Dual Thermal Analysis of Fractional Convective Flow Through Aluminum Oxide and Titanium Dioxide Nanoparticles

1. Aman S, Abdeljawad T, Al-Mdallal Q. Natural convection flow of a fluid using Atangana and Baleanu fractional model. Advances in Difference Equations. 2020(1):305. AmanS AbdeljawadT Al-MdallalQ Natural convection flow of a fluid using Atangana and Baleanu fractional model Advances in Difference Equations. 2020 1 305 Search in Google Scholar

2. Ali FH, Hamzah HK, Egab K, Arıcı M, Shahsavar A. Non-Newtonian nanofluid natural convection in a U-shaped cavity under magnetic field. International Journal of Mechanical Sciences. 2020;186:105887. AliFH HamzahHK EgabK ArıcıM ShahsavarA Non-Newtonian nanofluid natural convection in a U-shaped cavity under magnetic field International Journal of Mechanical Sciences. 2020 186 105887 Search in Google Scholar

3. Tayebi T, Öztop HF, Chamkha AJ. Natural convection and entropy production in hybrid nanofluid filled-annular elliptical cavity with internal heat generation or absorption. Thermal Science and Engineering Progress. 2020;19:100605. TayebiT ÖztopHF ChamkhaAJ Natural convection and entropy production in hybrid nanofluid filled-annular elliptical cavity with internal heat generation or absorption Thermal Science and Engineering Progress 2020 19 100605 Search in Google Scholar

4. Paul A, Deka RK. Unsteady natural convection flow past an infinite cylinder with thermal and mass stratification. International Journal of Engineering Mathematics. 2017(1):8410691. PaulA DekaRK Unsteady natural convection flow past an infinite cylinder with thermal and mass stratification International Journal of Engineering Mathematics. 2017 1 8410691 Search in Google Scholar

5. Shaikh TS, Akgül A, Rehman MA, Ahmed N, Iqbal MS, Shahid N, Rafiq M, De la Sen M. A nonlinear structure of a chemical reaction model and numerical modeling with the new aspect of existence and uniqueness. Mathematics. 2022;11(1):37. ShaikhTS AkgülA RehmanMA AhmedN IqbalMS ShahidN RafiqM De la SenM A nonlinear structure of a chemical reaction model and numerical modeling with the new aspect of existence and uniqueness Mathematics 2022 11 1 37 Search in Google Scholar

6. Amir M, Ali Q, Raza A, Almusawa MY, Hamali W, Ali AH. Computational results of convective heat transfer for fractionalized Brinkman type tri-hybrid nanofluid with ramped temperature and non-local kernel. Ain Shams Engineering Journal. 2024;15(3):102576. AmirM AliQ RazaA AlmusawaMY HamaliW AliAH Computational results of convective heat transfer for fractionalized Brinkman type tri-hybrid nanofluid with ramped temperature and non-local kernel Ain Shams Engineering Journal 2024 15 3 102576 Search in Google Scholar

7. Ali Q, Riaz S, Memon IQ, Chandio IA, Amir M, Sarris IE, Abro KA. Investigation of magnetized convection for second-grade nanofluids via Prabhakar differentiation. Nonlinear Engineering. 2023;12(1):20220286. AliQ RiazS MemonIQ ChandioIA AmirM SarrisIE AbroKA Investigation of magnetized convection for second-grade nanofluids via Prabhakar differentiation Nonlinear Engineering 2023 12 1 20220286 Search in Google Scholar

8. Yasin MW, Ahmed N, Iqbal MS, Rafiq M, Raza A, Akgül A. Reliable numerical analysis for stochastic reaction-diffusion system. Physica Scripta. 2022;98(1):015209. YasinMW AhmedN IqbalMS RafiqM RazaA AkgülA Reliable numerical analysis for stochastic reaction-diffusion system Physica Scripta 2022 98 1 015209 Search in Google Scholar

9. Awan AU, Ali Q, Riaz S, Shah NA, Chung JD. A thermal optimization throughan innovative mechanism of free convection flow of Jeffrey fluid using non-local kernel. Case Studies in Thermal Engineering. 2021;24:100851. AwanAU AliQ RiazS ShahNA ChungJD A thermal optimization throughan innovative mechanism of free convection flow of Jeffrey fluid using non-local kernel Case Studies in Thermal Engineering. 2021 24 100851 Search in Google Scholar

