System-Level Heat Exchanger (TL-MA)

Heat exchanger based on performance data between thermal liquid and moist air networks

Since R2022a

• 

Libraries:
Simscape / Fluids / Heat Exchangers / Thermal Liquid - Moist Air

Description

The System-Level Heat Exchanger (TL-MA) block models a heat exchanger based on performance data between a thermal liquid network and a moist air network.

The block uses performance data from the heat exchanger datasheet, rather than the detailed geometry of the exchanger. You can adjust the size and performance of the heat exchanger during design iterations, or model heat exchangers with uncommon geometries. You can also use this block to model heat exchangers with a certain level of performance at an early design stage, when detailed geometry data is not yet available.

You parameterize the block by the nominal operating condition. The heat exchanger is sized to match the specified performance at the nominal operating condition at steady state.

The Moist Air 2 side models water vapor condensation based on convective water vapor mass transfer with the heat transfer surface. Condensed water is removed from the moist air flow.

This block is similar to the Heat Exchanger (TL-MA) block, but uses a different parameterization model. The table compares the two blocks:

Heat Exchanger (TL-MA)	System-Level Heat Exchanger (TL-MA)
Block parameters are based on the heat exchanger geometry	Block parameters are based on performance and operating conditions
Heat exchanger geometry may be limited by the available geometry parameter options	Model is independent of the specific heat exchanger geometry
You can adjust the block for different performance requirements by tuning geometry parameters, such as fin sizes and tube lengths	You can adjust the block for different performance requirements by directly specifying the desired heat and mass flow rates
You can select between parallel, counter, or cross flow configurations	You can select between parallel, counter, or cross-flow arrangement at nominal operating conditions to help with sizing
Predictively accurate results over a wide range of operating conditions, subject to the applicability of the E-NTU equations and the heat transfer coefficient correlations	Very accurate results around the specified operating condition; accuracy may decrease far away from the specified operating conditions
Heat transfer calculations account for the variation of temperature along the flow path by using the E-NTU model	Heat transfer calculations approximate the variation of temperature along the flow path by dividing it into three segments
Accounts for water vapor condensation and the latent heat on the moist air flow	Accounts for water vapor condensation and the latent heat on the moist air flow
Does not model the wall thermal mass; you can approximate the effect by connecting a pipe block with a thermal mass downstream	Includes an option to model the wall thermal mass

Heat Transfer

The block divides the moist air flow and the thermal liquid flow each into three segments of equal size and calculates heat transfer between the fluids is in each segment. For simplicity, the equation in this section are for one segment.

If you clear the Wall thermal mass check box, then the heat balance in the heat exchanger is

$$Q_{seg,TL}+Q_{seg,MA}=0,$$

where:

• Q_seg,TL is the heat flow rate from the wall that is the heat transfer surface to the thermal liquid in the segment.

• Q_seg,MA is the heat flow rate from the wall to the moist air in the segment.

If you select Wall thermal mass, then the heat balance in the heat exchanger is

$$Q_{seg,TL}+Q_{seg,MA}=-\frac{M_{wall}{c}_{p_{wall}}}{N}\frac{d{T}_{seg,wall}}{dt},$$

where:

• M_wall is the mass of the wall.

• c_pwall is the specific heat of the wall.

• N = 3 is the number of segments.

• T_seg,wall is the average wall temperature in the segment.

• t is time.

The heat flow rate from the wall to the thermal liquid in the segment is

$$Q_{seg,TL}=U{A}_{seg,TL}\left(T_{seg,wall}-T_{seg,TL}\right),$$

where:

• UA_seg,TL is the heat transfer conductance for the thermal liquid in the segment.

• T_seg,TL is the average liquid temperature in the segment.

The heat flow rate from the wall to the moist air in the segment is

$$Q_{seg,MA}=\frac{U{A}_{seg,MA}}{{\overline{c}}_{p_{seg,MA}}}\left({\overline{h}}_{seg,wall}-{\overline{h}}_{seg,MA}\right)+{\dot{m}}_{w,seg,cond}{h}_{l,wall},$$

where:

• UA_seg,MA is the heat transfer conductance for the moist air in the segment.

• $${\overline{c}}_{p_{seg,MA}}$$ is the moist air mixture specific heat per unit mass of dry air and trace gas in the segment.

• $${\overline{h}}_{seg,wall}$$ is the moist air mixture enthalpy per unit mass of dry air and trace gas at the average wall segment temperature.

• $${\overline{h}}_{seg,MA}$$ is the moist air mixture enthalpy per unit mass of dry air and trace gas in the segment.

• $${\dot{m}}_{w,seg,cond}$$ is the rate of water vapor condensation on the wall surface.

• h_l,wall is the specific enthalpy of liquid water at the average wall segment temperature.

Using mixture enthalpy in this equation accounts for both differences in temperature and differences in humidity due to condensation [3].

Note

For the moist air quantities, the bar above the symbols indicates that they are quantities for mixture divided by the mass of dry air and trace gas only, as opposed to dividing by the mass of the whole mixture. The whole mixture includes dry air, water vapor, and trace gas.

Thermal Liquid Heat Transfer Correlation

The heat transfer conductance is

$$U{A}_{seg,TL}=a_{TL}{\left({\mathrm{Re}}_{seg,TL}\right)}^{b_{TL}}{\left({\mathrm{Pr}}_{seg,TL}\right)}^{c_{TL}}{k}_{seg,TL}\frac{G_{TL}}{N},$$

where:

• a_TL, b_TL, and c_TL are the coefficients of the Nusselt number correlation. These coefficients are block parameters in the Correlation Coefficients section.

• Re_seg,TL is the average Reynolds number for the segment.

• Pr_seg,TL is the average Prandtl number for the segment.

