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Optimizing of a metal foam-assisted solar air heater performance: a thermo-hydraulic analysis of porous insert placement

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Abstract

A numerical assessment of the heat transfer efficacy of a solar air heater (SAH) was carried out. The SAH is supplied with a porous metal foam layer to improve thermal mixing. Both the local thermal non-equilibrium (LTNE) and Darcy-extended Forchheimer (DEF) models were employed to forecast fluid and thermal transport within the partly filled SAH channel. The analysis was performed for various values of dimensionless foam layer lengths (\(S=0-1\)), pore densities (\(\omega =10-40 {\text{PPI}}\)), and Reynolds numbers (\(Re = 4000-1\mathrm{6,000}\)) at a fixed value of layer thickness (\({H}_{f} =0.6\)). Based on the position of the porous layer, three distinct arrangements, marked as Case 1, Case 2, and Case 3, were explored. Regarding the parameters examined, the findings indicate a definite improvement in the average Nusselt number (\(Nu\)), but unfortunately, the friction factor also increases unfavorably. By reducing the length of the porous layer, a reasonable reduction in heat transfer rate and a significant decrease in pressure drop were noticed. The results showed about 26.64%, 48.73%, and 70.74% reductions in pressure drop by reducing the dimensionless foam length from 1 to 0.25, 0.5, and 0.75 respectively for \(\omega =10\) at \(Re = \mathrm{16,000}\). On the other side, there are only about 11.05%, 23.11%, and 40.78% reductions in \(Nu\). The exhaustive analysis of the thermal performance of SAH was conducted using the thermal performance factor (TPF), which considers the trade-off between the SAH channel’s potential for improved heat transmission and its cost for pressure loss. The TPF may reach a maximum of 2.82 compared to the empty channel when the metal foam layer is inserted with \(S=1\), for \(\omega =10\), and \(Re = \mathrm{16,000}\).

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Data availability

The data supporting the conclusions of this study are available within the work itself.

Abbreviations

\({a}_{sf}\) :

specific surface area, M−1

C :

Forchheimer coefficient

\({C}_{\upepsilon 1}, {C}_{\upepsilon 2}, {C}_{\mu }, {\sigma }_{k}, {\sigma }_{\epsilon }\) :

Constants in the \(k \_\varepsilon\) turbulent model

\({D}_{h}\) :

Hydraulic diameter, m

\({d}_{p}\) :

Pore diameter (m)

\({d}_{f}\) :

Fiber diameter (m)

f :

Friction factor

\(h\) :

heat transfer coefficient, Wm−2 K−1

H:

Duct height (m)

\({\text{t}}\) :

Metal foam layer thickness (m)

\({H}_{f}={\text{t}}/H\) :

Dimensionless metal foam height

\(K\) :

permeability (m2)

\(k\) :

Turbulent kinetic energy (m2/s2)

L 1 :

Inlet section length (m)

L 2 :

Absorber plate length (m)

L 3 :

Outlet section length (m)

\(l\) :

Metal foam layer length (m)

\(Nu=\frac{\overline{h} {D }_{h}}{{\lambda }_{f}}\) :

Nusselt number

P:

pressure (Pa)

\(Re=\frac{\rho {u}_{av}{D}_{h}}{{\mu }_{f}}\) :

Reynolds number

\(S=\frac{l}{{L}_{1}}\) :

Dimensionless metal foam length

T:

temperature (K)

\(u,v\) :

Velocity component, m s−1

\(x, y\) :

Cartesian coordinates (m)

\(X, Y\) :

Non-dimensional Cartesian coordinates, \(X=x/{L}_{2}\), \(Y=y/H\)

\(\overset{{^\prime}^\prime}q\)  :

Heat flux (W m−2)

\(\rho\) :

density, kg/m3

µ:

dynamic viscosity, kg. m−1.s−1

\(\varnothing\) :

porosity

\(\omega\) :

pore density, PPI

λ:

thermal conductivity, Wm−1 K.−1

\(\varepsilon\) :

dissipation rate of k, (m2s−3)

av :

average

s :

smooth duct, solid

f :

fluid

e :

effictive

i :

inlet

o :

Outlet

DEF :

