# Thermoelectric Generation with Impinging Nano-Jets

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Model

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Abbreviations

A${}_{p,n}$ | pellet cross-sectional area, (m${}^{2}$) |

a | length of corrugation, (m) |

E | electric field intensity vector, (V/m) |

H | channel height, (m) |

h | local heat transfer coefficient, (W/m${}^{2}$·K) |

h | height of corrugation, (m) |

J | electric current density vector, (A/m${}^{2}$) |

k | thermal conductivity, (W/m${}^{2}$·K) |

L | channel length, (m) |

L${}_{m}$ | module length, (m) |

N | number of corrugated waves |

n | unit normal vector |

Nu | Nusselt number |

p | pressure, (Pa) |

P | power output, (W) |

Pr | Prandtl number |

R${}_{int}$ | internal resistance, ($\mathsf{\Omega}$) |

R${}_{L}$ | load resistance, ($\mathsf{\Omega}$) |

Re | Reynolds number |

T | temperature, (K) |

u, v, w | x-y,z velocity components, (m/s) |

V | voltage, (V) |

W | channel width, (m) |

x, y, z | Cartesian coordinates, (m) |

ZT | figure of merit |

Greek Characters | |

$\alpha $${}_{nf}$ | nanofluid thermal diffusivity, (m${}^{2}$/s) |

$\alpha $ | Seeback coefficient, (V/K) |

$\mu $ | dynamic viscosity, (Pa·s) |

$\nu $ | kinematic viscosity, (m${}^{2}$/s) |

$\rho $ | density of the fluid, (kg/m${}^{3}$) |

$\sigma $ | electrical conductivity, (S/m) |

$\varphi $ | solid volume fraction |

$\eta $ | efficiency |

Subscripts | |

c | cold wall |

h | hot wall |

m | average |

nf | nanofluid |

## References

- Pourkiaei, S.M.; Ahmadi, M.H.; Sadeghzadeh, M.; Moosavi, S.; Pourfayaz, F.; Chen, L.; Yazdi, M.A.P.; Kumar, R. Thermoelectric cooler and thermoelectric generator devices: A review of present and potential applications, modeling and materials. Energy
**2019**, 186, 115849. [Google Scholar] [CrossRef] - Karthick, K.; Suresh, S.; Hussain, M.M.M.; Ali, H.M.; Kumar, C.S. Evaluation of solar thermal system configurations for thermoelectric generator applications: A critical review. Sol. Energy
**2019**, 188, 111–142. [Google Scholar] [CrossRef] - Irshad, K.; Habib, K.; Saidur, R.; Kareem, M.; Saha, B.B. Study of thermoelectric and photovoltaic facade system for energy efficient building development: A review. J. Clean. Prod.
**2019**, 209, 1376–1395. [Google Scholar] [CrossRef] - Weigand, B.; Spring, S. Multiple jet impingement—A review. Heat Transf. Res.
**2011**, 42, 101–142. [Google Scholar] [CrossRef] - Krishan, G.; Aw, K.C.; Sharma, R.N. Synthetic jet impingement heat transfer enhancement—A review. Appl. Therm. Eng.
**2019**, 149, 1305–1323. [Google Scholar] [CrossRef] - Nadda, R.; Kumar, A.; Maithani, R. Efficiency improvement of solar photovoltaic/solar air collectors by using impingement jets: A review. Renew. Sustain. Energy Rev.
**2018**, 93, 331–353. [Google Scholar] [CrossRef] - Chen, Y.; Ma, C.; Qin, M.; Li, Y. Theoretical study on impingement heat transfer with single-phase free-surface slot jets. Int. J. Heat Mass Transf.
**2005**, 48, 3381–3386. [Google Scholar] [CrossRef] - Tepe, A.Ü.; Yetişken, Y.; Uysal, Ü.; Arslan, K. Experimental and numerical investigation of jet impingement cooling using extended jet holes. Int. J. Heat Mass Transf.
**2020**, 158, 119945. [Google Scholar] [CrossRef] - Aldabbagh, L.B.Y.; Mohamad, A.A. A three-dimensional numerical simulation of impinging jet arrays on a moving plate. Int. J. Heat Mass Transf.
**2009**, 52, 4894–4900. [Google Scholar] [CrossRef] - Chattopadhyay, H.; Saha, S.K. Turbulent flow and heat transfer from a slot jet impinging on a moving plate. Int. J. Heat Fluid Flow
**2003**, 24, 685–697. [Google Scholar] [CrossRef] - Chiriac, V.A.; Ortega, A. A numerical study of the unsteady flow and heat transfer in a transitional confined slot jet impinging on an isothermal surface. Int. J. Heat Mass Transf.