• k_seg,TL is the average thermal conductivity for the segment.

• G_TL is the geometry scale factor for the thermal liquid side of the heat exchanger. The block calculates the geometry scale factor so that the total heat transfer over all segments matches the specified performance at the nominal operating conditions.

The average Reynolds number is

$${\mathrm{Re}}_{seg,\text{TL}}=\frac{{\dot{m}}_{seg,\text{TL}}{D}_{ref,\text{TL}}}{{\mu }_{seg,\text{TL}}{S}_{ref,\text{TL}}},$$

where:

• $${\dot{m}}_{seg,\text{TL}}$$ is the mass flow rate through the segment.

• μ_seg,TL is the average dynamic viscosity for the segment.

• D_ref,TL is an arbitrary reference diameter.

• S_ref,TL is an arbitrary reference flow area.

Note

The D_ref,TL and S_ref,TL terms are included in this equation for unit calculation purposes only, to make Re_seg,TL nondimensional. The values of D_ref,TL and S_ref,TL are arbitrary because the G_TL calculation overrides these values.

Moist Air Heat Transfer Correlation

The heat transfer conductance is

$$U{A}_{seg,MA}=a_{MA}{\left({\mathrm{Re}}_{seg,MA}\right)}^{b_{MA}}{\left({\mathrm{Pr}}_{seg,MA}\right)}^{c_{MA}}{k}_{seg,MA}\frac{G_{MA}}{N},$$

where:

• a_MA, b_MA, and c_MA are the coefficients of the Nusselt number correlation. These coefficients are block parameters in the Correlation Coefficients section.

• Re_seg,MA is the average Reynolds number for the segment.

• Pr_seg,MA is the average Prandtl number for the segment.

• k_seg,MA is the average thermal conductivity for the segment.

• G_MA is the geometry scale factor for the moist air side of the heat exchanger. The block calculates the geometry scale factor so that the total heat transfer over all segments matches the specified performance at the nominal operating conditions.

The average Reynolds number is

$${\mathrm{Re}}_{seg,MA}=\frac{{\dot{m}}_{seg,MA}{D}_{ref,MA}}{{\mu }_{seg,MA}{S}_{ref,MA}},$$

where:

• $${\dot{m}}_{seg,MA}$$ is the mass flow rate through the segment.

• μ_seg,MA is the average dynamic viscosity for the segment.

• D_ref,MA is an arbitrary reference diameter.

• S_ref,MA is an arbitrary reference flow area.

Note

The D_ref,MA and S_ref,MA terms are included in this equation for unit calculation purposes only, to make Re_seg,MA nondimensional. The values of D_ref,MA and S_ref,MA are arbitrary because the G_MA calculation overrides these values.

Moist Air Condensation

The equation describing the heat flow rate from the wall to the moist air in the segment (the last equation in the Heat Transfer section) uses the average moist air mixture enthalpy, $${\overline{h}}_{seg,MA}$$, and the wall segment moist air mixture enthalpy, $${\overline{h}}_{seg,wall}$$.

The average moist air mixture enthalpy is based on the temperature and humidity of the moist air flow through the segment:

$${\overline{h}}_{seg,MA}=h_{seg,ag,MA}+W_{seg,MA}{h}_{seg,w,MA},$$

where:

• h_seg,ag,MA is the average specific enthalpy of dry air and trace gas for the segment.

• h_seg,w,MA is the average specific enthalpy of water vapor for the segment.

• W_seg,MA is the humidity ratio of the segment.

The wall segment moist air mixture enthalpy is based on the temperature and humidity at the wall segment:

$${\overline{h}}_{seg,wall}=h_{seg,ag,wall}+W_{seg,wall}{h}_{seg,w,wall},$$

where:

• h_seg,ag,wall is the specific enthalpy of dry air and trace gas at the wall segment temperature.

• h_seg,w,wall is the specific enthalpy of water vapor at the wall segment temperature.

• W_seg,wall is the humidity ratio at the wall segment:

  $$W_{seg,wall}=\min \left(W_{seg,MA},W_{seg,s,wall}\right),$$

  where W_seg,s,wall is the saturated humidity ratio at the wall segment temperature. In other words, the humidity ratio at the wall is the same as the humidity ratio of the moist air flow but not more than the maximum that can be supported at the wall segment temperature.

When W_seg,s,wall < W_seg,MA, water vapor condensation occurs on the wall surface. The rate of water vapor condensation is

$${\dot{m}}_{w,seg,cond}=\frac{U{A}_{seg,MA}}{{\overline{c}}_{p_{seg,MA}}}\left(W_{seg,MA}-W_{seg,wall}\right).$$

The block assumes that the condensed water is drained from the wall surface and is thus removed from the moist air flow downstream.

Pressure Loss

The pressure losses on the thermal liquid side are

$$\begin{array}{l}{p}_{A,\text{TL}}-p_{\text{TL}}=\frac{K_{\text{TL}}}{2}\frac{{\dot{m}}_{A,\text{TL}}\sqrt{{\dot{m}}^2{}_{A,\text{TL}}+{\dot{m}}^2{}_{thres,\text{TL}}}}{2{\rho }_{avg,2P}}\\ p_{B,\text{TL}}-p_{\text{TL}}=\frac{K_{\text{TL}}}{2}\frac{{\dot{m}}_{B,\text{TL}}\sqrt{{\dot{m}}^2{}_{B,\text{TL}}+{\dot{m}}^2{}_{thres,\text{TL}}}}{2{\rho }_{avg,\text{TL}}}\end{array}$$

where:

• p_A,TL and p_B,TL are the pressures at ports A2 and B2, respectively.

• p_TL is internal thermal liquid pressure at which the heat transfer is calculated.