10. Riaz S, Sattar M, Abro KA, Ali Q. Thermo-dynamical investigation of constitutive equation for rate type fluid: a semi-analytical approach. International Journal of Modelling and Simulation. 2023;43(3):123–34. RiazS SattarM AbroKA AliQ Thermo-dynamical investigation of constitutive equation for rate type fluid: a semi-analytical approach International Journal of Modelling and Simulation 2023 43 3 123 34 Search in Google Scholar

11. Ali Q, Riaz S, Awan AU, Abro KA. A mathematical model for thermography on viscous fluid based on damped thermal flux. Zeitschrift für Naturforschung A. 2021;76(3):285–94. AliQ RiazS AwanAU AbroKA A mathematical model for thermography on viscous fluid based on damped thermal flux Zeitschrift für Naturforschung A 2021 76 3 285 94 Search in Google Scholar

12. Ajeel RK, Salim WI, Hasnan K. Design characteristics of symmetrical semicircle-corrugated channel on heat transfer enhancement with nanofluid. International Journal of Mechanical Sciences. 2019;151:236–50. AjeelRK SalimWI HasnanK Design characteristics of symmetrical semicircle-corrugated channel on heat transfer enhancement with nanofluid International Journal of Mechanical Sciences 2019 151 236 50 Search in Google Scholar

13. Abro KA, Atangana A, Gomez-Aguilar JF. An analytic study of bioheat transfer Pennes model via modern non-integers differential techniques. The European Physical Journal Plus. 2021;136:1–1. AbroKA AtanganaA Gomez-AguilarJF An analytic study of bioheat transfer Pennes model via modern non-integers differential techniques The European Physical Journal Plus 2021 136 1 1 Search in Google Scholar

14. Abro KA, Abdon A. A computational technique for thermal analysis in coaxial cylinder of one-dimensional flow of fractional Oldroyd-B nanofluid. International Journal of Ambient Energy. 2022;43(1): 5357–65. AbroKA AbdonA A computational technique for thermal analysis in coaxial cylinder of one-dimensional flow of fractional Oldroyd-B nanofluid International Journal of Ambient Energy. 2022 43 1 5357 65 Search in Google Scholar

15. Ganvir RB, Walke PV, Kriplani VM. Heat transfer characteristics in nanofluid—A review. Renewable and sustainable energy reviews. 2017;75:451–60. GanvirRB WalkePV KriplaniVM Heat transfer characteristics in nanofluid—A review Renewable and sustainable energy reviews 2017 75 451 60 Search in Google Scholar

16. Aman S, Khan I, Ismail Z, Salleh MZ. Applications of fractional derivatives to nanofluids: exact and numerical solutions. Mathematical Modelling of Natural Phenomena. 2018;13(1):2. AmanS KhanI IsmailZ SallehMZ Applications of fractional derivatives to nanofluids: exact and numerical solutions Mathematical Modelling of Natural Phenomena 2018 13 1 2 Search in Google Scholar

17. Hussanan A, Trung NT. Heat transfer analysis of sodium carboxymethyl cellulose based nanofluid with titania nanoparticles. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences. 2019;56(2):248–56. HussananA TrungNT Heat transfer analysis of sodium carboxymethyl cellulose based nanofluid with titania nanoparticles Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 2019 56 2 248 56 Search in Google Scholar

18. Farhana K, Kadirgama K, Noor MM, Rahman MM, Ramasamy D, Mahamude AS. CFD modelling of different properties of nanofluids in header and riser tube of flat plate solar collector. InIOP Conference Series: Materials Science and Engineering 2019, 469: 012041. FarhanaK KadirgamaK NoorMM RahmanMM RamasamyD MahamudeAS CFD modelling of different properties of nanofluids in header and riser tube of flat plate solar collector InIOP Conference Series: Materials Science and Engineering 2019 469 012041 Search in Google Scholar

19. Jamshed W, Aziz A. A comparative entropy based analysis of Cu and Fe3O4/methanol Powell-Eyring nanofluid in solar thermal collectors subjected to thermal radiation, variable thermal conductivity and impact of different nanoparticles shape. Results in physics. 2018; 9:195–205. JamshedW AzizA A comparative entropy based analysis of Cu and Fe3O4/methanol Powell-Eyring nanofluid in solar thermal collectors subjected to thermal radiation, variable thermal conductivity and impact of different nanoparticles shape Results in physics. 2018 9 195 205 Search in Google Scholar

