Heat exchanger for systems with thermal liquid and controlled flows

**Library:**Simscape / Fluids / Fluid Network Interfaces / Heat Exchangers

The Heat Exchanger (TL) block models the cooling and
heating of fluids through conduction over a thin wall. The properties of a single-phase
thermal liquid are defined on the **Thermal Liquid** tab. The second fluid is
a controlled fluid, which is specified only by the user-defined parameters on the
**Controlled Fluid** tab. It does not receive any properties from the
domain fluid network. The heat exchange between the fluids is based on the thermal liquid
sensible heat.

Two heat transfer models are available:

The E-NTU Model

The Simple Model

To set one of these models, right-click the block and select **Simscape** > **Block Choices**.

`E-NTU Model`

VariantThe E-NTU model, based on the Effectiveness-NTU method, is the block default variant. Steady-state heat transfer is determined based on a coefficient relating ideal to real losses in the system:

$${Q}_{\text{Act}}=\u03f5{Q}_{\text{Max}},$$

where

*Q*_{Act}the actual heat transfer rate.*Q*_{Max}is the ideal heat transfer rate.*ε*is the heat exchanger effectiveness, which is based on the ratio of heat capacity rates, $$\frac{{C}_{\text{Min}}}{{C}_{\text{Max}}}$$, and the exchanger Number of Transfer Units:$$NTU=\frac{1}{R{C}_{\text{Min}}},$$

where

*R*is the overall thermal resistance, which is discussed in Thermal Resistance below.*C*_{Min}is the lesser heat capacity rate of the two fluids and*C*_{Max}is the greater heat capacity rate of the two fluids. The heat capacity rate is calculated as $$C={c}_{\text{p}}\dot{m}.$$

Additionally, the exchanger effectiveness depends on the number of passes between the
fluids and the fluid mixing conditions. For different parameterizations of
*ε*, see E-NTU Heat Transfer. Connect an E-NTU
Heat Transfer block to a Heat Exchanger (TL) block to specify the heat
transfer properties in with the E-NTU method.

Use the **Flow arrangement** parameter to define the flow
configuration in terms of pipe orientation or effectiveness tables. When using the
shell-and-tube configuration, you can select the number of passes in the exchanger. A
multi-pass exchanger resembles the image below.

A single-pass exchanger resembles the image below.

Other flow arrangements are possible through a generic parameterization by tabulated effectiveness data. This table does not require specific heat exchanger configuration details, such as flow arrangement, mixing, and passes, for modeling the heat transfer between the fluids.

Use the **Cross flow type** parameter to model flows that are not
restricted by baffles or walls, which homogenizes fluid temperature along the direction of
flow of the second fluid and varies perpendicular to the second fluid flow. Unmixed flows
vary in temperature both along and perpendicular to the flow direction of the second
fluid. An example of a heat exchanger with one mixed and one unmixed fluid resembles the
configuration below.

A heat exchanger with two unmixed fluids resembles the configuration below.

In counter and parallel flow arrangements, longitudinal temperature variation in one fluid results in a longitudinal change in temperature variation in the second fluid and mixing is not taken into account.

Shell-and-tube exchangers with multiple passes (**iv.b**-**e** in the figure for 2, 3, and 4
passes) are the most effective type of heat exchanger. For single-pass heat exchangers,
the counter-flow configuration (**ii**) is the most
effective, and parallel flow (**i**) is the least.

Cross-flow exchangers are intermediate in effectiveness, with mixing condition playing
a factor. They are most effective when both flows are unmixed (**iii.a**) and least effective when both flows are mixed (**iii.b**). Mixing just the flow with the smallest heat capacity rate (**iii.c**) lowers the effectiveness more than mixing just the flow
with the largest heat capacity rate (**iii.d**).

The overall thermal resistance, *R*, is the sum of the local
resistances to heat transfer due to convection, conduction, and fouling along the heat
exchanger walls:

$$R=\frac{1}{{U}_{Th}{A}_{\text{Th}}}+\frac{{F}_{Th}}{{A}_{\text{Th}}}+{R}_{\text{W}}+\frac{{F}_{\text{C}}}{{A}_{\text{C}}}+\frac{1}{{U}_{C}{A}_{\text{C}}},$$

where:

*U*_{Th}is the heat transfer coefficient between the thermal liquid and the wall.*U*_{C}is the heat transfer coefficient between the controlled fluid and the wall, which is received as a physical signal at port**HC2**.*F*_{Th}is the thermal liquid**Fouling factor**.*F*_{C}is the controlled fluid**Fouling factor**.*A*_{Th}is the thermal liquid**Heat transfer surface area**.*A*_{C}is the controlled fluid**Heat transfer surface area**.*R*_{W}is the**Wall thermal resistance**.

The heat transfer coefficients depend on the heat exchanger configuration and fluid properties. See the E-NTU Heat Transfer reference page for more information.

When the Heat Exchanger (TL) block employs the `E-NTU Model`

variant, it is a composite of the Heat
Exchanger Interface (TL) and E-NTU
Heat Transfer blocks:

`Simple Model`

VariantHeat transfer by the simple model is based on specific dissipation:

$$Q=\xi ({T}_{\text{In,Th}}-{T}_{\text{In,C}}),$$

where:

*ξ*is specific dissipation, which is a function of the mass flow rates of the thermal and controlled liquids.*T*_{In,Th}is the thermal liquid inlet temperature.*T*_{In,C}is the controlled liquid inlet temperature.

The simple model is based on linear interpolation of user-provided tabulated data and does not capture individual features of the heat exchanger.

When the Heat Exchanger (TL) block employs the `Simple Model`

variant, it is a composite of the Simple Heat Exchanger
Interface (TL) and Specific Dissipation Heat
Transfer blocks:

E-NTU Heat Transfer | Heat Exchanger Interface (TL) | Simple Heat Exchanger Interface (TL) | Specific Dissipation Heat Transfer