• $${\dot{m}}_{A,TL}$$ and $${\dot{m}}_{B,TL}$$ are the mass flow rates into ports A2 and B2, respectively.

• ρ_avg,TL is the average thermal liquid density over all segments.

• $${\dot{m}}_{thres,TL}$$ is the laminar threshold for pressure loss, approximated as 1e-4 of the nominal mass flow rate. The block calculates the pressure loss coefficient, K_TL, so that p_A,TL – p_B,TL matches the nominal pressure loss at the nominal mass flow rate.

The pressure losses on the moist air side are

$$\begin{array}{l}{p}_{A,MA}-p_{MA}=\frac{K_{MA}}{2}\frac{{\dot{m}}_{A,MA}\sqrt{{\dot{m}}^2{}_{A,MA}+{\dot{m}}^2{}_{thres,MA}}}{2{\rho }_{avg,2P}}\\ p_{B,MA}-p_{MA}=\frac{K_{MA}}{2}\frac{{\dot{m}}_{B,MA}\sqrt{{\dot{m}}^2{}_{B,MA}+{\dot{m}}^2{}_{thres,MA}}}{2{\rho }_{avg,MA}}\end{array}$$

where:

• p_A,MA and p_B,MA are the pressures at ports A2 and B2, respectively.

• p_MA is internal moist air pressure at which the heat transfer is calculated.

• $${\dot{m}}_{A,MA}$$ and $${\dot{m}}_{B,MA}$$ are the mass flow rates into ports A2 and B2, respectively.

• ρ_avg,MA is the average moist air density over all segments.

• $${\dot{m}}_{thres,MA}$$ is the laminar threshold for pressure loss, approximated as 1e-4 of the nominal mass flow rate. The block calculates the pressure loss coefficient, K_MA, so that p_A,MA – p_B,MA matches the nominal pressure loss at the nominal mass flow rate.

Thermal Liquid Mass and Energy Conservation

The mass conservation for the overall thermal liquid flow is

$$\left(\frac{d{p}_{TL}}{dt}{\displaystyle \sum _{segments}\left(\frac{\partial {\rho }_{seg,TL}}{\partial p}\right)}+{\displaystyle \sum _{segments}\left(\frac{d{T}_{seg,TL}}{dt}\frac{\partial {\rho }_{seg,TL}}{\partial T}\right)}\right)\frac{V_{TL}}{N}={\dot{m}}_{A,TL}+{\dot{m}}_{B,TL},$$

where:

• $$\frac{\partial {\rho }_{seg,TL}}{\partial p}$$ is the partial derivative of density with respect to pressure for the segment.

• $$\frac{\partial {\rho }_{seg,TL}}{\partial T}$$ is the partial derivative of density with respect to temperature for the segment.

• T_seg,TL is the temperature for the segment.

• V_TL is the total thermal liquid volume.

The summation is over all segments.

Note

Although the block divides the thermal liquid flow into N=3 segments for heat transfer calculations, it assumes all segments are at the same internal pressure, p_TL. Consequentially, p_TL is outside of the summation.

The energy conservation equation for each segment is

$$\begin{array}{l}\left(\frac{d{p}_{TL}}{dt}\frac{\partial u_{seg,TL}}{\partial p}+\frac{d{T}_{seg,TL}}{dt}\frac{\partial u_{seg,TL}}{\partial T}\right)\frac{M_{TL}}{N}+u_{seg,TL}\left({\dot{m}}_{seg,in,TL}-{\dot{m}}_{seg,out,TL}\right)=\\ {\Phi }_{seg,in,TL}-{\Phi }_{seg,out,TL}+Q_{seg,TL},\end{array}$$

where:

• $$\frac{\partial u_{seg,TL}}{\partial p}$$ is the partial derivative of specific internal energy with respect to pressure for the segment.

• $$\frac{\partial u_{seg,TL}}{\partial T}$$ is the partial derivative of specific internal energy with respect to temperature for the segment.

• M_TL is the total thermal liquid mass.

• $${\dot{m}}_{seg,in,TL}$$ and $${\dot{m}}_{seg,out,TL}$$ are the mass flow rates into and out of the segment.

• Φ_seg,in,TL and Φ_seg,out,TL are the energy flow rates into and out of the segment.

The block assumes the mass flow rates between segments are linearly distributed between the values of $${\dot{m}}_{A,TL}$$ and $${\dot{m}}_{B,TL}$$.

Moist Air Mass and Energy Conservation

The mass conservation for the overall moist air mixture flow is

$$\begin{array}{l}\left(\frac{d{p}_{MA}}{dt}{\displaystyle \sum _{segments}\left(\frac{\partial {\rho }_{seg,MA}}{\partial p}\right)}+{\displaystyle \sum _{segments}\left(\frac{d{T}_{seg,MA}}{dt}\frac{\partial {\rho }_{seg,MA}}{\partial T}+\frac{d{x}_{w,seg,MA}}{dt}\frac{\partial {\rho }_{seg,MA}}{\partial x_w}+\frac{d{x}_{g,seg,MA}}{dt}\frac{\partial {\rho }_{seg,MA}}{\partial x_g}\right)}\right)\frac{V_{MA}}{N}\\ ={\dot{m}}_{A,MA}+{\dot{m}}_{B,MA}-{\displaystyle \sum _{segments}\left({\dot{m}}_{w,seg,cond}+{\dot{m}}_{w,seg,conv}\right)}+{\displaystyle \sum _{segments}{\dot{m}}_{d,seg,evap}},\end{array}$$

where:

• $$\frac{\partial {\rho }_{seg,MA}}{\partial p}$$ is the partial derivative of density with respect to pressure for the segment.

• $$\frac{\partial {\rho }_{seg,MA}}{\partial T}$$ is the partial derivative of density with respect to temperature for the segment.

