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A comparative study on entropy and thermal performance of Cu/CuO/Fe3O4-based engine oil Carreau nanofluids in PTSCs: a theoretical model for solar-powered aircraft applications

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Abstract

This study marks the pioneering utilization of thermal efficiency involving non-Newtonian Carreau nanofluids within parabolic trough solar collectors (PTSCs). The research delves into nanofluids encompassing copper-engine oil, copper (II) oxide-engine oil, and iron (II, III) oxide-engine oil Carreau nanofluids within PTSCs. Evaluation of PTSC’s heat efficiency encompasses a spectrum of physical phenomena, including porous medium effects, slanted magnetic fields, non-uniform heat sources/sinks, thermal radiation, viscous dissipation, and thermophoresis. Additionally, the study investigates the influence of several parameters governing nanofluid flow on velocity, temperature, entropy generation, skin friction coefficient, and local Nusselt number of the Carreau nanofluids within PTSC setups. The research adopts a theoretical model that represents the flow and thermal dynamics of PTSCs integrated into a solar-powered aircraft, highlighting the pivotal role of nanoparticle thermal conductivity. Numerical results reveal substantial enhancements in heat efficiency within engine-oil Carreau nanofluids, encompassing copper, copper (II) oxide, and iron (II, III) oxide. These enhancements translate to relative increments of 68.490%, 50.292%, and 42.013% in maximum heat performance, underscoring the potential of Carreau nanofluids to elevate PTSC efficiency, suggesting a theoretical model for their potential application in solar-powered aircraft. Overall, this study holds promise for cleaner and more sustainable energy applications in the realms of solar energy and solar-powered aircraft. The execution of intricate engineering simulations falls beyond the scope of our current study.

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Data availability

The data from this study is only presented in the paper article to support the results.

Abbreviations

\(a\) :

Primary stretching rate \(\left( {{\text{s}}^{ - 1} } \right)\)

\(a^{*}\) :

Thermal discrepancy rate \(\left( {{\text{s}}^{ - 1} } \right)\)

\(A_{{{\text{r1}}}}\) :

First Rivlin–Erickson tensor

\(B_{0}\) :

Strength of the magnetic field \(\left( T \right)\)

\({\text{B}}_{{\text{K}}}\) :

Brinkmann number

\({\text{Bi}}_{{\text{T}}}\) :

Thermal Biot number

\(C_{\text f}\) :

Skin friction constant \(\left( {{\text{N m}}^{{ - {2}}} } \right)\)

\(C_{{\text{p}}}\) :

Specific heat \(\left( {{\text{J Kg}}^{{ - {1}}} {\text{ K}}^{{ - {1}}} } \right)\)

\(D_{{\text{T}}}\) :

Thermophoretic diffusion coefficient \({\text{(m}}^{{2}} {\text{s}}^{{ - {1}}} {)}\)

\({\text{Ec}}\) :

Eckert number

\(f^{\prime }\) :

Dimensionless velocity

\(h_{{\text{f}}}\) :

Heat transfer coefficient \(\left( {{\text{W m}}^{{ - {2}}} {\text{ K}}^{{ - {1}}} } \right)\)

\(I\) :

Identity tensor

\(k\) :

Thermal conductivity \(\left( {{\text{W m}}^{{ - {1}}} {\text{ K}}^{{ - {1}}} } \right)\)

\(k_{{\text{p}}}\) :

Porosity \({\text{(m}}^{{2}} {)}\)

\(k^{*}\) :

Mean absorption coefficient \(\left( {{\text{m}}^{ - 1} } \right)\)

\(K\) :

Porosity parameter

m :

Nanoparticle shape factor

\({\text{M}}\) :

Magnetic number

\(N_{{\text{G}}}\) :

Entropy generation dimensionless factor

\(N_{{\text{r}}}\) :

Thermal radiation parameter

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

Thermophoretic parameter

\({\text{Nu}}_{{\text{x}}}\) :

Local Nusselt number

\(N_{{\text{w}}}\) :

Slip length \(\left( {\text{m}} \right)\)

\(p\) :

Pressure \(\left( {{\text{N m}}^{{ - {2}}} } \right)\)

\({\text{Pr}}\) :

Prandtl number

\(q_{{\text{r}}}\) :

Radiative heat flux \(\left( {{\text{W m}}^{{ - {2}}} } \right)\)

\(Re\) :

Reynolds number

\({\text{Re}}_{{\text{x}}}\) :

Local Reynolds number

\(S\) :

Mass transfer parameter

\(t\) :

Time \(\left( {\text{s}} \right)\)

\(T\) :

Temperature \(\left( {\text{K}} \right)\)

\(u,v\) :

Velocity components \(\left( {{\text{m s}}^{{ - {1}}} } \right)\)

\(V_{{\text{w}}}\) :

Surface permeability

x, y :

Dimensional space coordinates \(\left( {\text{m}} \right)\)

\(\alpha\) :