Darcy-extended Forchheimer model

FPSC :

flat-plate solar collector

LTE :

local thermal equilibrium

LTNE :

local thermal non-equilibrium

PEC :

performance evaluation criteria

PPI :

pore per inch

SAH :

solar air heater

TPF :

thermal performance factor

References

  • Alazmi B, Vafai K (2002) Constant wall heat flux boundary conditions in porous media under local thermal non-equilibrium conditions. Int J Heat Mass Transf 45(15):3071–3087

    Article  Google Scholar 

  • Albojamal A, Haghighi A, Hamzah H (2017) Analysis of thermal transport through a flat-plate solar collector integrated with metal-foam blocks. Int J Energy Eng Sci 2(2):55–68

    Google Scholar 

  • Al-Chlaihawi KKI, Hasan MR, Ekaid AL (2024a) Compound passive heat transfer augmentation techniques: a comprehensive review. Heat Transfer 53(2):363–421

    Article  Google Scholar 

  • Al-Chlaihawi KKI, Hasan MR, Ekaid AL (2024b) Thermohydraulic performance assessment of a solar air heater with equilateral-triangular, trapezoidal, and square sectional ribs on the absorber plate: a comparative study. Heat Transfer 53(2):441–471

    Article  Google Scholar 

  • Al-Chlaihawi KKI, Alyas BH, Badr AA (2023) CFD Based numerical performance assessment of a solar air heater duct roughened by transverse-trapezoidal sectioned ribs. Int J Heat Technol 41:5

  • Ali RMK, Ghashim SL (2023) Numerical analysis of the heat transfer enhancement by using metal foam. Case Stud Therm Eng 49:103336

    Article  Google Scholar 

  • Anirudh K, Dhinakaran S (2020a) Numerical study on performance improvement of a flat-plate solar collector filled with porous foam. Renew Energy 147:1704–1717

    Article  Google Scholar 

  • Anirudh K, Dhinakaran S (2020b) Performance improvement of a flat-plate solar collector by inserting intermittent porous blocks. Renew Energy 145:428–441. https://doi.org/10.1016/j.renene.2019.06.015

    Article  Google Scholar 

  • Anirudh K, Dhinakaran S (2021) Numerical analysis of the performance improvement of a flat-plate solar collector using conjugated porous blocks. Renew Energy 172:382–391. https://doi.org/10.1016/j.renene.2021.02.145

    Article  Google Scholar 

  • Balakrishnan P, Vengadesan E, Bhowal B, Senthil R (2023) Energy and enviro-economic analysis of a solar air heater with wedge turbulators. Environ Sci Pollut Res 30(57):120844–120862. https://doi.org/10.1007/s11356-023-30792-2

    Article  CAS  Google Scholar 

  • Bashria A, Adam NM (2008) Performance analysis of single and double passes flat plate collector with and without porous media. J Mech Eng 58(5–6):275–290

    Google Scholar 

  • Bayrak F, Oztop HF (2015) Experimental analysis of thermal performance of solar air collectors with aluminum foam obstacles. J Therm Sci Technol 35(1):11–20

    Google Scholar 

  • Boomsma K, Poulikakos D (2001) On the effective thermal conductivity of a three-dimensionally structured fluid-saturated metal foam. Int J Heat Mass Transf 44(4):827–836

    Article  CAS  Google Scholar 

  • Bovand M, Rashidi S, Esfahani JA (2016) Heat transfer enhancement and pressure drop penalty in porous solar heaters: numerical simulations. Sol Energy 123:145–159. https://doi.org/10.1016/j.solener.2015.10.054

    Article  Google Scholar 

  • Calmidi VV, Mahajan RL (2000) Forced convection in high porosity metal foams. J Heat Transfer 122(3):557–565

    Article  CAS  Google Scholar 

  • Calmidi VV (1998) Transport phenomena in high porosity fibrous metal foams. University of Colorado at Boulder. Ph.D. thesis

  • Chen C-C, Huang P-C (2012) Numerical study of heat transfer enhancement for a novel flat-plate solar water collector using metal-foam blocks. Int J Heat Mass Transf 55(23):6734–6756. https://doi.org/10.1016/j.ijheatmasstransfer.2012.06.082

