# Embedded Heat Exchanger (HX)

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## Introduction

The Embedded Heat Exchanger is used in the Evaporator models. It allows heating or cooling of Evaporator contents with external media (heating or cooling fluid).

It is enabled by connecting the HX_Shell streams, show in the picture below.

### Diagram

To enable the embedded heater, the HX_Shell connections (to and from) must be made, these are highlighted in red in the above picture.

## Behaviour when Model is OFF

If the user disables the unit, by un-ticking the On tick box, then the following actions occur:

• All streams connected to the 'Shell' inlet will flow out of the 'Shell' outlet with no temperature or phase change;
• All streams connected to the 'Tube' inlet will flow out of the 'Tube' outlet with no temperature or phase change;
• No energy exchange will occur.

So basically, the unit will be 'bypassed' without the user having to change any connections.

## Model Theory

The unit is based on traditional heat exchanger theory1,

$\mathbf{\mathit{Q=UA\boldsymbol{\Delta}T_{LM}}}$
where
Q - Rate of Heat Transfer
U - Overall coefficient of Heat Transfer
A - Area available for Heat Transfer
$\mathbf{\mathit{\boldsymbol{\Delta}T_{LM} = \cfrac{\Delta T_2 -\Delta T_1}{\ln \left( \cfrac{\Delta T_2}{\Delta T_1} \right) }}}$ - Log Mean Temperature Difference (LMTD)
For Counter Current Flow $\; \Delta T_2 = T_{H_{in}} - T_{C_{out}} \quad$ and $\; \Delta T_1 = T_{H_{out}} - T_{C_{in}}$

Notes:

1. If the flow through the heat exchanger is not completely counter current, then user must input a LMTD correction factor to correct for the different flow configuration. These correction factors are available in most references on Heat Transfer theory, and should be available from specific heat exchanger suppliers.
2. If the heat exchanger has Superheated Steam condensing on the shell side, then the LMTD method will produce small inaccuracies, please see Log Mean Temperature Difference (LMTD) Discussion.

Heat transfer to the individual streams is calculated using the following equation:

$\mathbf{\mathit{Q=m(H_{in}-H_{out})}}$
where
Q - Rate of Heat Transfer
m - Mass flow of the stream
Hin - Enthalpy of entering stream
Hout - Enthalpy of leaving stream

Using the stream enthalpies in the heat transfer calculations ensures that the variation of specific heat with temperature is taken into consideration.

In the case of one of the streams condensing the heat transfer is based on the assumption that the vapour is condensed at the saturation temperature. The condensate leaves the unit at this temperature, i.e. there is no further cooling of the liquid. If the vapour enters the unit above the saturation temperature, it will be cooled to the saturation temperature and then condensed.

The unit uses an iterative technique to determine the LMTD of the unit. This is then used to calculate the heat transfer between the two streams.

Reference

1. Perry, R.H., Perry's Chemical Engineers' Handbook, McGraw Hill Inc, 6th Edition, 1984.