Thermal diffusion rate \({\text{(m}}^{{2}} {\text{s}}^{{ - {1}}} {)}\)

\(\gamma\) :

The magnetic field’s angle of inclination

\(\Gamma\) :

Carreau fluid time constant \(\left( s \right)\)

\(\eta\) :

Dimensionless space variable

\(\theta\) :

Dimensionless temperature

\(\kappa_{0}\) :

Surface thermal conductance \(\left( {{\text{W m}}^{{ - {1}}} {\text{ K}}^{{ - {1}}} } \right)\)

\(\Lambda\) :

Velocity parameter

\(\mu\) :

Viscosity \(\left( {{\text{Kg m}}^{{ - {1}}} {\text{s}}^{{ - {1}}} } \right)\)

\(\nu\) :

Kinematic viscosity \({\text{(m}}^{{2}} {\text{s}}^{{ - {1}}} {)}\)

\(\rho\) :

Density \(\left( {{\text{Kg m}}^{{ - {3}}} } \right)\)

\(\sigma\) :

Electrical conductivity \(\left( {{\text{S m}}^{{ - {1}}} } \right)\)

\({\upsigma }^{*}\) :

Stefan–Boltzmann constant \(\left( {{\text{W m}}^{{ - {2}}} {\text{ K}}^{{ - {4}}} } \right)\)

\(\tau\) :

Stress tensor

\(\varphi\) :

Nanoparticle concentration \(\left( {{\text{mol m}}^{{ - {3}}} } \right)\)

\(\chi\) :

Ratio of the operative heat capability

\(\Omega\) :

Difference in temperature parameter

\(f\) :

Base fluid

\({\text{nf}}\) :

Nanofluid

\(s\) :

Solid particles

\(W\) :

Wall

\(\infty\) :

Free stream

References

  1. Soeder DJ. Fossil fuels and climate change, in: fracking and the environment. Cham: Springer; 2021.

    Book  Google Scholar 

  2. Holmberg K, Erdemir A. The impact of tribology on energy use and CO2 emission globally and in combustion engine and electric cars. Tribol Int. 2019;135:389–96. https://doi.org/10.1016/j.triboint.2019.03.024.

    Article  Google Scholar 

  3. Shahzad F, Jamshed W, et al. Thermal analysis characterization of solar-powered ship using Oldroyd hybrid nanofluids in parabolic trough solar collector: an optimal thermal application. Nanotechnol Rev. 2022;11:2015–37. https://doi.org/10.1515/ntrev-2022-0108.

    Article  CAS  Google Scholar 

  4. Jamshed W, Sirin C, Selimefendigil F, Shamshuddin MD, Altowairqi Y, Eid MR. Thermal characterization of coolant Maxwell type nanofluid flowing in parabolic trough solar collector (PTSC) used inside solar powered ship application. Coatings. 2021;12:1552. https://doi.org/10.3390/coatings11121552.

    Article  CAS  Google Scholar 

  5. Shahzad F, Jamshed W, et al. Thermal cooling efficacy of a solar water pump using Oldroyd-B (aluminum alloy-titanium alloy/engine oil) hybrid nanofluid by applying new version for the model of Buongiorno. Sci Rep. 2022;12:19817. https://doi.org/10.1038/s41598-022-24294-3.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. Ouni M, Ladhar L, Omri M, Jamshed W, Eid MR. Solar water-pump thermal analysis utilizing copper-gold/engine oil hybrid nanofluid flowing in parabolic trough solar collector: thermal case study. Case Stud Therm Eng. 2022;30:101756. https://doi.org/10.1016/j.csite.2022.101756.

    Article  Google Scholar 

  7. Munawwar S, Ghedira H. A review of renewable energy and solar industry growth in the GCC region. Energy Procedia. 2014;57:3191–202. https://doi.org/10.1016/j.egypro.2015.06.069.

    Article  Google Scholar 

  8. Mahian O, Kianifar A, Kalogirou SA, et al. A review of the applications of nanofluids in solar energy. Int J Heat Mass Transfer. 2013;57:582–94.

    Article  CAS  Google Scholar 

  9. Swiss solar plane makes history with night flight. https://web.archive.org/web/20100710042340/http://www.swisster.ch/news/science-tech/swiss-solar-plane-makes-history-with-night-flight.html

  10. Solar impulse lands in Hawaii after longest non-stop solo flight in history. https://www.theguardian.com/environment/2015/jul/03/solar-impulse-lands-in-hawaii-after-longest-non-stop-solo-flight-in-history

  11. We made it around the world. 40'000km without fuel, a first for energy. https://aroundtheworld.solarimpulse.com/adventure, Accessed 2023

  12. Inside the first solar-powered flight around the world, a new documentary highlights the challenges overcome by the experimental aircraft, solar impulse, future of energy, a smithsonian magazine special reports, https://www.smithsonianmag.com/innovation/, 2018

  13. Ten most breathtaking photos from the first round-the-world solar flight, https://blog.solarimpulse.com, Accessed 2023

  14. Exploration to change the world, The Solar Impulse Foundation, https://solarimpulse.com/, Accessed 2023

  15. Kalogirou SA. Solar thermal collectors and applications. Prog Energy Combust Sci. 2004;30:231–95. https://doi.org/10.1016/j.pecs.2004.02.001.

