Simple heat transfer model between two general fluids

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

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.

Pressure losses and other aspects of flow mechanics are ignored. To capture such effects, use the heat exchanger interface blocks provided in the same library. Combine heat transfer and heat exchanger blocks to model a custom heat exchanger. See the composite block diagrams of the heat exchanger blocks for examples.

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:

$$Q=SD\left({T}_{1,\text{in}}-{T}_{2,\text{in}}\right),$$

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

$$SD=SD\left({\dot{m}}_{1},{\dot{m}}_{2}\right),$$

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 can be calculated for a set of entrance mass flow
rates ($${\dot{m}}_{1}$$, $${\dot{m}}_{2}$$) given the experimental values of the heat transfer rate and the
corresponding entrance temperature difference:

$$SD=\frac{Q}{{T}_{1,in}-{T}_{2,in}}.$$

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

$$S{D}_{\text{max}}=\text{min}\left({C}_{1},{C}_{2}\right),$$

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:

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

A warning is issued whenever the heat flow rate exceeds the
maximum value, $$S{D}_{max}\left({T}_{1,in}-{T}_{2,in}\right)$$, if the **Check if violating maximum specific
dissipation** block parameter is set to
`Warning`

.