**2002**, 45, 1237–1248. [Google Scholar] [CrossRef] - Koseoglu, M.F.; Baskaya, S. The role of jet inlet geometry in impinging jet heat transfer, modeling and experiments. Int. J. Therm. Sci.
**2010**, 49, 1417–1426. [Google Scholar] [CrossRef] - Rehman, M.M.U.; Qu, Z.; Fu, R.; Xu, H. Numerical study on free-surface jet impingement cooling with nanoencapsulated phase-change material slurry and nanofluid. Int. J. Heat Mass Transf.
**2017**, 109, 312–325. [Google Scholar] [CrossRef] - Nakharintr, L.; Naphon, P. Magnetic field effect on the enhancement of nanofluids heat transfer of a confined jet impingement in mini-channel heat sink. Int. J. Heat Mass Transf.
**2017**, 110, 753–759. [Google Scholar] [CrossRef] - Selimefendigil, F.; Öztop, H.F. Pulsating nanofluids jet impingement cooling of a heated horizontal surface. Int. J. Heat Mass Transf.
**2014**, 69, 54–65. [Google Scholar] [CrossRef] - Ahmadi, M.H.; Ghazvini, M.; Sadeghzadeh, M.; Nazari, M.A.; Ghalandari, M. Utilization of hybrid nanofluids in solar energy applications: A review. Nano-Struct. Nano-Objects
**2019**, 20, 100386. [Google Scholar] [CrossRef] - Arshad, W.; Ali, H.M. Graphene nanoplatelets nanofluids thermal and hydrodynamic performance on integral fin heat sink. Int. J. Heat Mass Transf.
**2017**, 107, 995–1001. [Google Scholar] [CrossRef] - Hamzah, M.H.; Sidik, N.A.C.; Ken, T.L.; Mamat, R.; Najafi, G. Factors affecting the performance of hybrid nanofluids: A comprehensive review. Int. J. Heat Mass Transf.
**2017**, 115, 630–646. [Google Scholar] [CrossRef] - Kasaeian, A.; Daneshazarian, R.; Mahian, O.; Kolsi, L.; Chamkha, A.J.; Wongwises, S.; Pop, I. Nanofluid flow and heat transfer in porous media: A review of the latest developments. Int. J. Heat Mass Transf.
**2017**, 107, 778–791. [Google Scholar] [CrossRef] - Mohammed, K.A.; Talib, A.A.; Nuraini, A.; Ahmed, K. Review of forced convection nanofluids through corrugated facing step. Renew. Sustain. Energy Rev.
**2017**, 75, 234–241. [Google Scholar] [CrossRef] - Pordanjani, A.H.; Aghakhani, S.; Afrand, M.; Mahmoudi, B.; Mahian, O.; Wongwises, S. An updated review on application of nanofluids in heat exchangers for saving energy. Energy Convers. Manag.
**2019**, 198, 111886. [Google Scholar] [CrossRef] - Sahin, A.Z.; Uddin, M.A.; Yilbas, B.S.; Al-Sharafi, A. Performance enhancement of solar energy systems using nanofluids: An updated review. Renew. Energy
**2020**, 145, 1126–1148. [Google Scholar] [CrossRef] - Sajid, M.U.; Ali, H.M. Recent advances in application of nanofluids in heat transfer devices: A critical review. Renew. Sustain. Energy Rev.
**2019**, 103, 556–592. [Google Scholar] [CrossRef] - Qiu, L.; Zhu, N.; Feng, Y.; Michaelides, E.E.; Żyła, G.; Jing, D.; Zhang, X.; Norris, P.M.; Markides, C.N.; Mahian, O. A review of recent advances in thermophysical properties at the nanoscale: From solid state to colloids. Phys. Rep.
**2020**, 843, 1–81. [Google Scholar] [CrossRef] - Taherian, H.; Alvarado, J.L.; Languri, E.M. Enhanced thermophysical properties of multiwalled carbon nanotubes based nanofluids. Part 1: Critical review. Renew. Sustain. Energy Rev.
**2018**, 82, 4326–4336. [Google Scholar] [CrossRef] - Yang, L.; Jiang, W.; Ji, W.; Mahian, O.; Bazri, S.; Sadri, R.; Badruddin, I.A.; Wongwises, S. A review of heating/cooling processes using nanomaterials suspended in refrigerants and lubricants. Int. J. Heat Mass Transf.
**2020**, 153, 119611. [Google Scholar] [CrossRef] - Ambreen, T.; Kim, M.H. Influence of particle size on the effective thermal conductivity of nanofluids: A critical review. Appl. Energy
**2020**, 264, 114684. [Google Scholar] [CrossRef] - Bahiraei, M.; Heshmatian, S. Graphene family nanofluids: A critical review and future research directions. Energy Convers. Manag.
