# Thermal Performance Analysis of Micro Pin Fin Heat Sinks under Different Flow Conditions

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## Abstract

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^{®}for comparing the simulation results with the experimental data, showing that the highest micro pin fins configuration provides a more uniform and lowest wall temperature distribution compared to the lowest configuration. There is a good agreement between the experimental results and the numerical analysis, with a mean absolute error of 6% for all the considered parameters. For the two-phase flow condition, experimental tests were performed, and for the highest subcooling, an increase in mass flux causes an enhancement in the heat transfer for low heat flux; by increasing heat flux, there is a gradual predominance of boiling heat transfer over convection as the heat transfer mechanism. The pressure drop drastically increases with the vapor amount flowing into the system, regardless of the pin fin height; the boiling curves for the higher fin height show a much smaller slope and a smaller wall superheat than the fin with the smallest height, and consequently, a high heat transfer performance. A larger region of the heat sink is filled with vapor for lower inlet subcooling temperatures, degrading the heat transfer performance compared to higher inlet subcooling temperatures.

## 1. Introduction

^{2}s). An increase of 39–284% was observed in the heat transfer coefficient (HTC) for water and 29–220% for ethanol compared to parallel microchannels. Authors attributed this enhancement to the interconnected microchannels, which provide different paths for the vapor bubbles reducing the confinement effect. In addition, the interconnected spaces provided ideal conditions for the nucleation of vapor bubbles, contributing to the heat transfer improvement for the PFIRM. For pressure drop, Deng et al. [5] reported an increase with increasing heat flux and vapor quality; moreover, the mass flux strongly influenced pressure drop at moderated and high heat fluxes.

^{2}s) and inlet temperatures (between 13 and 18 °C). The authors reported that HTC increased with increasing mass flux for the single-phase flow regime. For the two-phase flow regime, they compared the results with their previous works [7]; the new device showed better thermal performance than the previous one. Regarding pressure drop and vapor quality, Asrar et al. [6] found the same behavior as Woodcock et al. [8] and Chien et al. [9], in which these parameters were independent of the heat flux in the single-phase regime but increased remarkably with the intensification of convective boiling.

## 2. Materials and Methods

#### 2.1. Experimental Apparatus

_{i}and T

_{o}, respectively). Flow homogenization channels with a depth of 0.75 mm were manufactured between the plenums and the heat sink to minimize flow entrance turbulence. Flow visualization (using a high-speed camera Photron SA3 model with 1000 fps and 1024 × 1024 resolution) is allowed by a polycarbonate plate (8 mm thick) covering the heat sink.

^{®}SteREO DiscoveryV8 and SEM EVO LS15 Zeiss

^{®}(Table 1).

#### 2.2. Experimental Procedure

^{®}Fluent 2020 R2. The computational domain with appropriate boundary conditions is shown in Figure 4.

^{−5}for the continuity equation and 10

^{−6}for momentum and energy equations. The simulations used the segregated algorithm with the SIMPLE algorithm for pressure-velocity coupling.

^{2}s, and for different footprint heat fluxes from 10 kW/m

^{2}to the system limit, characterized by intense instability in the flow (reverse flow). The gear pump’s rotation was set to achieve the desired mass flux; the preheater was adjusted until its outlet temperature was equal to the desired subcooling. A data acquisition system (Agilent 34970A) recorded the data every 2 s after the system achieved the steady-state regime, characterized by temperature variations lower than the thermocouples uncertainties (±0.3 °C). At least 250 data points were recorded, corresponding to 500 s steady-state. The pressure, temperatures, mass flux, and electrical voltage are constantly monitored. Flow visualization was carried out using a high-speed camera. The same procedure is adopted during all the experimental tests to ensure repeatability.