    Article  CAS  Google Scholar 

  16. Jamshed W, Alanazi AK, Isa SSPM, et al. Thermal efficiency enhancement of solar aircraft by utilizing unsteady hybrid nanofluid: a single-phase optimized entropy analysis. Sustain Energy Technol Assess. 2022. https://doi.org/10.1016/j.seta.2021.101898.

    Article  Google Scholar 

  17. Jamshed W. Thermal augmentation in solar aircraft using tangent hyperbolic hybrid nanofluid: a solar energy application. Energy Environ. 2021. https://doi.org/10.1177/0958305X211036671.

    Article  Google Scholar 

  18. Hussain SM, Jamshed W, Akgül EK, et al. Mechanical improvement in solar aircraft by using tangent hyperbolic single-phase nanofluid. Proc Inst Mech Eng Part E. 2021. https://doi.org/10.1177/09544089211059377.

    Article  Google Scholar 

  19. Shahzad F, Jamshed W, Sathyanarayanan SUD, et al. Thermal analysis on -Forchheimer swirling Casson hybrid nanofluid flow inside parallel plates in parabolic trough solar collector: an application to solar aircraft. Int J Energy Res. 2021;45:20812–34. https://doi.org/10.1002/er.7140.

    Article  CAS  Google Scholar 

  20. Sajid, Jamshed W, Shahzad F, et al. Study on heat transfer aspects of solar aircraft wings for the case of Reiner-Philippoff hybrid nanofluid past a parabolic trough: Keller box method. Phys Scrip. 2021. https://doi.org/10.1088/1402-4896/ac0a2a.

    Article  Google Scholar 

  21. Jamshed W, Nisar KS, Ibrahim RW, et al. Thermal expansion optimization in solar aircraft using tangent hyperbolic hybrid nanofluid: a solar thermal application. J Market Res. 2021;14:985–1006. https://doi.org/10.1016/j.jmrt.2021.06.031.

    Article  CAS  Google Scholar 

  22. Hussain SM. Entropy generation and thermal performance of Williamson hybrid nanofluid flow used in solar aircraft application as the main coolant in parabolic trough solar collector. Waves Random Complex Med. 2023. https://doi.org/10.1080/17455030.2022.2110624.

    Article  Google Scholar 

  23. Salawu SO, Obalalu AM, Shamshuddin MD. Nonlinear solar thermal radiation efficiency and energy optimization for magnetized hybrid prandtl-eyring nanoliquid in aircraft. Arab J Sci Eng. 2022. https://doi.org/10.1007/s13369-022-07080-1.

    Article  Google Scholar 

  24. Jamshed W. Thermal augmentation in solar aircraft using tangent hyperbolic hybrid nanofluid: a solar energy application. Energy Environ. 2022;33:1090–133. https://doi.org/10.1177/0958305X211036671.

    Article  CAS  Google Scholar 

  25. Sajid T, Jamshed W, Shahzed F, et al. Study on heat transfer aspects of solar aircraft wings for the case of Reiner-Philippoff hybrid nanofluid past a parabolic trough: Keller box method. Phys Scrip. 2021. https://doi.org/10.1088/1402-4896/ac0a2a.

    Article  Google Scholar 

  26. Hussain SM. Entropy generation and thermal performance of Williamson hybrid nanofluid flow used in solar aircraft application as the main coolant in parabolic trough solar collector. Waves Random Complex Med. 2022. https://doi.org/10.1080/17455030.2022.2110624.

    Article  Google Scholar 

  27. Hussain SM, Jamshed W, Akgul EK, Nasir NAAM. Mechanical improvement in solar aircraft by using tangent hyperbolic single-phase nanofluid. J Process Mech Eng. 2021. https://doi.org/10.1177/09544089211059377.

    Article  Google Scholar 

  28. AbuGhanem M, Raafat PB, Ibrahim FN, et al. Comparative characterization of entropy and heat transfer in carbon-based magnetohydrodynamic Cross nanofluids flowing through PTSCs: advancing thermal applications for solar-powered aircraft. Int J Model Simul. 2024. https://doi.org/10.1080/02286203.2023.2301211.

    Article  Google Scholar 

  29. Petrescu RV, Aversa R, Akash B, et al. Sustainable energy for aerospace vessels. J Aircraft Spacecraft Technol. 2017;1:234–40.

    Article  Google Scholar 

  30. Mori M, Kagawa H, Saito Y. Summary of studies on space solar power systems of Japan Aerospace Exploration Agency (JAXA). Acta Astronaut. 2006;59:132–8. https://doi.org/10.1016/j.actaastro.2006.02.033.