**2019**, 196, 1222–1256. [Google Scholar] [CrossRef] - Liang, G.; Mudawar, I. Review of single-phase and two-phase nanofluid heat transfer in macro-channels and micro-channels. Int. J. Heat Mass Transf.
**2019**, 136, 324–354. [Google Scholar] [CrossRef] - Li, Q.; Xuan, Y.; Yu, F. Experimental investigation of submerged single jet impingement using Cu-water nanofluid. Appl. Therm. Eng.
**2012**, 36, 426–433. [Google Scholar] [CrossRef] - Mahdavi, M.; Sharifpur, M.; Meyer, J.P.; Chen, L. Thermal analysis of a nanofluid free jet impingement on a rotating disk using volume of fluid in combination with discrete modelling. Int. J. Therm. Sci.
**2020**, 158, 106532. [Google Scholar] [CrossRef] - Jajja, S.A.; Ali, W.; Ali, H.M.; Ali, A.M. Water cooled minichannel heat sinks for microprocessor cooling: Effect of fin spacing. Appl. Therm. Eng.
**2014**, 64, 76–82. [Google Scholar] [CrossRef] - Manca, O.; Mesolella, P.; Nardini, S.; Ricci, D. Numerical study of a confined slot impinging jet with nanofluids. Nanoscale Res. Lett.
**2011**, 6, 188. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Arshad, W.; Ali, H.M. Experimental investigation of heat transfer and pressure drop in a straight minichannel heat sink using TiO
_{2}nanofluid. Int. J. Heat Mass Transf.**2017**, 110, 248–256. [Google Scholar] [CrossRef] - Selimefendigil, F.; Oztop, H.F. Jet impingement cooling and optimization study for a partly curved isothermal surface with CuO-water nanofluid. Int. Commun. Heat Mass Transf.
**2017**, 89, 211–218. [Google Scholar] [CrossRef] - Naphon, P.; Nakharintr, L.; Wiriyasart, S. Continuous nanofluids jet impingement heat transfer and flow in a micro-channel heat sink. Int. J. Heat Mass Transf.
**2018**, 126, 924–932. [Google Scholar] [CrossRef] - Mohammadpour, J.; Lee, A. Investigation of nanoparticle effects on jet impingement heat transfer: A review. J. Mol. Liq.
**2020**, 316, 113819. [Google Scholar] [CrossRef] - Kramer, L.R.; Mara, A.L.O.; Souza, S.S.; Ando, O.H. Analytical and numerical study for the determination of a thermoelectric generator’s internal resistance. Energies
**2019**, 12, 3053. [Google Scholar] [CrossRef] [Green Version] - Kim, C.N. Development of a numerical method for the performance analysis of thermoelectric generators with thermal and electric contact resistance. Appl. Therm. Eng.
**2018**, 1305, 408–417. [Google Scholar] [CrossRef] - Zuckerman, N.; Lior, N. Jet impingement heat transfer: Physics, correlations, and numerical modeling. Adv. Heat Transf.
**2006**, 39, 565–631. [Google Scholar] - Sajjadi, H.; Delouei, A.A.; Izadi, M.; Mohebbi, R. Investigation of MHD natural convection in a porous media by double MRT lattice Boltzmann method utilizing MWCNT-Fe
_{3}O_{4}/water hybrid nanofluid. Int. J. Heat Mass Transf.**2019**, 132, 1087–1104. [Google Scholar] [CrossRef] - Brinkman, H. The viscosity of concentrated suspensions and solutions. J. Chem. Phys.
**1952**, 20, 571–581. [Google Scholar] [CrossRef] - Xue, Q. Model for thermal conductivity of carbon nanotube—Based composites. Physica B
**2005**, 368, 302–307. [Google Scholar] [CrossRef] - COMSOL A.B. COMSOL Multiphysics v. 5.4; COMSOL: Stockholm, Sweden, 2018. [Google Scholar]
- Sharif, M.A. Heat transfer from an isothermally heated flat surface due to confined laminar twin oblique slot-jet impingement. J. Therm. Sci. Eng. Appl.
**2015**, 7. [Google Scholar] [CrossRef] - Sahoo, D.; Sharif, M. Numerical modeling of slot-jet impingement cooling of a constant heat flux surface confined by a parallel wall. Int. J. Therm. Sci.
**2004**, 43, 877–887. [Google Scholar] [CrossRef] - Chen, M.; Rosendahl, L.A.; Condra, T. A three-dimensional numerical model of thermoelectric generators in fluid power systems. Int. J. Heat Mass Transf.
**2011**, 54, 345–355. [Google Scholar] [CrossRef]

