# Application of Second Law Analysis in Heat Exchanger Systems

## Abstract

**:**

## 1. Introduction

- It is possible to minimize entropy production (exergy destruction) in a heat exchanger;
- It is desirable to minimize entropy production (exergy destruction) in a heat exchanger;
- Similar to isentropic efficiency, heat exchanger effectiveness is associated with irreversibility.

## 2. Sink–Source Model Exergy Analyses in Heat Transfer Processes

_{source}and ΔEX

_{sink}are the source and sink exergy changes, respectively. As shown in Equations (1) and (2), if the exergy sink can absorb higher amounts of exergy from the source, exergy losses and exergy efficiency become lower and higher, respectively. Exergy losses in convection heat transfer systems are divided into two components, one associated with temperature differences and the other one with fluid pressure drops. In the first component (if the system temperature is above the environment temperature), the part of the system with the higher temperature is the source, while the other part is the sink. In the second component, the instrument that moves the fluids (pump, compressor, etc.) is the source, and the pressure change of the fluids is the exergy sink.

#### 2.1. Basic Relations

#### 2.2. Calculation of Exergy Losses in Heat Exchangers

#### 2.3. The Second Law Analysis of Heat Exchangers

- Process heat exchangers, where hot and cold fluids are both process fluids;
- Utility heat exchangers, where one of the fluids (hot or cold) comes from a utility unit and another from a process fluid.

- Liquid-cold utility heat exchangers;
- Liquid-hot utility heat exchangers;
- Gas-cold utility heat exchangers;
- Gas-hot utility heat exchangers.

#### 2.3.1. Liquid-Cold Utility Heat Exchangers

_{co}= T

_{ci}. In other words, if there is a phase change in the cold fluid, the entropy generation or exergy losses are at a maximum.

#### 2.3.2. Liquid-Hot Utility Heat Exchangers

#### 2.3.3. Gas-Cold Utility Heat Exchangers

#### 2.3.4. Gas-Hot Utility Heat Exchangers

## 3. Experiments on Modeling Accuracy Investigation

#### 3.1. The Applied System

#### 3.2. Experiments

## 4. Results and Discussion

## 5. Conclusions

## Funding

## Conflicts of Interest

## Abbreviations

Nomenclature | |

c | specific heat capacity (J∙kg^{−1}∙K^{−1}) |

d | Differential |

EL | exergy losses (W) |

EX | exergy (W) |

h | specific enthalpy (J∙kg^{−1}) |

H | enthalpy (J) |

M | molecular weight |

n | number of moles (gmol) |

q | rate of heat transfer (W) |

Q | heat (J) |

P | pressure (Pa) |

R | ideal gas constant (J∙gmol^{−1}∙K^{−1}) |

s | specific entropy (J∙K^{−1}∙kg^{−1}) |

S | entropy (J∙K^{−1}) |

T | temperature (K) |

u | specific internal energy (J∙kg^{−1}) |

v | specific volume (m^{3}∙kg^{−1}) |

V | volume (m^{3}) |

W | work (J) |

Greek symbols | |

Δ | Difference |

η | Efficiency |

Subscripts | |

0 | Reference state |

1,2 | initial and final state |

c | Cold |

ci | cold inlet |

co | cold outlet |

h | hot |

hi | hot inlet |

ho | hot outlet |

LM | log. Mean |

LMC | log. mean cold |

LMH | log. mean hot |

LMTD | log mean temperature difference |

m | Mean |

max | Maximum |

P | pressure constant |

s | Shaft |

Sink | sink of exergy |

Source | source of exergy |

T | temperature constant |

Superscript | |

ig | ideal gas |

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Tube Internal Diameter (mm) | Tube External Diameter (mm) | Shell External Diameter (mm) | Length (m) |
---|---|---|---|

21.3 | 36.2 | 42.4 | 2.5 |

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Ashrafizadeh, S.A.
Application of Second Law Analysis in Heat Exchanger Systems. *Entropy* **2019**, *21*, 606.
https://doi.org/10.3390/e21060606

**AMA Style**

Ashrafizadeh SA.
Application of Second Law Analysis in Heat Exchanger Systems. *Entropy*. 2019; 21(6):606.
https://doi.org/10.3390/e21060606

**Chicago/Turabian Style**

Ashrafizadeh, Seyed Ali.
2019. "Application of Second Law Analysis in Heat Exchanger Systems" *Entropy* 21, no. 6: 606.
https://doi.org/10.3390/e21060606