    Article  Google Scholar 

  31. Verduci R, Romano V, Brunetti G, et al. Solar energy in space applications: review and technology perspectives. Adv Energy Mater. 2022;2:2200125. https://doi.org/10.1002/aenm.202200125.

    Article  CAS  Google Scholar 

  32. Okolie JA, Patra BR, Mukherjee A, et al. Futuristic applications of hydrogen in energy, biorefining, aerospace, pharmaceuticals and metallurgy. Int J Hydrog Energy. 2021;46:8885–905. https://doi.org/10.1016/j.ijhydene.2021.01.014.

    Article  CAS  Google Scholar 

  33. Choi S. Enhancing thermal conductivity of fluids with nanoparticles. Int Mech Eng Congr Exhib. 1995;66:99–105.

    Google Scholar 

  34. Bouslimi J, Alkathiri AA, et al. Thermal properties, flow and comparison between Cu and Ag nanoparticles suspended in sodium alginate as Sutterby nanofluids in solar collector. Case Stud Therm Eng. 2022;39:102358.

    Article  Google Scholar 

  35. Shahzad F, Jamshed W, et al. Thermal amelioration in heat transfer rate using Oldroyd-B model hybrid nanofluid by CNTs-based kerosene oil flow in solar collectors applications. Waves Random Complex Med. 2022. https://doi.org/10.1080/17455030.2022.2157511.

    Article  Google Scholar 

  36. Hamada MA, Khalil H, Al-Sood MMA, Sharsir SW. An experimental investigation of nanofluid, nanocoating and energy storage materials on the performance of parabolic trough collector. Appl Therm Eng. 2023. https://doi.org/10.1016/j.applthermaleng.2022.119450.

    Article  Google Scholar 

  37. Ekiciler R, Arslan K, Turgut O, Kursun B. The effect of hybrid nanofluid on heat transfer performance of parabolic trough solar collector receiver. J Therm Anal Calorim. 2021;143:1637–54. https://doi.org/10.1007/s10973-020-09717-5.

    Article  CAS  Google Scholar 

  38. Ekiciler R, Arslan K, Turgut O. Application of nanofluid flow in entropy generation and thermal performance analysis of parabolic trough solar collector: experimental and numerical study. J Therm Anal Calorim. 2023;148:7299–318. https://doi.org/10.1007/s10973-023-12187-0.

    Article  CAS  Google Scholar 

  39. Abidi A, Sajadi SM. Impact of fin and hybrid nanofluid on hydraulic-thermal performance and entropy generation in a solar collector using a two-phase approach. Eng Anal Boundary Elem. 2023;156:311–20. https://doi.org/10.1016/j.enganabound.2023.08.016.

    Article  Google Scholar 

  40. Ajbar W, Parrales A, Huicochea A, Hernández JA. Different ways to improve parabolic tough solar collectors’ performance over the last four decades and their applications: a comprehensive review. Renew Sustain Energy Rep. 2022;156:111947. https://doi.org/10.1016/j.rser.2021.111947.

    Article  CAS  Google Scholar 

  41. Jamshed W, Shahzad F, Safdar R, Sajid T, Eid MR, Nisar KS. Implementing renewable solar energy in presence of Maxwell nanofluid in parabolic trough solar collector: a computational study. Waves Random Complex Med. 2021. https://doi.org/10.1080/17455030.2021.1989518.

    Article  Google Scholar 

  42. Nabwey HA, Reddy MG, Kumar BKN, Sandeep N. Effect of resistive and radiative heats on enhanced heat transfer of parabolic trough solar collector. J Process Mech Eng. 2022. https://doi.org/10.1177/09544089221117317.

    Article  Google Scholar 

  43. Moatimid GM, Mohamed MAA, Elagamy K. A Casson nanofuid fow within the conical gap between rotating surfaces of a cone and a horizontal disc. Sci Rep. 2022;12:11275. https://doi.org/10.1038/s41598-022-15094-w.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. Mohamed YM, et al. Peristaltic transport of Carreau coupled stress nanofluid with Cattaneo-Christov heat flux model inside a symmetric channel. J Adv Res Fluid Mech Therm Sci. 2022;98(1):1–1.

    Article  Google Scholar 

  45. Elshekh SS, Abd Elhady MK, Ibrahim FN. Fluid film squeezed between two rotating disks in the presence of a magnetic field. Int J Eng Sci. 1996;34(10):1183–95. https://doi.org/10.1016/0020-7225(96)00010-9.

    Article  CAS  Google Scholar 

  46. Raafat PB, Ibrahim FN. Entropy and heat transfer investigation of Casson-Maxwell, Casson-Jeffrey, and Casson–Oldroyd-B binary nanofluids in a parabolic trough solar collector: a comparative study. J Therm Anal Calorim. 2023;148:4477–93. https://doi.org/10.1007/s10973-023-12003-9.