**Figure 1.**3D schematic view of confined nanojet impinging system with TEG module (

**a**) and 2D representation with boundary conditions (

**b**).

**Figure 2.**Mesh independence test results for two different jet stream Reynolds number combinations ( (r${}_{1}$, r${}_{2}$) = (1, 1), z${}_{h}$ = 3w${}_{s}$, $\varphi \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0.02$).

**Figure 4.**Comparison of generated TEG power with the present code and available results in Ref. [47].

**Figure 5.**Effects of different jet stream Reynolds number combinations on the variation of streamlines within the channels, electric potential and temperature distributions within the TEG module ( (r${}_{1}$,r${}_{2}$) = (1,1), z${}_{h}$ = 3w${}_{s}$, $\varphi =0.02$).

**Figure 6.**Impacts of hot jet stream Reynolds number on the variation of interface temperatures of the cold and hot side (mid-axis) (

**a**,

**b**) and generated TEG power (

**c**) (Re${}_{2}$ = 500, (r${}_{1}$,r${}_{2}$) = (1,1), z${}_{h}$ = 3w${}_{s}$, $\varphi =0.02$).

**Figure 7.**Effects of different jet stream Reynolds number combinations on the distribution of hot (

**a**) and cold (

**b**) interface temperatures (mid-axis) ((r${}_{1}$, r${}_{2}$) = (1, 1), z${}_{h}$ = 3w${}_{s}$, $\varphi =0.02$).

**Figure 8.**Generated powers (

**a**) and efficiencies of the TEG device (

**b**) with varying jet stream Reynolds number combinations ((r${}_{1}$, r${}_{2}$) = (1, 1), z${}_{h}$ = 3w${}_{s}$, $\varphi =0.02$).

**Figure 9.**Effects of varying jet-stream inlet horizontal location combinations on the distribution of streamlines in the mid-plane channels (

**a**–

**c**) and electric potential variations in the TEG device (

**d**–

**f**) ((Re${}_{1}$, Re${}_{2}$) = (500, 500), z${}_{h}$ = 3w${}_{s}$, $\varphi =0.02$).

**Figure 10.**Impacts of jet inlet horizontal location combinations on the variation of the interface temperatures at the cold (

**a**) and hot side (

**b**) of the TEG module ((Re${}_{1}$, Re${}_{2}$) = (500, 500), z${}_{h}$ = 3w${}_{s}$, $\varphi =0.02$).

**Figure 11.**Generated powers (

**a**,

**b**) and efficiency (

**c**) variation of the TEG device with respect to changes in the jet inlet horizontal location combinations ((Re${}_{1}$, Re${}_{2}$) = (500, 500), z${}_{h}$ = 3w${}_{s}$, $\varphi =0.02$).

**Figure 12.**Impacts of distance from the inlet to target surface on the variation of interface temperatures at the cold (

**a**) and hot (

**b**) side ((Re${}_{1}$, Re${}_{2}$) = (500, 500), (r${}_{1}$, r${}_{2}$) = (1, 1), $\varphi =0.02$).

**Figure 13.**Generated power (

**a**) and efficiency (

**b**) of the TEG module with varying distance from the inlet to target surface ((Re${}_{1}$, Re${}_{2}$) = (500, 500), (r${}_{1}$, r${}_{2}$) = (1,1), $\varphi =0.02$).

**Figure 14.**Impacts of solid nanoparticle volume fractions of CNT on the variation of cold and hot interface temperatures ((Re${}_{1}$, Re${}_{2}$) = (500, 500), (r${}_{1}$, r${}_{2}$) = (1, 1), z${}_{h}$ = 3w${}_{s}$).

**Figure 15.**Generated power (

**a**) and efficiency (

**b**) of the TEG module with varying solid nanoparticle volume fractions of CNT and for different inlet horizontal distance of the hot jet stream ((Re${}_{1}$, Re${}_{2}$) = (500, 500), r${}_{2}$ = 1, z${}_{h}$ = 3w${}_{s}$).

**Figure 16.**Polynomial surface fit (

**a**) and residual (

**b**) plot for the generated TEG power with varying jet stream Reynolds numbers at $\varphi =0.02$.

**Figure 17.**Contour plot (

**a**) and residual (

**b**) obtained with the polynomial fit for the efficiency of the TEG device with varying jet stream Reynolds numbers at $\varphi =0.02$.