• $$\frac{\partial {\rho }_{seg,MA}}{\partial x_w}$$ is the partial derivative of density with respect to specific humidity for the segment.

• $$\frac{\partial {\rho }_{seg,MA}}{\partial x_g}$$ is the partial derivative of density with respect to trace gas mass fraction for the segment.

• x_w,seg,MA is the specific humidity, also referred to as the water vapor mass fraction, for the segment.

• x_g,seg,MA is the trace gas mass fraction for the segment.

• V_MA is the total moist air volume.

• $$\dot{m}$$_w,seg,conv is the rate of condensation on the wall surface for the segment.

• $$\dot{m}$$_d,seg,evap is the rate of water droplet evaporation for the segment.

The summation is over all segments.

Note

Although the block divides the moist air flow into N=3 segments for heat transfer calculations, it assumes all segments are at the same internal pressure, p_MA. Consequentially, p_MA is outside of the summation.

The energy conservation equation for each segment is

$$\begin{array}{l}\frac{d{T}_{seg,MA}}{dt}\left({\overline{c}}_{seg,MA}-R_{seg}\right)\frac{M_{MA}}{N}+u_{a,seg,MA}\left({\dot{m}}_{seg,in,MA}-{\dot{m}}_{seg,out,MA}\right)+\left(u_{w,seg,MA}-u_{a,seg,MA}\right)\left({\dot{m}}_{w,seg,in,MA}-{\dot{m}}_{w,seg,out,MA}\right)+\\ \left(u_{g,seg,MA}-u_{a,seg,MA}\right)\left({\dot{m}}_{g,seg,in,MA}-{\dot{m}}_{g,seg,out,MA}\right)+h_d\left({\dot{m}}_{d,seg,in,MA}-{\dot{m}}_{d,seg,out,MA}\right)\\ ={\Phi }_{seg,in,MA}-{\Phi }_{seg,out,MA}+Q_{seg,MA}-\left(1-{\lambda }_d\right)\left({\dot{m}}_{w,seg,cond}{h}_d+{\dot{m}}_{w,seg,conv}{h}_{l,wall}\right),\end{array}$$

where:

• u_a,seg,MA is the dry air specific internal energy for the segment.

• u_g,seg,MA is the trace gas specific internal energy for the segment.

• u_w,seg,MA is the water vapor specific internal energy for the segment.

• M_MA is the total moist air mass.

• $${\dot{m}}_{seg,in,MA}$$ and $${\dot{m}}_{seg,out,MA}$$ are the moist air mass flow rates into and out of the segment.

• $${\dot{m}}_{w,seg,in,MA}$$ and $${\dot{m}}_{w,seg,out,MA}$$ are the water vapor mass flow rates into and out of the segment.

• $${\dot{m}}_{g,seg,in,MA}$$ and $${\dot{m}}_{g,seg,out,MA}$$ are the trace gas mass flow rates into and out of the segment.

• $${\dot{m}}_{d,seg,in,MA}$$ and $${\dot{m}}_{d,seg,out,MA}$$ are the water droplets mass flow rate into and out of the segment.

• R_seg is the segment volume specific gas constant.

• Φ_seg,in,MA and Φ_seg,out,MA are the energy flow rates into and out of the segment.

• h_d is the water droplet specific enthalpy in the segment.

• λ_d is the value of the Fraction of condensate entrained as water droplets parameter.

The block assumes the mass flow rates between segments are linearly distributed between the values of $${\dot{m}}_{A,MA}$$ and $${\dot{m}}_{B,MA}$$.

The water vapor mass conservation equation for each segment is

$$\begin{array}{l}\frac{d{x}_{w,seg,MA}}{dt}\frac{M_{MA}}{N}+x_{w,seg,MA}\left({\dot{m}}_{seg,in,MA}-{\dot{m}}_{seg,out,MA}\right)=\\ {\dot{m}}_{w,seg,in,MA}-{\dot{m}}_{w,seg,out,MA}-{\dot{m}}_{w,seg,cond}-{\dot{m}}_{w,seg,conv}+{\dot{m}}_{d,seg,evap}.\end{array}$$

The trace gas mass conservation equation for each segment is

$$\begin{array}{l}\frac{d{x}_{g,seg,MA}}{dt}\frac{M_{MA}}{N}+x_{g,seg,MA}\left({\dot{m}}_{seg,in,MA}-{\dot{m}}_{seg,out,MA}\right)=\\ {\dot{m}}_{g,seg,in,MA}-{\dot{m}}_{g,seg,out,MA}.\end{array}$$

The water droplet mass balance conservation equation for each segment is

$$\begin{array}{l}\frac{d{r}_{d,seg}}{dt}\frac{M_{MA}}{N}+r_{d,seg}\left({\dot{m}}_{seg,in,MA}-{\dot{m}}_{seg,out,MA}\right)=\\ {\dot{m}}_{d,seg,in}-{\dot{m}}_{d,seg,out}+{\lambda }_d\left({\dot{m}}_{w,seg,cond}+{\dot{m}}_{w,seg,conv}\right)-{\dot{m}}_{d,seg,evap},\end{array}$$

where r_d,seg is the mass ratio of the water droplets to the moist air in the fluid volume in the segment.

Note

If the Trace gas model parameter is None in the Moist Air Properties (MA) block, the moist air network does not model trace gas. In this case, in the System-Level Heat Exchanger (TL-MA) block, the conservation equation for trace gas is set to 0.

If you clear the Enable entrained water droplets in the Moist Air Properties (MA) block, the moist air network does not model entrained water droplets. In this case, in the System-Level Heat Exchanger (TL-MA) block, the conservation equation for water droplets is set to 0.

Assumptions and Limitations

• When determining the heat exchanger size, the block ignores the value of the Fraction of condensate entrained as water droplets parameter and assumes that the condensate is not entrained as droplets.

