monotonically from left to right. Their number must equal the size of the Pressure drop vector parameter, with which they are to combine to complete the tabulated breakpoints.

Pressure drop at each breakpoint in its lookup table over the mass flow rate. The block inter- and extrapolates the breakpoints to obtain the pressure drop at any mass flow rate. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.

The pressure drops can be positive, zero, or negative, and they can span across laminar, transient, and turbulent zones. They must, however, increase monotonically from left to right. Their number must equal the size of the Mass flow rate vector parameter, with which they are to combine to complete the tabulated breakpoints.

Absolute temperature established at the inlet in the gathering of the tabulated pressure drops. The reference inflow temperature and pressure determine the fluid density assumed in the tabulated data. During simulation, the ratio of reference to actual fluid densities multiplies the tabulated pressure drop to obtain the actual pressure drop.

Absolute pressure established at the inlet in the gathering of the tabulated pressure drops. The reference inflow temperature and pressure determine the fluid density assumed in the tabulated data. During simulation, the ratio of reference to actual fluid densities multiplies the tabulated pressure drop to obtain the actual pressure drop.

Mass flow rate below which its value is numerically smoothed to avoid discontinuities known to produce simulation errors at zero flow. See the Specific Dissipation Heat Exchanger Interface (TL) block for detail on the calculations.

Volume of fluid in the thermal liquid 1 or thermal liquid 2 flow channel.

Flow area at the inlet and outlet of the thermal liquid 1 or thermal liquid 2 flow channel. Ports in the same flow channel are of the same size.

### Effects and Initial Conditions

Option to model the pressure dynamics in the thermal liquid 1 channel. If you clear this checkbox, the block removes the pressure derivative terms from the component energy and mass conservation equations. The pressure inside the heat exchanger is then reduced to the weighted average of the two port pressures.

Temperature in the thermal liquid 1 channel at the start of simulation.

Pressure in the thermal liquid 1 channel at the start of simulation.

Option to model the pressure dynamics in the thermal liquid 2 channel. If you clear this checkbox, the block removes the pressure derivative terms from the component energy and mass conservation equations. The pressure inside the heat exchanger is then reduced to the weighted average of the two port pressures.

Temperature in the thermal liquid 2 channel at the start of simulation.

Pressure in the thermal liquid 2 channel at the start of simulation.

## Version History

Introduced in R2024a

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