    Article  Google Scholar 

  • Chen Z, Gu M, Peng D (2010) Heat transfer performance analysis of a solar flat-plate collector with an integrated metal foam porous structure filled with paraffin. Appl Therm Eng 30(14–15):1967–1973

    Article  CAS  Google Scholar 

  • Diganjit R, Gnanasekaran N, Mobedi M (2022) Numerical study for enhancement of heat transfer using discrete metal foam with varying thickness and porosity in solar air heater by LTNE method. Energies 15(23):8952

    Article  CAS  Google Scholar 

  • Dukhan N, Al-Rammahi MA, Suleiman AS (2013) Fluid temperature measurements inside metal foam and comparison to Brinkman-Darcy flow convection analysis. Int J Heat Mass Transf 67:877–884

    Article  CAS  Google Scholar 

  • Dukhan N, Bağcı Ö, Özdemir M (2015) Thermal development in open-cell metal foam: an experiment with constant wall heat flux. Int J Heat Mass Transf 85:852–859

    Article  CAS  Google Scholar 

  • Fu Y, Xia Y, Lin X, Cheng Z, Zhang Z, Feng J, Wang H (2023) A novel structure design and numerical analysis of porous media-assisted enhanced thermal performance of flat-plate solar collector. Therm Sci Eng Prog 40:101777. https://doi.org/10.1016/j.tsep.2023.101777

    Article  Google Scholar 

  • Garrity PT, Klausner JF, Mei R (2010) Performance of aluminum and carbon foams for air side heat transfer augmentation. J Heat Transfer 132(12):121901

  • Granqvist CG (2007) Transparent conductors as solar energy materials: a panoramic review. Sol Energy Mater Sol Cells 91(17):1529–1598

    Article  CAS  Google Scholar 

  • Handbook AA, Atlanta G (2003) UAS: American Society of Heating. Refrigerating and Air Conditioning Engineers

  • Jadhav PH, Gnanasekaran N (2021) Optimum design of heat exchanging device for efficient heat absorption using high porosity metal foams. Int Commun Heat Mass Transfer 126:105475

    Article  Google Scholar 

  • Jasim NM, Fayyadh EM, Razoki Hasan M (2023) Numerical analysis to study the effect of foam thickness on the thermal-hydraulic performance of the metal foam heat exchanger. ICPER 2020, Singapore

  • Jouybari HJ, Saedodin S, Zamzamian A, Nimvari ME (2017) Experimental investigation of thermal performance and entropy generation of a flat-plate solar collector filled with porous media. Appl Therm Eng 127:1506–1517

    Article  Google Scholar 

  • Kotresha B, Gnanasekaran N (2020) Numerical simulations of fluid flow and heat transfer through aluminum and copper metal foam heat exchanger – a comparative study. Heat Transfer Eng 41(6–7):637–649. https://doi.org/10.1080/01457632.2018.1546969

  • Kurtbas I, Celik N (2009) Experimental investigation of forced and mixed convection heat transfer in a foam-filled horizontal rectangular channel. Int J Heat Mass Transf 52(5–6):1313–1325

    Article  CAS  Google Scholar 

  • Lin W, Xie G, Yuan J, Sundén B (2016) Comparison and analysis of heat transfer in aluminum foam using local thermal equilibrium or nonequilibrium model. Heat Transfer Eng 37(3–4):314–322

    Article  CAS  Google Scholar 

  • Lu W, Zhao C, Tassou S (2006) Thermal analysis on metal-foam filled heat exchangers. Part I: Metal-foam filled pipes. Int J Heat Mass Tran 49(15–16):2751–2761

    Article  Google Scholar 

  • Nimvari ME, Maerefat M, El-Hossaini M (2012) Numerical simulation of turbulent flow and heat transfer in a channel partially filled with a porous media. Int J Therm Sci 60:131–141

    Article  Google Scholar 

  • Nimvari ME, Jouybari NF, Esmaili Q (2018) A new approach to mitigate intense temperature gradients in ceramic foam solar receivers. Renew Energy 122:206–215

    Article  Google Scholar 

  • Patel SS, Lanjewar A (2022) A critical review on different roughness geometries and their effect on heat transfer and friction factor. Environ Sci Pollut Res 29(11):15391–15431. https://doi.org/10.1007/s11356-021-16298-9