Examples

Liquid Air Energy Storage System

Models a grid-scale energy storage system based on cryogenic liquid air. When there is excess power, the system liquefies ambient air based on a variation of the Claude cycle. The cold liquid air is stored in a low-pressure insulated tank until needed. When there is high power demand, the system expands the stored liquid air to produce power based on the Rankine cycle.

• Open Model

Ports

Output

Q1 — Rate of heat transfer to thermal liquid, W

physical signal

Rate of heat transfer to thermal liquid, returned as a physical signal, in W. The physical signals at ports Q1 and Q2 are usually equal in value with opposite sign. However, if you select Wall thermal mass, then these two signals may have different values because the wall may absorb and release some of the heat being transferred.

Q2 — Rate of heat transfer to moist air, W

physical signal

Rate of heat transfer to moist air, returned as a physical signal, in W. The physical signals at ports Q1 and Q2 are usually equal in value with opposite sign. However, if you select Wall thermal mass, then these two signals may have different values because the wall may absorb and release some of the heat being transferred.

W — Moist air condensation rate, kg/s

physical signal

Water condensation rate that leaves the moist air flow, returned as a physical signal. The value of this port does not include the portion of condensation that is entrained as water droplets. The condensate does not accumulate on the heat transfer surface.

Conserving

A1 — Thermal liquid port

thermal liquid

Inlet or outlet port associated with the thermal liquid.

B1 — Thermal liquid port

thermal liquid

Inlet or outlet port associated with the thermal liquid.

A2 — Moist air port

moist air

Inlet or outlet port associated with the moist air.

B2 — Moist air port

moist air

Inlet or outlet port associated with the moist air.

Parameters

Configuration

Flow arrangement at nominal operating conditions — Flow path alignment

Counter flow - Thermal Liquid 1 flows from A to B, Moist Air 2 flows from B to A (default) | Parallel flow - Both fluids flow from A to B | Cross flow - Both fluids flow from A to B

Flow path alignment between the heat exchanger sides at nominal operating condition. The available flow arrangements are:

• Counter flow - Thermal Liquid 1 flows from A to B, Moist Air 2 flows from B to A — The flows run parallel to each other, in the opposite directions.

• Parallel flow - Both fluids flow from A to B — The flows run in the same direction.

• Cross flow - Both fluids flow from A to B — The flows run perpendicular to each other.

The choice between parallel flow and counter flow affects how the block determines the size of the heat exchanger. The counter flow setting is the most effective, and needs the smallest size to meet the specified performance. Conversely, parallel flow is the least effective, and needs the biggest size to meet the specified performance.

Flow direction at the nominal condition (from A to B, or from B to A) only affects the model initialization, when you select Initialize thermal liquid to nominal operating conditions or Initialize moist air to nominal operating conditions. If you set different initial operating conditions, the flow directions can be different.

After the block determines the size of the heat exchanger, this setting does not play a role in how the block calculates the heat transfer during simulation. Instead, the heat transfer depends on the flow directions during simulation. For example, if you set the parameter to parallel flow but set up the model to run in counter flow, then the rate of heat transfer during simulation will not match the specified performance, even if the rest of the boundary conditions are the same.

If you set the parameter to cross flow, then the block models the flow paths as perpendicular inside the heat exchanger, so the flow directions during simulation do not matter.

Wall thermal mass — Whether to enable effect of thermal mass on heat transfer surface

off (default) | on

Whether to enable the effect of thermal mass on the heat transfer surface. When you select this parameter, the block introduces additional dynamics to the simulation and takes longer to reach steady state, but this parameter does not affect the results at steady-state simulation.

Wall mass — Mass of heat transfer surface

1 kg (default) | positive scalar

Mass of the heat transfer surface.

Dependencies

To enable this parameter, select Wall thermal mass.

Wall specific heat — Specific heat of heat transfer surface

490 J/(K*kg) (default) | positive scalar

Specific heat of the heat transfer surface.

Dependencies

To enable this parameter, select Wall thermal mass.

Initialize wall temperature to nominal operating conditions — Option for initializing wall temperature

on (default) | off

Option to initialize the wall temperature to nominal operating conditions or specified values. If you select this parameter, the block calculates the initial wall temperature from the nominal operating conditions specified for both fluid sides. If you clear this parameter, you can specify the initial wall temperature directly with the Initial wall temperature parameter.

Dependencies

To enable this parameter, select Wall thermal mass.

Initial wall temperature — Initial temperature of wall

293.15 K (default) | positive scalar or two-element vector

Initial temperature of the wall. If you specify a scalar, the block assumes that the initial wall temperature is uniform. If you specify a two-element vector, then the block assumes that the initial wall temperature varies linearly between ports A1 and A2 and ports B1 and B2. The first element corresponds to the temperature at ports A1 and A2 and the second element corresponds to the temperature at ports B1 and B2.

Dependencies

To enable this parameter, select Wall thermal mass and clear the Initialize wall temperature to nominal operating conditions check box.

Cross-sectional area at port A1 — Flow area at port A1

0.01 m^2 (default) | positive scalar

Flow area at the thermal liquid port A1.

Cross-sectional area at port B1 — Flow area at port B1

0.01 m^2 (default) | positive scalar

Flow area at the thermal liquid port B1.

Cross-sectional area at port A2 — Flow area at port A2

0.01 m^2 (default) | positive scalar

Flow area at the moist air port A2.

Cross-sectional area at port B2 — Area normal to flow at port B2

0.01 m^2 (default) | positive scalar

Flow area at the moist air port B2.