    Article  CAS  Google Scholar 

  47. Gu C, Qiu R, Liu S, You Z, Qin R. Shear thickening effects of drag-reducing nanofluids for low permeability reservoir. Adv Geo-Energy Res. 2020;4:317–25.

    Article  CAS  Google Scholar 

  48. Kalaitzis A, Makrygianni M, Theodorakos I, Hatziapostolou A, Melamed S, Kabla A, de la Vega F, Zergioti I. Jetting dynamics of Newtonian and non-Newtonian fluids via laser-induced forward transfer: experimental and simulation studies. Appl Surf Sci. 2019;465:136–42. https://doi.org/10.1016/j.apsusc.2018.09.084.

    Article  CAS  Google Scholar 

  49. Chen YH, Yue YF, Zhang Y, Li RP, Xu X. Numerical investigation of vibration suppression for the combined device of non-newtonian fluids coupled elastic baffle. J Appl Fluid Mech. 2023;16:591–602.

    Google Scholar 

  50. Santos TF, Santos CM, Aquino MS, Oliveira FR, Medeiros JI. Statistical study of performance properties to impact of Kevlar® woven impregnated with non-Newtonion fluid (NNF). J Mater Res Technol. 2020. https://doi.org/10.1016/j.jmrt.2020.01.027.

    Article  Google Scholar 

  51. Deblais A, Hollander ED, Boucon C, et al. Predicting thickness perception of liquid food products from their non-Newtonian rheology. Nat Commun. 2021. https://doi.org/10.1038/s41467-021-26687-w.

    Article  PubMed  PubMed Central  Google Scholar 

  52. Loix F, Orgéas L, Geindreau C, Badel P, Boisse P, Bloch J-F. Flow of non-Newtonian liquid polymers through deformed composites reinforcements. Compos Sci Technol. 2009;69:612–9. https://doi.org/10.1016/j.compscitech.2008.12.007.

    Article  CAS  Google Scholar 

  53. Ji S, Song H, Ke L, Aizikovich SM. The size-dependent elastohydrodynamic lubrication contact of a coated half-plane with non-Newtonian fluid. Applied Mathematics and Mechanics (English Edition). 2021;42:915–30. https://doi.org/10.1007/s10483-021-2744-7.

    Article  Google Scholar 

  54. Carreau PJ, MacDonald IF, Bird RB. A nonlinear viscoelastic model for polymer solutions and melts—II. Chem Eng Sci. 1968;23:901–11. https://doi.org/10.1016/0009-2509(68)80024-7.

    Article  CAS  Google Scholar 

  55. El Din SM, Darvesh A, Ayub A, et al. Quadratic multiple regression model and spectral relaxation approach for carreau nanofluid inclined magnetized dipole along stagnation point geometry. Sci Rep. 2022. https://doi.org/10.1038/s41598-022-22308-8.

    Article  PubMed  PubMed Central  Google Scholar 

  56. Rehman MIU, Chen H, Jamshed W, et al. Thermal radiative flux and energy of Arrhenius evaluation on stagnating point flowing of Carreau nanofluid: a thermal case study. Case Stud Therm Eng. 2022. https://doi.org/10.1016/j.csite.2022.102583.

    Article  Google Scholar 

  57. Jiann LY, Shafie S, Ullah I, et al. Effectiveness of non-uniform heat generation (sinking) and thermal characterization of Carreau fluid flowing across nonlinear elongating cylinder: convergence analysis aspect. J Appl Math Mech. 2022. https://doi.org/10.1002/zamm.202200049.

    Article  Google Scholar 

  58. Eid MR, Mahny KL, Dar A, et al. Numerical study for Carreau nanofluid flow over a convectively heated nonlinear stretching surface with chemically reactive species. Phys A: Stat Mech Appl. 2020. https://doi.org/10.1016/j.physa.2019.123063.

    Article  Google Scholar 

  59. Eid MR, Mahny KL, Muhammad T, et al. Numerical treatment for Carreau nanofluid flow over a porous nonlinear stretching surface. Results Phys. 2018. https://doi.org/10.1016/j.rinp.2018.01.070.

    Article  Google Scholar 

  60. Sandeep N, Shivakumara U, Nanda P, et al. Heat transfer mechanism of Falkner-Skan flow of Carreau nanoliquid induced by a wedge surface with radiation effect. Numer Heat Transf Part B Fundam. 2023. https://doi.org/10.1080/10407790.2023.2287602.

    Article  Google Scholar 

  61. Jamshed W, Nisar KS. Computational single-phase comparative study on a Williamson nanofluid in a parabolic trough solar collector via the Keller box method. Energy Rep. 2021;45:10696–718. https://doi.org/10.1002/er.6554.

    Article  CAS  Google Scholar 

  62. Sharafeldin MA, Grof G, Abu-Nada E, Mahian O. Evacuated tube solar collector performance using copper nanofluid: energy and environmental analysis. Appl Thermal Eng. 2019. https://doi.org/10.1016/j.applthermaleng.2019.114205.