Symbol | P Type Leg (Bi${}_{2}$Te${}_{3}$) | N type leg (Bi${}_{2}$Te${}_{3}$) | Electrode (Copper) | Ceramic (Alumina) | |
---|---|---|---|---|---|

Thermal conductivity | k (W/m K) | 1.6 | 1.6 | 400 | 27 |

Electric conductivity | $\sigma $ (S/m) | $0.8\times {10}^{5}$ | $0.81\times {10}^{5}$ | $5.9\times {10}^{8}$ | - |

Seebeck coefficient | $\alpha $ (V/K) | $2.1\times {10}^{-4}$ | $-2.1\times {10}^{-4}$ | $6.5\times {10}^{-6}$ | - |

Heat capacity | C${}_{p}$ (J/kg K) | 154 | 154 | 385 | 900 |

Density | $\rho $ (kg/m${}^{3}$) | 7700 | 7700 | 8960 | 3900 |

Property | Water | Single-Walled CNT |
---|---|---|

$\rho \phantom{\rule{4pt}{0ex}}(\mathrm{kg}/{\mathrm{m}}^{3})$ | 997.1 | 2600 |

$\phantom{\rule{4.pt}{0ex}}{\mathrm{c}}_{p}\phantom{\rule{4pt}{0ex}}(\mathrm{J}/\mathrm{kg}\phantom{\rule{4.pt}{0ex}}\mathrm{K})$ | 4179 | 425 |

$\mathrm{k}\phantom{\rule{4pt}{0ex}}(\mathrm{W}/\mathrm{m}\phantom{\rule{4.pt}{0ex}}\mathrm{K})$ | 0.61 | 6600 |

$\mu $ (kg/ms) | 8.55 $\times {10}^{-4}$ | - |

Coefficient | Value ($\mathit{\varphi}=0$) | Value ($\mathit{\varphi}=0.02$) |
---|---|---|

p00 | 0.3809 (0.3744, 0.3873) | 0.4233 (0.4172, 0.4293) |

p10 | 0.04377 (0.0405, 0.04704) | 0.04445 (0.04136, 0.04754) |

p01 | 0.04111 (0.03784, 0.04438) | 0.04174 (0.03866, 0.04483) |

p20 | −0.01668 (−0.02091, −0.01246) | −0.01655 (−0.02054, −0.01256) |

p11 | 0.007408 (0.00403, 0.01079) | 0.006836 (0.003646, 0.01003) |

p02 | −0.0158 (−0.02002, −0.01157) | −0.01565 (−0.01963, −0.01166) |

Coefficient | Value ($\mathit{\varphi}=0$) | Value ($\mathit{\varphi}=0.02$) |
---|---|---|

p00 | 4.814 (4.767, 4.861) | 4.981 (4.938, 5.025) |

p10 | 0.09867 (0.07455, 0.1228) | 0.1542 (0.1323, 0.1762) |

p01 | 0.2611 (0.237, 0.2852) | 0.2405 (0.2185, 0.2624) |

p20 | −0.05066 (−0.0818, −0.01951) | −0.07421 (−0.1025, −0.04591) |

p11 | 0.01082 (−0.01409, 0.03574) | 0.01314 (−0.009496, 0.03578) |

p02 | −0.09839 (−0.1295, −0.06724) | −0.0921 (−0.1204, −0.0638) |

Fit Name | Value-Power ($\mathit{\varphi}=0$) | Value-Power ($\mathit{\varphi}=0.02$) |
---|---|---|

SSE | 0.0003231 | 0.0002882 |

R-square | 0.9946 | 0.9953 |

RMSE | 0.005685 | 0.005368 |

Fit Name | Value-Efficiency ($\mathbf{\varphi}=\mathbf{0}$) | Value-Efficiency ($\mathbf{\varphi}=\mathbf{0}.\mathbf{02}$) |

SSE | 0.01758 | 0.01452 |

R-square | 0.9865 | 0.9894 |

RMSE | 0.04193 | 0.0381 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Selimefendigil, F.; Oztop, H.F.; Sheremet, M.A.
Thermoelectric Generation with Impinging Nano-Jets. *Energies* **2021**, *14*, 492.
https://doi.org/10.3390/en14020492

**AMA Style**

Selimefendigil F, Oztop HF, Sheremet MA.
Thermoelectric Generation with Impinging Nano-Jets. *Energies*. 2021; 14(2):492.
https://doi.org/10.3390/en14020492

**Chicago/Turabian Style**

Selimefendigil, Fatih, Hakan F. Oztop, and Mikhail A. Sheremet.
2021. "Thermoelectric Generation with Impinging Nano-Jets" *Energies* 14, no. 2: 492.
https://doi.org/10.3390/en14020492