Thermal Liquid 1

Nominal operating condition — Nominal operating condition

Heat transfer from Thermal Liquid 1 to Moist Air 2 (default) | Heat transfer from Moist Air 2 to Thermal Liquid 1

Nominal operating condition:

• Heat transfer from Thermal Liquid 1 to Moist Air 2 — The thermal liquid is cooled and the moist air is heated.

• Heat transfer from Moist Air 2 to Thermal Liquid 1 — The moist air is cooled and the thermal liquid is heated.

This setting relates only to the nominal operating condition parameters. It does not mean that heat transfer can only happen in the specified direction during simulation.

Nominal mass flow rate — Mass flow rate between thermal liquid ports during nominal operating condition

0.1 kg/s (default) | positive scalar

Mass flow rate from port A1 to port B1 during the nominal operating condition.

Nominal pressure drop — Pressure drop between thermal liquid ports during nominal operating condition

0.01 MPa (default) | positive scalar

Pressure drop from port A1 to port B1 during the nominal operating condition.

Nominal inlet pressure — Pressure at the thermal liquid inlet

0.101325 MPa (default) | positive scalar

Pressure at the thermal liquid inlet of the heat exchanger during nominal operating condition.

Nominal inlet temperature — Temperature at the thermal liquid inlet

333.15 K (default) | positive scalar

Temperature at the thermal liquid inlet of the heat exchanger during the nominal operating condition.

Heat transfer capacity specification — How to specify heat transfer capacity of the thermal liquid

Rate of heat transfer (default) | Outlet condition

Whether to specify the performance of the heat exchanger for the thermal liquid at the nominal operating condition directly, by the rate of heat transfer, or indirectly, by the outlet condition.

Nominal rate of heat transfer — Rate of heat transfer

1 kW (default) | positive scalar

Rate of heat transfer. The Nominal Operating condition parameter determines the network that the heat transfers from and to:

• If Nominal operating condition is Heat transfer from Thermal Liquid 1 to Moist Air 2, this parameter is the rate of the heat transfer from the thermal liquid to the moist air during the nominal operating condition.

• If Nominal operating condition is Heat transfer from Moist Air 2 to Thermal Liquid 1, this parameter is the rate of the heat transfer from the moist air to the thermal liquid during the nominal operating condition.

Dependencies

To enable this parameter, set Heat transfer capacity specification to Rate of heat transfer.

Nominal outlet temperature — Outlet temperature

323.15 K (default) | positive scalar

Temperature at the outlet of the thermal liquid side of the heat exchanger during the nominal operating condition.

Dependencies

To enable this parameter, set Heat transfer capacity specification to Outlet condition.

Thermal liquid volume — Total volume of thermal liquid

0.001 m^3 (default) | positive scalar

Total volume of thermal liquid inside the heat exchanger.

Initialize thermal liquid to nominal operating conditions — Option for initializing thermal liquid

on (default) | off

Option to initialize the thermal liquid to nominal operating conditions or specified values. If you select this parameter, the block initializes the thermal liquid to the nominal operating conditions. If you clear this check box, you can specify the initial conditions directly with additional parameters.

Initial thermal liquid pressure — Thermal liquid pressure at start of simulation

0.101325 MPa (default) | positive scalar

Thermal liquid pressure at the start of simulation.

Dependencies

To enable this parameter, clear the Initialize thermal liquid to nominal operating conditions check box.

Initial thermal liquid temperature — Thermal liquid temperature at start of simulation

293.15 K (default) | positive scalar

Thermal liquid temperature at the start of simulation.

Dependencies

To enable this parameter, clear the Initialize thermal liquid to nominal operating conditions check box.

Moist Air 2

Nominal mass flow rate — Mass flow rate between moist air ports during nominal operating condition

0.1 kg/s (default) | positive scalar

Mass flow rate from port A2 to port B2 during the nominal operating condition.

Nominal pressure drop — Pressure drop between moist air ports during nominal operating condition

0.001 MPa (default) | positive scalar

Pressure drop from port A2 to port B2 during the nominal operating condition.

Nominal inlet pressure — Pressure at the moist air side inlet

0.101325 MPa (default) | positive scalar

Pressure at the moist air inlet of the heat exchanger during nominal operating condition.

Nominal inlet temperature — Temperature at the moist air side inlet

293.15 K (default) | positive scalar

Temperature at the moist air inlet of the heat exchanger during the nominal operating condition.

Inlet humidity specification — Quantity used to describe the humidity level at the moist air side inlet

Relative humidity (default) | Specific humidity | Mole fraction | Humidity ratio | Wet-bulb temperature

Select quantity used to describe the humidity level at the inlet during the nominal operating condition.

Nominal inlet relative humidity — Relative humidity at the inlet

0.5 (default) | scalar in the range [0,1]

Relative humidity at the moist air inlet of the heat exchanger during the nominal operating conditions.

Dependencies

To enable this parameter, set Inlet humidity specification to Relative humidity.

Nominal inlet specific humidity — Specific humidity at the inlet

0.01 (default) | scalar in the range [0,1]

Specific humidity, defined as the mass fraction of water vapor in a moist air mixture, at the moist air inlet of the heat exchanger during the nominal operating condition.

Dependencies

To enable this parameter, set Inlet humidity specification to Specific humidity.

Nominal inlet water vapor mole fraction — Mole fraction of water vapor at the inlet

0.01 (default) | scalar in the range [0,1]

Mole fraction of water vapor in a moist air mixture at the moist air inlet of the heat exchanger during the nominal operating condition.

Dependencies

To enable this parameter, set Inlet humidity specification to Mole fraction.

Nominal inlet humidity ratio — Humidity ratio at the inlet

0.01 (default) | positive scalar in the range [0,1]

Humidity ratio, defined as the mass ratio of water vapor to dry air and trace gas, at the moist air inlet of the heat exchanger during the nominal operating condition.