    Article  Google Scholar 

  63. Dogonchi AS, Sheremet MA, Ganji DD. I, Pop, Free convection of copper-water nanofluid in a porous gap between hot rectangular cylinder and cold circular cylinder under the effect of inclined magnetic field. J Therm Anal Calorim. 2019;135:1171–84. https://doi.org/10.1007/s10973-018-7396-3.

    Article  CAS  Google Scholar 

  64. Olia H, Torabi M, Bahiraei M, Ahmadi MH, Goodarzi M, Safaei MR. Application of nanofluids in thermal performance enhancement of parabolic trough solar collector: State of the art. Appl Sci. 2019. https://doi.org/10.3390/app9030463.

    Article  Google Scholar 

  65. Q. Xiong, A. Hajjar, B. Alshuraiaan, M, Izadi, S. Altnji, S.A. Shehzad, State-of-the-art review of nanofluids in solar collectors: A review based on the type of the dispersed nanoparticles, Journal of Cleaner Production 310 (2021). https://doi.org/10.1016/j.jclepro.2021.127528

  66. Lin Y, Li BT, Zheng L, Chen G. Particle shape and radiation effects on Marangoni boundary layer flow and heat transfer of copper-water nanofluid driven by an exponential temperature. Powder Technol. 2016;301:379–86. https://doi.org/10.1016/j.powtec.2016.06.029.

    Article  CAS  Google Scholar 

  67. Sandeep N, Ranjana B, Sulochana C, et al. Significance of nanoparticle shape factors on MHD nanofluid flow across a slender surface. Int J Model Simul. 2023. https://doi.org/10.1080/02286203.2023.2296520.

    Article  Google Scholar 

  68. Poojari AG, Ranjana B, Sandeep N, et al. Enhanced heat transmission in unsteady magneto-nanoliquid flow due to a nonlinear extending sheet with convective boundary conditions, numerical heat transfer. Part A: Appl. 2023. https://doi.org/10.1080/10407782.2023.2207730.

    Article  Google Scholar 

  69. Giri SS, Das K, Kundu PK, et al. Inclined magnetic field effects on unsteady nanofluid flow and heat transfer in a finite thin film with non-uniform heat source/sink. Multidiscip Model Mater Struct. 2019;15:265–82. https://doi.org/10.1108/MMMS-04-2018-0065.

    Article  CAS  Google Scholar 

  70. Ashwinkumar GP. Computational analysis on MHD Sakiadis flow of hybrid nanoliquid past an incessantly moving thin needle. Int J Model Simul. 2023. https://doi.org/10.1080/02286203.2023.2212345.

    Article  Google Scholar 

  71. Pal D, Chatterjee D, Vajravelu K. Influence of magneto-thermo radiation on heat transfer of a thin nanofluid film with non-uniform heat source/sink. Propuls Power Res. 2020;9:169–80. https://doi.org/10.1016/j.jppr.2020.03.003.

    Article  Google Scholar 

  72. Vajravelu K, Hadjinicolaou A. Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation. Int Commun Heat Mass Transf. 1993;20:417–30. https://doi.org/10.1016/0735-1933(93)90026-R.

    Article  CAS  Google Scholar 

  73. Kalpana G, Madhura KR, Kudenatti RB. Numerical study on the combined effects of Brownian motion and thermophoresis on an unsteady magnetohydrodynamics nanofluid boundary layer flow. Math Comput Simul. 2022;200:78–96. https://doi.org/10.1016/j.matcom.2022.04.010.

    Article  Google Scholar 

  74. Hatami M, Jing D. Nanofluids - mathematical, numerical, and experimental analysis. 1st ed. Amsterdam: Elsevier; 2020.

    Google Scholar 

  75. Sulochana C, Ranjana B, Sandeep N, et al. Impact of Joule heating on magnetohydrodynamic dissipative flow above a slendering surface with thermophoresis and Brownian movement with slip/no-slip conditions. Int J Model Simul. 2023. https://doi.org/10.1080/02286203.2023.2234229.

    Article  Google Scholar 

  76. Alkathiri AA, Jamshed W, Devi SSU, Eid MR, Bouazizi ML. Galerkin finite element inspection of thermal distribution of renewable solar energy in presence of binary nanofluid in parabolic trough solar collector. Alex Eng J. 2022;61:11063–76. https://doi.org/10.1016/j.aej.2022.04.036.

    Article  Google Scholar 

  77. Wang Y. Principles of aero engines. 1st ed. Beijing: Beijing University of Aeronautics and Astronautics Press; 2009.

    Google Scholar 

  78. Nicolosi F, Della Vecchia P, Corcione S. Design and aerodynamic analysis of a twin-engine commuter aircraft. Aerosp Sci Technol. 2015;40:1–16. https://doi.org/10.1016/j.ast.2014.10.008.

