Specific Dissipation Heat Transfer

Simple heat transfer model between two general fluids

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Libraries:
Simscape / Fluids / Heat Exchangers / Fundamental Components

Description

The Specific Dissipation Heat Transfer block models the heat transfer between two fluids given only minimal knowledge of component parameters. The fluids are controlled by physical signals, with these providing the entrance mass flow rate and isobaric specific heat for each. Thermal ports set the entrance temperatures of the fluids.

The rate of heat transfer is calculated from the specific dissipation, a parameter specified in tabulated form as a function of the entrance mass flow rates. The specific dissipation quantifies the amount of heat exchanged between the fluids per unit of time when the entrance temperatures differ by one degree.

This block does not model pressure losses and other aspects of flow mechanics. These effects are captured by the heat exchanger interface blocks. Combine this block with either the Specific Dissipation Heat Exchanger Interface (G) or Specific Dissipation Heat Exchanger Interface (TL) blocks to model a heat exchanger.

Heat Transfer Rate

Heat flows from the warmer fluid to the cooler fluid, at a rate proportional to the difference between the fluid entrance temperatures. The heat flow rate is positive if fluid 1 enters at a higher temperature than fluid 2 and therefore if heat flows from fluid 1 to fluid 2:

$$Q=\xi (T_{\text{In,1}}-T_{\text{In,2}}),$$

where T_*,in are the fluid entrance temperatures, determined by the conditions at thermal port H1 for fluid 1 and H2 for fluid 2. ξ is the specific dissipation obtained from the specified tabulated data at the given mass flow rates:

$$\xi =f({\dot{m}}_{\text{1}},{\dot{m}}_{\text{2}})$$

where $$\dot{m}$$ are the entrance mass flow rates, specified through physical signal port M1 for fluid 1 and M2 for fluid 2.

The specific dissipation is the heat exchanger heat transfer rate divided by the difference in inlet temperatures

$$\xi =\frac{Q}{T_{\text{In,1}}-T_{\text{In,2}}}$$

The specific dissipation is also equal to the overall heat transfer coefficient defined based on inlet temperature multiplied by the heat transfer surface area or the heat capacity rate multiplied by the effectiveness factor, for whichever fluid has a smaller value.

Maximum Heat Transfer Rate

The heat transfer rate is constrained so that the specific dissipation used in the calculations can never exceed the maximum value:

$${\xi }_{\text{max}}=\text{min}\left(C_1,C_2\right),$$

where C_* are the thermal capacity rates of the controlled fluids, each defined as:

$$C_{*}={\dot{m}}_{*}{c}_{p,*},$$

with c_p,* denoting the isobaric specific heat of the fluid, specified through physical signal port CP1 for fluid 1 and CP2 for fluid 2. The constraint on the maximum heat transfer rate is implemented in the form of a piecewise function:

$$Q=\{\begin{array}{c}\begin{array}{ll}{\xi }_{max}\left(T_{1,in}-T_{2,in}\right),\hfill & \text{if }SD>S{D}_{max}\hfill \\ \xi \left(T_{1,in}-T_{2,in}\right),\hfill & \text{otherwise}\hfill \end{array}\end{array},$$

The block issues a warning whenever the heat flow rate exceeds the maximum value, if the Check if violating maximum specific dissipation parameter is Warning.

Ports

Input

CP1 — Isobaric specific heat of controlled fluid 1

physical signal

Isobaric specific heat of controlled fluid 1.

CP2 — Isobaric specific heat of controlled fluid 2

physical signal

Isobaric specific heat of controlled fluid 2.

M1 — Entrance mass flow rate of controlled fluid 1

physical signal

Entrance mass flow rate of controlled fluid 1. Positive mass flow rate values correspond to specific dissipation values for normal operating conditions. Specific dissipation values obtained during reversed flow correspond to negative mass flow rate values.

M2 — Entrance mass flow rate of controlled fluid 2

physical signal

Entrance mass flow rate of controlled fluid 2. Positive mass flow rate values correspond to specific dissipation values for normal operating conditions. Specific dissipation values obtained during reversed flow correspond to negative mass flow rate values.

Conserving

H1 — Entrance temperature of controlled fluid 1

thermal

Entrance temperature of controlled fluid 1.

H2 — Entrance temperature of controlled fluid 2

thermal

Entrance temperature of controlled fluid 2.

Parameters

Thermal Liquid mass flow rate vector, mdot1 — Entrance mass flow rate at which to specify specific-dissipation data

[.3, .5, .6, .7, 1, 1.4, 1.9, 2.3] kg/s (default) | M-element array with units of mass/time

Array of mass flow rates at the inlet for controlled fluid 1. Each value corresponds to a row in the specific dissipation lookup table. Positive mass flow rate values correspond to specific dissipation values for normal operating conditions. Specific dissipation values obtained during reversed flow correspond to negative mass flow rate values.

Controlled fluid mass flow rate vector, mdot2 — Entrance mass flow rate at which to specify specific-dissipation data

[.3, .5, 1, 1.3, 1.7, 2, 2.6, 3.3] kg/s (default) | N-element array with units of mass/time

Array of mass flow rates at the inlet for controlled fluid 2. Each value corresponds to a row in the specific dissipation lookup table. Positive mass flow rate values correspond to specific dissipation values for normal operating conditions. Specific dissipation values obtained during reversed flow correspond to negative mass flow rate values.

Specific dissipation table, SD(mdot1, mdot2) — Specific dissipation values corresponding to specified mass flow rates

8-by-8 matrix with units of kW/K (default) | M-by-N matrix with units of power/temperature

Matrix of specific dissipation values corresponding to the specified mass flow rate arrays for controlled fluids 1 and 2. The block uses the tabulated data to calculate the heat transfer at the simulated operating conditions.

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

Mass flow rate threshold for flow reversal — Mass flow rate below which to smooth numerical data

1e-3 kg/s (default) | scalar with units of mass/time

Mass flow rate below which to initiate a smooth flow reversal to prevent discontinuities in the simulation data.

Check if violating maximum specific dissipation — Option to warn if the specific dissipation exceeds the maximum allowed value

Warning (default) | None | Error

Option to warn if the specific dissipation exceeds the maximum value described in the block description.

Extended Capabilities

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

Version History

Introduced in R2017b