Dependencies

To enable this parameter, set Inlet humidity specification to Humidity ratio.

Nominal inlet wet-bulb temperature — Wet-bulb temperature at the start of simulation

287 K (default) | positive scalar in the range [0,1]

Wet-bulb temperature at the moist air inlet of the heat exchanger during the nominal operating condition.

Dependencies

To enable this parameter, set Inlet humidity specification to Wet-bulb temperature.

Inlet trace gas specification — Quantity used to describe trace gas level at the inlet

Mass fraction (default) | Mole fraction

Select quantity used to describe the trace gas level at the inlet during the nominal operating condition: mass fraction or mole fraction.

Nominal inlet trace gas mass fraction — Mass fraction of trace gas at the inlet

0.001 (default) | scalar in the range [0,1]

Mass fraction of trace gas in a moist air mixture at the moist air inlet of the heat exchanger during the nominal operating condition.

This parameter is ignored if the Trace gas model parameter in the Moist Air Properties (MA) block is set to None.

Dependencies

To enable this parameter, set Inlet trace gas specification to Mass fraction.

Nominal inlet trace gas mole fraction — Mole fraction of trace gas at the inlet

0.001 (default) | scalar in the range [0,1]

Mole fraction of trace gas in a moist air mixture at the moist air inlet of the heat exchanger during the nominal operating condition.

This parameter is ignored if the Trace gas model parameter in the Moist Air Properties (MA) block is set to None.

Dependencies

To enable this parameter, set Inlet trace gas specification to Mole fraction.

Moist air volume — Total volume of moist air in the heat exchanger

0.1 m^3 (default) | positive scalar

Total volume of moist air in the heat exchanger.

Initialize moist air to nominal operating conditions — Option for initializing moist air

on (default) | off

Option to initialize the moist air to nominal operating conditions or specified values. If you select this parameter, the block initializes the moist air to the nominal operating conditions. If you clear this check box, you can specify the initial conditions directly with additional parameters.

Initial moist air pressure — Moist air pressure at start of simulation

0.101325 MPa (default) | positive scalar

Moist air pressure at the start of the simulation.

Dependencies

To enable this parameter, clear the Initialize moist air to nominal operating conditions check box.

Initial moist air temperature — Moist air temperature at start of simulation

293.15 K (default) | positive scalar | two-element vector

Moist air temperature at the start of simulation. If the value is a scalar, then the initial temperature is assumed uniform. If the value is a two-element vector, then the initial temperature is assumed to vary linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

Dependencies

To enable this parameter, clear the Initialize moist air to nominal operating conditions check box.

Initial humidity specification — Quantity used to describe the initial humidity level

Relative humidity (default) | Specific humidity | Mole fraction | Humidity ratio | Wet-bulb temperature

Select quantity used to describe the initial humidity level: relative humidity, specific humidity, water vapor mole fraction, or humidity ratio.

Dependencies

To enable this parameter, clear the Initialize moist air to nominal operating conditions check box.

Initial moist air relative humidity — Relative humidity at start of simulation

0.5 (default) | scalar in the range [0,1] | two-element vector

Moist air relative humidity at the start of simulation. If the value is a scalar, then the initial relative humidity is assumed uniform. If the value is a two-element vector, then the initial relative humidity is assumed to vary linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

Dependencies

To enable this parameter, clear the Initialize moist air to nominal operating conditions check box and set Initial humidity specification to Relative humidity.

Initial moist air specific humidity — Specific humidity at start of simulation

0.01 (default) | scalar in the range [0,1] | two-element vector

Moist air specific humidity, defined as the mass fraction of water vapor in a moist air mixture, at the start of simulation. If the value is a scalar, then the initial specific humidity is assumed uniform. If the value is a two-element vector, then the initial specific humidity is assumed to vary linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

Dependencies

To enable this parameter, clear the Initialize moist air to nominal operating conditions check box and set Initial humidity specification to Specific humidity.

Initial moist air water vapor mole fraction — Mole fraction of water vapor at start of simulation

0.01 (default) | scalar in the range [0,1] | two-element vector

Mole fraction of water vapor in a moist air mixture at the start of simulation. If the value is a scalar, then the initial mole fraction is assumed uniform. If the value is a two-element vector, then the initial mole fraction is assumed to vary linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

Dependencies

To enable this parameter, clear the Initialize moist air to nominal operating conditions check box and set Initial humidity specification to Mole fraction.

Initial moist air humidity ratio — Humidity ratio at start of simulation

0.01 (default) | positive scalar in the range [0,1] | two-element vector

Moist air humidity ratio, defined as the mass ratio of water vapor to dry air and trace gas, at the start of simulation. If the value is a scalar, then the initial humidity ratio is assumed uniform. If the value is a two-element vector, then the initial humidity ratio is assumed to vary linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

Dependencies

To enable this parameter, clear the Initialize moist air to nominal operating conditions check box and set Initial humidity specification to Humidity ratio.

Initial moist air wet-bulb temperature — Wet-bulb temperature at the start of simulation

287 K (default) | positive scalar in the range [0,1]

Wet-bulb temperature at the start of the simulation. The block uses this value to calculate humidity.

This parameter can be a scalar or a two-element vector. A scalar value represents the mean initial wet-bulb temperature in the channel. A vector value represents the initial wet-bulb temperature at the inlet and outlet in the form [inlet, outlet]. The block calculates a linear gradient between the two ports. The inlet and the outlet ports are identified according to the initial flow direction.

Dependencies

To enable this parameter, clear the Initialize moist air to nominal operating conditions check box and set Initial humidity specification to Wet-bulb temperature.

Initial trace gas specification — Quantity used to describe initial trace gas level

Mass fraction (default) | Mole fraction

Select the quantity used to describe the trace gas level at the start of simulation: mass fraction or mole fraction.