    Article  Google Scholar 

  79. Md Ariffin L, Rostam AH, Shibani WME. Study of Aircraft Thrust-to-Weight Ratio. J Aviat Aerosp Technol. 2019;1:1–9.

    Google Scholar 

  80. Zhang C, Yang B, Wang Y, et al. Preliminary research on a high thrust to-weight ratio of double-sided composite impeller microturbine engine. Int J Aerosp Eng. 2021. https://doi.org/10.1155/2021/9931701.

    Article  Google Scholar 

  81. Ganglin W. Key parameters and conceptual configuration of unmanned combat aerial vehicle concept. Chin J Aeronaut. 2009;22:393–400. https://doi.org/10.1016/S1000-9361(08)60116-8.

    Article  Google Scholar 

  82. Waqas M, Khan MI, Hayat T, Alsaedi A. Numerical simulation for magneto Carreau nanofluid model with thermal radiation: a revised model. Comput Methods Appl Mech Eng. 2017;324:640–53. https://doi.org/10.1016/j.cma.2017.06.012.

    Article  Google Scholar 

  83. Irfan M, Anwar MS, Rashid M, Waqas M, Khan WA. Arrhenius activation energy aspects in mixed convection Carreau nanofluid with nonlinear thermal radiation. Appl Nanoscience. 2020;10:4403–13. https://doi.org/10.1007/s13204-020-01498-5.

    Article  CAS  Google Scholar 

  84. Kumar KG, Ramesh GK, Gireesha BJ, Gorla RSR. Characteristics of Joule heating and viscous dissipation on three-dimensional flow of Oldroyd B nanofluid with thermal radiation. Alex Eng J. 2018;57:2139–49. https://doi.org/10.1016/j.aej.2017.06.006.

    Article  Google Scholar 

  85. Reddy NB, Poornima T, Sreenivasulu P. Influence of variable thermal conductivity on MHD boundary layer slip flow of ethylene-glycol based Cu nanofluids over a stretching sheet with convective boundary convection. Int J Eng Math. 2014. https://doi.org/10.1155/2014/905158.

    Article  Google Scholar 

  86. Shahzad F, Jamshed W, Safdar R, et al. Thermal analysis characterization of solar-powered ship using Oldroyd hybrid nanofluids in parabolic trough solar collector: an optimal thermal application. Nanotechnol Rev. 2022;11:2015–37. https://doi.org/10.1515/ntrev-2022-0108.

    Article  CAS  Google Scholar 

  87. Jamshed W, Devi SSU, Safdar R, Redouane F, Nisar KS, Eid MR. Comprehensive analysis on copper-ion (II, III)/oxide-engine oil Casson nanofluid flowing and thermal features in parabolic trough solar collector. J Taibah Univ Sci. 2021;15:619–36. https://doi.org/10.1080/16583655.2021.1996114.

    Article  Google Scholar 

  88. Xu X, Chen S. Cattaneo-Christov heat flux model for heat transfer of Marangoni boundary layer flow in a copper-water nanofluid. Heat Transfer Asian Res. 2017;46:1281–93. https://doi.org/10.1002/htj.21273.

    Article  Google Scholar 

  89. Abid N, Ramzan M, Chung JD, Kadry S, Chu Y. Comparative analysis of magnetized partially ionized copper, copper oxide,-water and kerosene oil nanofluid flow with Cattaneo-Christov heat flux. Sci Rep. 2020. https://doi.org/10.1038/s41598-020-74865-5.

    Article  PubMed  PubMed Central  Google Scholar 

  90. Sandeep N, Reddy MG, Suresh BR, et al. A theoretical investigation on heat transport feature of Sutterby nanofluid flow above a conical surface. Int J Model Simul. 2023. https://doi.org/10.1080/02286203.2023.2270673.

    Article  Google Scholar 

  91. Sandeep N, Ranjana B, Sulochana C, et al. Flow and heat transfer mechanism of engine-oil based hybrid nanofluid due to a nonlinearly extending surface: a comparative study. Int J Model Simul. 2023. https://doi.org/10.1080/02286203.2023.2235539.

    Article  Google Scholar 

  92. Jamshed W, Akgul EK, Nisar KS. Keller box study for inclined magnetically driven Casson nanofluid over a stretching sheet: single phase model. Phys Scripta. 2021. https://doi.org/10.1088/1402-4896/abecfa.

    Article  Google Scholar 

  93. Paul A, Sarma N, Patgiri B. Thermal and mass transfer analysis of Casson-Maxwell hybrid nanofluids through an unsteady horizontal cylinder with variable thermal conductivity and Arrhenius activation energy, numerical heat transfer. Part A: Applications. 2023. https://doi.org/10.1080/10407782.2023.2297000.

    Article  Google Scholar 

  94. Althobaiti N. Importance of activation energy on magnetized dissipative casson-maxwell fluid through porous medium incorporating chemical reaction, joule heating, and soret effects: numerical study. J Appl Math. 2024. https://doi.org/10.1155/2024/5730530.