#### 2.3. Data Reduction

_{p}to the specific heat capacity [J/kg·K]; and T

_{i}and T

_{o}are the coolant temperature at the inlet and outlet, respectively. In the current study, heat loss (${\dot{Q}}_{loss}$) varied from 15 to 30% over the range of varying parameters. The heat flux, ${q}^{\u2033}$, dissipated by the test section is given by:

_{p}is the footprint area of the heating surface. The effective heat flux, ${q}_{eff}^{\u2033}$ [W/m

^{2}], based on the total surface area in contact with the working fluid (A

_{t}), is calculated by:

_{t}, the fin parameters and efficiency (η) concepts have been calculated considering the adiabatic fin tip, since a polycarbonate plate is used to cover the heat sink. Thus, A

_{t}is given by Equation (4), where N is the total number of micropillars.

_{c}is the cross-sectional area, P

_{ma}is the pin fin perimeter, and H is the height of the micro pin fins.

_{w}is the average temperature of the heat sink provided by three K-type thermocouples fixed within the heat sink wall. The T

_{f}is the average temperature of the fluid given by the same procedure as Leão et al. [14]

## 3. Results and Discussion

#### 3.1. Effect of the Inlet Subcooling Temperature

^{2}) is negligible. However, in the case of the two-phase flow region, the pressure drop becomes more significant as the inlet subcooling temperature decreases, regardless of the mass flux and micro pin fin height; a lower inlet subcooling temperature leads to a higher vapor quality through the heat sink, which increases the pressure drop.

#### 3.2. Effect of the Mass Flux

#### 3.3. Effect of the Fin Height

^{2}s and subcooling of 20 °C, with the respective visualization points. It is worth mentioning that similar behavior was observed for all test conditions. Flow boiling videos under these conditions can be found in the Supplementary Material.

## 4. Conclusions

^{2}s) and two levels of inlet subcooling temperatures (10 and 20 °C). The boiling heat transfer and pressure drop behaviors were evaluated for each test condition. The visualization of the experimental tests was performed using a high-speed camera to observe the transition from single-phase to two-phase flow and to identify possible flow patterns and the occurrence of reverse flow. The main conclusions are summarized below:

- ✓
- As the mass flux increases, HTC increases in the region where the effects of forced convection are dominant for each sample. However, when the effects of nucleate boiling overlap, the increase in mass flux does not guarantee a gain in HTC, especially for aligned arrays.
- ✓
- The lower the inlet subcooling temperature, the lower the heat flux for the ONB occurrence, and a larger region of the heat sink is filled with vapor, which can promote the dryout incipience (decreasing the maximum heat flux).
- ✓
- With a lower mass flux and inlet subcooling, the system becomes more sensitive to the effects of nucleate boiling, with significant gains in HTC due to the phase-change heat transfer (for S1 with G = 1000 kg/m
^{2}s and ΔT_{sub}= 10 °C, the HTC was increased about 39% compared to ΔT_{sub}= 20 °C for a heat flux of 30 kW/m^{2}). However, this can lead to the early dryout process. - ✓
- Pressure drop increases substantially with an increase of vapor amount flowing into the heat sink, which becomes more pronounced for lower subcooling, leading to the fluid dynamic limit of the system at lower heat fluxes compared to higher subcooling.
- ✓
- An increase in the effective area leads to an increase in the HTC; thus, the taller the micro pin fins, the higher the heat exchange area, leading to an HTC enhancement.
- ✓
- The reverse flow occurrence was observed more intensely for the lowest inlet subcooling temperature; the high vapor core acts as a barrier to the flow, degrading the HTC, increasing the pressure drop, and causing thermal and fluid dynamic instabilities.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Tullius, J.; Tullius, T.; Bayazitoglu, Y. Optimization of short micro pin fins in minichannels. Int. J. Heat Mass Transf.
**2012**, 55, 3921–3932. [Google Scholar] [CrossRef] - Liang, G.; Mudawar, I. Review of pool boiling enhancement by surface modification. Int. J. Heat Mass Transf.
**2019**, 128, 892–933. [Google Scholar] [CrossRef] - Li, W.; Dai, R.; Zeng, M.; Wang, Q. Review of two types of surface modification on pool boiling enhancement: Passive and active. Renew. Sustain. Energy Rev.
**2020**, 130, 109926. [Google Scholar] [CrossRef] - McNeil, D.A.; Raeisi, A.H.; Kew, P.A.; Hamed, R.S. An investigation into flow boiling heat transfer and pressure drop in a pin–finned heat sink. Int. J. Multiph. Flow
**2014**, 67, 65–84. [Google Scholar] [CrossRef][Green Version] - Deng, D.; Chen, L.; Wan, W.; Fu, T.; Huang, X. Flow boiling performance in pin fin-interconnected reentrant microchannels heat sink in different operational conditions. Appl. Therm. Eng.
**2019**, 150, 1260–1272. [Google Scholar] [CrossRef] - Asrar, P.; Ghiaasiaan, S.M.; Joshi, Y.K. Two-Phase Heat Transfer and Flow Regimes in Pin Fin-Enhanced Microgaps—Effect of Pin Spacing. ASME J. Heat Transf.
**2021**, 143, 023001. [Google Scholar] [CrossRef] - Asrar, P.; Zhang, X.; Green, C.E.; Bakir, M.; Joshi, Y.K. Flow boiling of R245fa in a microgap with staggered circular cylindrical pin fins. Int. J. Heat Mass Transf.
**2018**, 121, 329–342. [Google Scholar] [CrossRef] - Woodcock, C.; Yu, X.; Plawsky, J.; Peles, Y. Piranha Pin Fin (PPF)—Advanced flow boiling microstructures with low surface tension dielectric fluids. Int. J. Heat Mass Transf.
**2015**, 90, 591–604. [Google Scholar] [CrossRef] - Chien, L.H.; Cheng, Y.T.; Lai, Y.L.; Yan, W.M.; Ghalambaz, M. Experimental and numerical study on convective boiling in a staggered array of micro pin-fin microgap. Int. J. Heat Mass Transf.
**2020**, 149, 119203. [Google Scholar] [CrossRef] - Jung, D.; Lee, H.; Kong, D.; Cho, E.; Jung, K.W.; Kharangate, C.R.; Iyengar, M.; Malone, C.; Asheghi, M.; Lee, H.; et al. Thermal design and management of micro-pin fin heat sinks for energy-efficient three-dimensional stacked integrated circuits. Int. J. Heat Mass Transf.
**2021**, 175, 121192. [Google Scholar] [CrossRef] - Ortegon, J.A.A.; Souza, R.R.; Silva, J.B.C.; Cardoso, E.M. Analytical, experimental, and numerical analysis of a microchannel cooling system for high-concentration photovoltaic cells. J. Braz. Soc. Mech. Sci. Eng.
**2019**, 41, 255. [Google Scholar] [CrossRef] - Computational Fluid Dynamics Committee. Guide for the Verification and Validation of Computational Fluid Dynamics Simulations (AIAA G-077-1998(2002)); American Institute of Aeronautics and Astronautics, Inc.: Washington, DC, USA, 1998. [Google Scholar]
- Prajapati, Y.K.; Pathak, M.; Khan, M.K. Bubble dynamics and flow boiling characteristics in three different microchannel configurations. Int. J. Therm. Sci.
**2017**, 112, 371–382. [Google Scholar] [CrossRef] - Leão, H.L.S.L.; Nascimento, F.J.; Ribatski, G. Flow boiling heat transfer of r407c in a microchannels based heat spreader. Exp. Therm. Fluid Sci.
**2014**, 59, 140–151. [Google Scholar] [CrossRef] - Chalfi, T.Y.; Ghiaasiaan, S. Pressure drop caused by flow area changes in capillaries under low flow conditions. Int. J. Multiph. Flow
**2008**, 34, 2–12. [Google Scholar] [CrossRef] - Yin, L.; Chauhan, A.; Recinella, A.; Jia, L.; Kandlikar, S.G. Subcooled flow boiling in an expanding microgap with a hybrid microstructured surface. Int. J. Heat Mass Transf.
**2020**, 151, 119379. [Google Scholar] [CrossRef] - Cheng, X.; Wu, H. Improved flow boiling performance in high-aspect-ratio interconnected microchannels. Int. J. Heat Mass Transf.
**2021**, 165, 120627. [Google Scholar] [CrossRef] - Yin, L.; Jiang, P.; Xu, R.; Hu, H. Water flow boiling in a partially modified microgap with shortened micro pin fins. Int. J. Heat Mass Transf.
**2020**, 155, 119819. [Google Scholar] [CrossRef] - Kiyomura, I.S.; Nunes, J.M.; de Souza, R.R.; Gajghate, S.S.; Bhaumik, S.; Cardoso, E.M. Effect of microfin surfaces on boiling heat transfer using HFE-7100 as working fluid. J. Braz. Soc. Mech. Sci. Eng.
**2020**, 42, 366. [Google Scholar] [CrossRef]

