# A Hybrid Numerical Methodology Based on CFD and Porous Medium for Thermal Performance Evaluation of Gas to Gas Micro Heat Exchanger

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## Abstract

**:**

## 1. Introduction

## 2. Background

## 3. Numerical Methodology

## 4. Results

#### 4.1. CHT Model

^{®}. In theory, for the range of inlet gas temperatures considered in this study pressure drop from hot side and cold side should be almost similar and furthermore it should be independent of the flow configuration. Therefore any side of the fluid stream (hot or cold) from CHT analysis can be used to evaluate porous medium coefficients. For the scope of this work, hot fluid side is used to evaluate porous medium coefficients. Resulting viscous and inertial coefficients are shown in Figure 7a,b,d,e for both cocurrent and counterflow configurations.

#### 4.2. Porous Model

## 5. Conclusions

- Porous medium coefficients for parallel channel $\mathsf{\mu}$Hx can be extracted for compressible fluids by modifying the existing Darcy–Forchheimer law to incorporate for the strong density variations with increasing mass flow rates in MCs.
- CHT analysis revealed that gas in both hot and cold fluid streams experiences a “self-cooling” phenomenon where the temperature of the gases keeps on decreasing from inlet to the outlet at higher mass flow rates ($Re$). Therefore for a $\mathsf{\mu}$Hx operating under balanced mass flow rates, smaller values of mass flow rates are recommended.
- Pressure drop of the porous model is much higher compared to the CHT due to the presence of collecting and dividing manifolds. Pressure drop estimation using the porous model is in good agreement with the experimental results of the same $\mathsf{\mu}$Hx.
- Overall heat exchanger effectiveness of a $\mathsf{\mu}$Hx in a counterflow configuration is identical to that of the CHT analysis on the range of mass flows investigated in this study. For a cocurrent configuration, however, heat exchanger effectiveness from porous model matches well with experimental results while the CHT model overpredicts it.
- Compared to the meshing strategy adopted in CHT analysis, the porous model results in saving of at least 20 million computational nodes for the double layer gas to gas $\mathsf{\mu}$Hx investigated in this study with good enough predictions of global pressure drop and heat exchanger effectiveness.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Experimental assembly for double layer Micro heat exchangers ($\mathsf{\mu}$Hx) (taken from [15]) (

**a**), and zoomed view of single layer (

**b**).

**Figure 4.**Heat transfer rate for CHT analysis when flow configuration is cocurrent (

**a**), and counterflow (

**b**).

**Figure 5.**Heat exchanger effectiveness for CHT analysis when flow configuration is cocurrent (

**a**), and counterflow (

**b**).

**Figure 6.**Temperature along the length of the hot and cold MCs for various $Re$ in cocurrent flow configuration.

**Figure 7.**Viscous coefficient (

**a**,

**d**), inertial coefficient (

**b**,

**e**), and volumetric heat source term (

**c**,

**f**) extracted from CHT analysis in both flow configurations.

**Figure 8.**Comparison between experimental and numerical total pressure drop of $\mathsf{\mu}$Hx (

**a**), and in the inlet and MCs only (

**b**).

**Figure 10.**Flow maldistribution with and without source term ${q}_{v}$ for counterflow configuration with ${\dot{m}}_{f}$ = 2.5 kg/s.

Parameter | Symbol (Units) | Value |
---|---|---|

MC width | $w\phantom{\rule{4pt}{0ex}}(\mathsf{\mu}$m) | 200 |

MC height | $h\phantom{\rule{4pt}{0ex}}(\mathsf{\mu}$m) | 200 |

MC Length | $L\phantom{\rule{4pt}{0ex}}(\mathsf{\mu}$m) | 40 |

Hydraulic Diameter | ${D}_{h}\phantom{\rule{4pt}{0ex}}(\mathsf{\mu}$m) | 200 |

Wall Thickness | ${t}_{w}\phantom{\rule{4pt}{0ex}}(\mathsf{\mu}$m) | 100 |

MC housing (PMMA) conductivity | ${k}_{MC}$ (W/m/K) | $0.25$ |

Partition Foil (Stainless Steel) thickness | $\delta \phantom{\rule{4pt}{0ex}}(\mathsf{\mu}$m) | 100 |

Partition Foil conductivity | ${k}_{PF}$ (W/m/K) | 15 |

Boundary | Value | |
---|---|---|

Hot Side | Cold Side | |

Inlet | $-\dot{m}$ evaluated using Equation (10) for cold side | |

$-{T}_{h,in}=90$${}^{\circ}$C | $-{T}_{c,in}=20$ ${}^{\circ}$C | |

Side Walls | Translational Periodicity | |

Top & Bottom Walls | Adiabatic | |

Outlet | Pressure outlet, p = ${p}_{atm}$ |

Boundary | Value |
---|---|

Inlet | $-\dot{m}$ from experimental testing |

$-{T}_{h,in}$ = 90 ${}^{\circ}$C | |

MCs walls | Free slip |

Inertial and visocus coefficients | Determined from CHT analysis |

Energy source term | Determined from CHT analysis |

Manifolds walls | Adiabatic/ No slip |

Outlet | Pressure outlet, p = ${p}_{atm}$ |

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**MDPI and ACS Style**

Rehman, D.; Joseph, J.; Morini, G.L.; Delanaye, M.; Brandner, J.
A Hybrid Numerical Methodology Based on CFD and Porous Medium for Thermal Performance Evaluation of Gas to Gas Micro Heat Exchanger. *Micromachines* **2020**, *11*, 218.
https://doi.org/10.3390/mi11020218

**AMA Style**

Rehman D, Joseph J, Morini GL, Delanaye M, Brandner J.
A Hybrid Numerical Methodology Based on CFD and Porous Medium for Thermal Performance Evaluation of Gas to Gas Micro Heat Exchanger. *Micromachines*. 2020; 11(2):218.
https://doi.org/10.3390/mi11020218

**Chicago/Turabian Style**

Rehman, Danish, Jojomon Joseph, Gian Luca Morini, Michel Delanaye, and Juergen Brandner.
2020. "A Hybrid Numerical Methodology Based on CFD and Porous Medium for Thermal Performance Evaluation of Gas to Gas Micro Heat Exchanger" *Micromachines* 11, no. 2: 218.
https://doi.org/10.3390/mi11020218