    Article  Google Scholar 

  95. Khan KA, Javed MF, Ullah MA, et al. Heat and Mass transport analysis for Williamson MHD nanofluid flow over a stretched sheet. Results in Physics. 2023. https://doi.org/10.1016/j.rinp.2023.106873.

    Article  PubMed  PubMed Central  Google Scholar 

  96. Nagisetty J, Golla VKA. Activation energy effect on MHD convective Maxwell nanofluid flow with Cattaneo-Christove heat flux over a porous stretching sheet. Special Topics Rev Porous Med: Int J. 2023. https://doi.org/10.1615/SpecialTopicsRevPorousMedia.2023050008.

    Article  Google Scholar 

  97. Madhukesh JK, Ramesh GK, Shehzad SA, et al. Thermal transport of MHD Casson-Maxwell nanofluid between two porous disks with Cattaneo-Christov theory, Numerical Heat Transfer. Part A: Applications. 2023. https://doi.org/10.1080/10407782.2023.2214322.

    Article  Google Scholar 

  98. Keskin AÜ. Solution of BVPs using bvp4c and bvp5c of MATLAB, in boundary value problems for engineers. Cham: Springer; 2019. p. 417–505.

    Book  Google Scholar 

  99. Khan WA, Khan M, Malik R. Three-dimensional flow of an Oldroyd-B nanofluid towards stretching surface with heat generation/absorption. PLoS ONE. 2014. https://doi.org/10.1371/journal.pone.0105107.

    Article  PubMed  PubMed Central  Google Scholar 

  100. Alsaedi A, Awais M. T, Hayat, Effects of heat generation/absorption on stagnation point flow of nanofluid over a surface with convective boundary conditions. Commun Nonlinear Sci Numer Simul. 2012;17:4210–23. https://doi.org/10.1016/j.cnsns.2012.03.008.

    Article  Google Scholar 

  101. Hayat T, Waqas M, Shehzad SA, Alsaedi A. Stretched flow of Carreau nanofluid with convective boundary conditions. Pramana. 2016;86:3–17. https://doi.org/10.1007/s12043-015-1137-y.

    Article  CAS  Google Scholar 

  102. Khan M, Yasir M, Alshomrani AS, et al. Variable heat source in stagnation-point unsteady flow of magnetized Oldroyd-B fluid with cubic autocatalysis chemical reaction. Ain Shams Eng J. 2022. https://doi.org/10.1016/j.asej.2021.10.005.

    Article  Google Scholar 

  103. Irfan M, Rafiq K, Khan M, Waqas M, Anwar MS. Theoretical analysis of new mass flux theory and Arrhenius activation energy in Carreau nanofluid with magnetic influence. Int Commun Heat Mass Transf. 2021;120:105051. https://doi.org/10.1016/j.icheatmasstransfer.2020.105051.

    Article  CAS  Google Scholar 

  104. Gopal D, Munjam SR, Kishan M. Analytical impact of Carreau nanofluid model under the influence of chemical reaction, Soret and Dufour over inclined stretching cylinder. Int Commun Heat Mass Transf. 2022;135:106148. https://doi.org/10.1016/j.icheatmasstransfer.2022.106148.

    Article  CAS  Google Scholar 

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Acknowledgements

We extend our sincere appreciation to the anonymous reviewers of this paper for their valuable insights, thoughtful engineering critiques, and expert evaluation of our manuscript. We are grateful for their thorough assessments, which have guided us in addressing various aspects of our research.

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Authors and Affiliations

  1. Faculty of Science, Ain Shams University, Cairo, 11566, Egypt

    Philopatir B. Raafat, Muhammad AbuGhanem & Fayez N. Ibrahim

  2. Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St, Yekaterinburg, 620002, Russia

    Ahmed S. Hendy

  3. Department of Mathematics, Faculty of Science, Benha University, Benha, 13511, Egypt

    Ahmed S. Hendy

  4. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia

    Mahmoud A. Zaky

  5. Department of Applied Mathematics, National Research Centre, Dokki, Cairo, 12622, Egypt

    Mahmoud A. Zaky

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Contributions

PBR: Conceptualization, Methodology, Visualization, Software, Formal Analysis, Writing Manuscript. MA: Conceptualization, Methodology, Software, Formal Analysis, Visualization. Writing Manuscript, Reviewing and Editing. FNI: Investigation, Validation, Reviewing and editing. MAZ: Software, Numerical analysis ASH: Software, Numerical analysis. All authors have approved the final article. All authors have approved the final article.

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Correspondence to Fayez N. Ibrahim.

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Raafat, P.B., AbuGhanem, M., Ibrahim, F.N. et al. A comparative study on entropy and thermal performance of Cu/CuO/Fe3O4-based engine oil Carreau nanofluids in PTSCs: a theoretical model for solar-powered aircraft applications. J Therm Anal Calorim 149, 3677–3697 (2024). https://doi.org/10.1007/s10973-024-12955-6

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