Dependencies

To enable this parameter, clear the Initialize moist air to nominal operating conditions check box.

Initial moist air trace gas mass fraction — Mass fraction of trace gas at start of simulation

0.001 (default) | scalar in the range [0,1] | two-element vector

Mass fraction of trace gas in a moist air mixture at the start of simulation. If the value is a scalar, then the initial mass fraction is assumed uniform. If the value is a two-element vector, then the initial mass fraction is assumed to vary linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

This parameter is ignored if the Trace gas model parameter in the Moist Air Properties (MA) block is set to None.

Dependencies

To enable this parameter, clear the Initialize moist air to nominal operating conditions check box and set Initial trace gas specification to Mass fraction.

Initial moist air trace gas mole fraction — Mole fraction of trace gas at start of simulation

0.001 (default) | scalar in the range [0,1] | two-element vector

Mole fraction of trace gas in a moist air mixture at the start of simulation. If the value is a scalar, then the initial mole fraction is assumed uniform. If the value is a two-element vector, then the initial mole fraction is assumed to vary linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

This parameter is ignored if the Trace gas model parameter in the Moist Air Properties (MA) block is set to None.

Dependencies

To enable this parameter, clear the Initialize moist air to nominal operating conditions check box and set Initial trace gas specification to Mole fraction.

Initial mass ratio of water droplets to moist air — Ratio of water droplets to moist air

0 (default) | positive scalar

Initial mass ratio of water droplets to moist air.

Dependencies

To enable this parameter, clear the Initialize moist air to nominal operating conditions check box.

Relative humidity at saturation — Relative humidity point of condensation

1 (default) | nonnegative scalar

Relative humidity point of condensation. Condensation occurs above this value. In most cases, this value is 1, that is, 100%. A value greater than 1 indicates a supersaturated vapor.

Water vapor condensation time constant — Time scale for condensation

1e-3 s (default) | positive scalar

Characteristic time scale at which an oversaturated moist air volume returns to saturation by condensing out excess humidity.

Water droplets evaporation time constant — Time scale for evaporation

1e-3 s (default) | positive scalar

Characteristic time scale at which water droplets evaporate to vapor.

Fraction of condensate entrained as water droplets — Fraction of condensate in water droplets

1 (default) | scalar in the range [0,1]

Fraction of the condensate in the moist air that is entrained as water droplets.

Correlation Coefficients

a in Nu = a*Re^b*Pr^c for thermal liquid — Correlation coefficient for thermal liquid

0.023 (default) | positive scalar

Proportionality constant in the correlation of the Nusselt number as a function of the Reynolds number and Prandtl number for thermal liquid. The default value is based on the Colburn equation.

b in Nu = a*Re^b*Pr^c for thermal liquid — Reynolds number exponent in correlation for thermal liquid

0.8 (default) | positive scalar

Reynolds number exponent in the correlation of the Nusselt number as a function of the Reynolds number and Prandtl number for thermal liquid.

c in Nu = a*Re^b*Pr^c for thermal liquid — Prandtl number exponent in correlation for thermal liquid

0.33 (default) | positive scalar

Prandtl number exponent in the correlation of the Nusselt number as a function of the Reynolds number and Prandtl number for thermal liquid.

a in Nu = a*Re^b*Pr^c for moist air — Correlation coefficient for moist air

0.023 (default) | positive scalar

Proportionality constant in the correlation of the Nusselt number as a function of the Reynolds number and Prandtl number for moist air. The default value is based on the Colburn equation.

b in Nu = a*Re^b*Pr^c for moist air — Reynolds number exponent in correlation for moist air

0.8 (default) | positive scalar

Reynolds number exponent in the correlation of the Nusselt number as a function of the Reynolds number and Prandtl number for moist air. The default value is based on the Colburn equation.

c in Nu = a*Re^b*Pr^c for moist air — Prandtl number exponent in correlation for moist air

0.33 (default) | positive scalar

Prandtl number exponent in the correlation of the Nusselt number as a function of the Reynolds number and Prandtl number for moist air. The default value is based on the Colburn equation.

References

[1] Ashrae Handbook: Fundamentals. Atlanta: Ashrae, 2013.

[2] Çengel, Yunus A. Heat and Mass Transfer: A Practical Approach. 3rd ed. McGraw-Hill Series in Mechanical Engineering. Boston: McGraw-Hill, 2007.

[3] Mitchell, John W., and James E. Braun. Principles of Heating, Ventilation, and Air Conditioning in Buildings. Hoboken, NJ: Wiley, 2013.

[4] Shah, R. K., and Dušan P. Sekulić. Fundamentals of Heat Exchanger Design. Hoboken, NJ: John Wiley & Sons, 2003.

[5] Cavallini, Alberto, and Roberto Zecchin. “A DIMENSIONLESS CORRELATION FOR HEAT TRANSFER IN FORCED CONVECTION CONDENSATION.” In Proceeding of International Heat Transfer Conference 5, 309–13. Tokyo, Japan: Begellhouse, 1974. https://doi.org/10.1615/IHTC5.1220.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2022a

R2024b: Model water droplets suspended in moist air flow

Blocks in the moist air domain can now model water droplets suspended in a moist air flow. To model water droplets, select Enable entrained water droplets in the Moist Air Properties (MA) block connected to your moist air network.

R2024a: New moisture specification options

The block has new options for the Inlet humidity specification and Initial humidity specification parameters. This option, called Wet-bulb temperature, allows you to input data in the form of a wet-bulb temperature.

R2023b: Specify initial wall temperature

If you select Wall thermal mass and clear the Initialize wall temperature to nominal operating conditions check box, you can use the new Initial wall temperature parameter to specify the initial conditions directly.