    Article  Google Scholar 

  • Patel YM, Jain SV, Lakhera VJ (2020) Thermo-hydraulic performance analysis of a solar air heater roughened with reverse NACA profile ribs. Appl Therm Eng 170:114940

    Article  Google Scholar 

  • Prakash C, Saini RP (2019) Use of artificial roughness for performance enhancement of solar air heaters—a review. Int J Green Energy 16(7):551–572. https://doi.org/10.1080/15435075.2019.1598418

    Article  Google Scholar 

  • Rajendran V, Singaraj K, Rajarathinam J (2023) Environmental, economic, and performance assessment of solar air heater with inclined and winglet baffle. Environ Sci Pollut Res 30(6):14337–14352. https://doi.org/10.1007/s11356-022-23213-3

    Article  Google Scholar 

  • Rashidi S, Bovand M, Esfahani JA (2015) Heat transfer enhancement and pressure drop penalty in porous solar heat exchangers: a sensitivity analysis. Energy Convers Manage 103:726–738. https://doi.org/10.1016/j.enconman.2015.07.019

    Article  Google Scholar 

  • Saedodin S, Zamzamian S, Nimvari ME, Wongwises S, Jouybari HJ (2017) Performance evaluation of a flat-plate solar collector filled with porous metal foam: experimental and numerical analysis. Energy Convers Manage 153:278–287

    Article  Google Scholar 

  • Sahu MK, Gorai VK, Saha BC (2023) Applications of extended surfaces for improvement in the performance of solar air heaters—a detailed systematic review. Environ Sci Pollut Res 30(19):54429–54447. https://doi.org/10.1007/s11356-023-26360-3

    Article  Google Scholar 

  • Singh AK, Saxena A, Agarwal N (2023) Performance analysis of a serrated absorber plate solar air heater with paraffin wax storage. Environ Sci Pollut Res. https://doi.org/10.1007/s11356-023-27961-8

    Article  Google Scholar 

  • Webb R, Eckert E (1972) Application of rough surfaces to heat exchanger design. Int J Heat Mass Transf 15(9):1647–1658

    Article  Google Scholar 

  • Xia Y, Lin X, Cheng Z, Xie F, Huang J (2023a) Numerical study on the enhanced thermal performance of the porous media-assisted flat-plate solar collector. Int J Energy Res 2023:2244771. https://doi.org/10.1155/2023/2244771

    Article  Google Scholar 

  • Xia Y, Lin X, Shu Y, Cheng Z (2023b) Enhanced thermal performance of a flat-plate solar collector inserted with porous media: a numerical simulation study. Therm Sci Eng Prog 44:102063. https://doi.org/10.1016/j.tsep.2023.102063

    Article  Google Scholar 

  • Zhao C (2012) Review on thermal transport in high porosity cellular metal foams with open cells. Int J Heat Mass Transf 55(13–14):3618–3632

    Article  CAS  Google Scholar 

  • Zhu Q, Xuan Y (2017) Pore scale numerical simulation of heat transfer and flow in porous volumetric solar receivers. Appl Therm Eng 120:150–159

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the University of Technology, Iraq for providing some data included in this work.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Al-Qadisiyah, Al Diwaniyah, Al-Qadisiyah, 58001, Iraq

    Kadhim Al-Chlaihawi

  2. Mechanical Engineering Department, University of Technology, Alsina’a Street, 10066, Baghdad, Iraq

    Kadhim Al-Chlaihawi, Moayed Hasan & Ali Ekaid

Authors
  1. Kadhim Al-Chlaihawi
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  2. Moayed Hasan
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  3. Ali Ekaid
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Contributions

All authors contributed to the study conception and design. Mathematical modeling, numerical simulations, and analysis were performed by Kadhim Al-Chlaihawi, Moayed Hasan, and Ali Ekaid. The first draft of the manuscript was written by Kadhim Al-Chlaihawi and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Kadhim Al-Chlaihawi.

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Al-Chlaihawi, K., Hasan, M. & Ekaid, A. Optimizing of a metal foam-assisted solar air heater performance: a thermo-hydraulic analysis of porous insert placement. Environ Sci Pollut Res 31, 34995–35017 (2024). https://doi.org/10.1007/s11356-024-33593-3

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