**Figure 2.**Design of the microfinned heat sink. (

**a**) Isometric view; (

**b**) front view with internal details (measurements in mm); (

**c**) linear temperature profiles used to estimate the wall temperatures.

**Figure 6.**Effect of inlet subcooling temperature on flow boiling heat transfer of HFE-7100 for S1 and S2. (

**a**) G = 1000 kg/m

^{2}s; (

**b**) G = 1200 kg/m

^{2}s.

**Figure 7.**Effect of inlet subcooling on the pressure drops for S1 and S2. (

**a**) G = 1000 kg/m

^{2}s; (

**b**) G = 1200 kg/m

^{2}s.

**Figure 8.**Effects of mass flux on the flow boiling heat transfer of HFE-7100. (

**a**) ΔT

_{sub}= 10 °C; (

**b**) ΔT

_{sub}= 20 °C.

**Figure 9.**Effect of pin fin height on flow boiling heat transfer of HFE-7100 for ΔT

_{sub}= 10 °C. (

**a**) G = 1000 kg/m

^{2}s; (

**b**) G = 1200 kg/m

^{2}s.

**Figure 10.**Boiling curve and high-speed camera images for S1. G = 1200 kg/m

^{2}s and ΔT

_{sub}= 20 °C.

Surface | STEREO | SEM (100×) | |
---|---|---|---|

Top View | Side View | ||

S1 H = 160 µm | |||

S2 H = 350 µm |

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## Share and Cite

**MDPI and ACS Style**

Nunes, J.M.; de Oliveira, J.D.; Copetti, J.B.; Gajghate, S.S.; Banerjee, U.; Mitra, S.K.; Cardoso, E.M. Thermal Performance Analysis of Micro Pin Fin Heat Sinks under Different Flow Conditions. *Energies* **2023**, *16*, 3175.
https://doi.org/10.3390/en16073175

**AMA Style**

Nunes JM, de Oliveira JD, Copetti JB, Gajghate SS, Banerjee U, Mitra SK, Cardoso EM. Thermal Performance Analysis of Micro Pin Fin Heat Sinks under Different Flow Conditions. *Energies*. 2023; 16(7):3175.
https://doi.org/10.3390/en16073175

**Chicago/Turabian Style**

Nunes, Jéssica Martha, Jeferson Diehl de Oliveira, Jacqueline Biancon Copetti, Sameer Sheshrao Gajghate, Utsab Banerjee, Sushanta K. Mitra, and Elaine Maria Cardoso. 2023. "Thermal Performance Analysis of Micro Pin Fin Heat Sinks under Different Flow Conditions" *Energies* 16, no. 7: 3175.
https://doi.org/10.3390/en16073175