20. Jamshed W, Goodarzi M, Prakash M, Nisar KS, Zakarya M, Abdel-Aty AH. Evaluating the unsteady Casson nanofluid over a stretching sheet with solar thermal radiation: An optimal case study. Case Studies in Thermal Engineering. 2021; 26:101160. JamshedW GoodarziM PrakashM NisarKS ZakaryaM Abdel-AtyAH Evaluating the unsteady Casson nanofluid over a stretching sheet with solar thermal radiation: An optimal case study Case Studies in Thermal Engineering. 2021 26 101160 Search in Google Scholar

21. Jamshed W, Nisar KS, Gowda RP, Kumar RN, Prasannakumara BC. Radiative heat transfer of second grade nanofluid flow past a porous flat surface: a single-phase mathematical model. Physica Scripta. 2021;96(6):064006. JamshedW NisarKS GowdaRP KumarRN PrasannakumaraBC Radiative heat transfer of second grade nanofluid flow past a porous flat surface: a single-phase mathematical model Physica Scripta 2021 96 6 064006 Search in Google Scholar

22. Jamshed W, Nisar KS, Ibrahim RW, Mukhtar T, Vijayakumar V, Ahmad F. Computational frame work of Cattaneo-Christov heat flux effects on Engine Oil based Williamson hybrid nanofluids: A thermal case study. Case Studies in Thermal Engineering. 2021; 26:101179. JamshedW NisarKS IbrahimRW MukhtarT VijayakumarV AhmadF Computational frame work of Cattaneo-Christov heat flux effects on Engine Oil based Williamson hybrid nanofluids: A thermal case study Case Studies in Thermal Engineering. 2021 26 101179 Search in Google Scholar

23. Jamshed W, Devi SU, Nisar KS. Single phase based study of Ag-Cu/EO Williamson hybrid nanofluid flow over a stretching surface with shape factor. Physica Scripta. 2021;96(6):065202. JamshedW DeviSU NisarKS Single phase based study of Ag-Cu/EO Williamson hybrid nanofluid flow over a stretching surface with shape factor Physica Scripta 2021 96 6 065202 Search in Google Scholar

24. Jamshed W, Eid MR, Rehman S, Mohamed Isa SS, Abd-Elmonem A, Alanzi AM, Farooq S. Numerical heat and solutal transfer simulation of fluid flowing via absorptive shrinkable sheet with Ohmic heat resistance. Numerical Heat Transfer, Part A: Applications. 2024;85(10):1552–68. JamshedW EidMR RehmanS Mohamed IsaSS Abd-ElmonemA AlanziAM FarooqS Numerical heat and solutal transfer simulation of fluid flowing via absorptive shrinkable sheet with Ohmic heat resistance Numerical Heat Transfer, Part A: Applications 2024 85 10 1552 68 Search in Google Scholar

25. Aziz A, Jamshed W, Aziz T, Bahaidarah HM, Ur Rehman K. Entropy analysis of Powell–Eyring hybrid nanofluid including effect of linear thermal radiation and viscous dissipation. Journal of Thermal Analysis and Calorimetry. 2021;143(2):1331–43. AzizA JamshedW AzizT BahaidarahHM Ur RehmanK Entropy analysis of Powell–Eyring hybrid nanofluid including effect of linear thermal radiation and viscous dissipation Journal of Thermal Analysis and Calorimetry 2021 143 2 1331 43 Search in Google Scholar

26. Sajid T, Gari AA, Jamshed W, Eid MR, Islam N, Irshad K, Altamirano GC, El Din SM. Case study of autocatalysis reactions on tetra hybrid binary nanofluid flow via Riga wedge: Biofuel thermal application. Case Studies in Thermal Engineering. 2023; 47:103058. SajidT GariAA JamshedW EidMR IslamN IrshadK AltamiranoGC El DinSM Case study of autocatalysis reactions on tetra hybrid binary nanofluid flow via Riga wedge: Biofuel thermal application Case Studies in Thermal Engineering. 2023 47 103058 Search in Google Scholar

27. Kai Y, Ali K, Ahmad S, Ahmad S, Jamshed W, Raizah Z, El Din SM. A case study of different magnetic strength fields and thermal energy effects in vortex generation of Ag-TiO2 hybrid nanofluid flow. Case Studies in Thermal Engineering. 2023; 47:103115. KaiY AliK AhmadS AhmadS JamshedW RaizahZ El DinSM A case study of different magnetic strength fields and thermal energy effects in vortex generation of Ag-TiO2 hybrid nanofluid flow Case Studies in Thermal Engineering. 2023 47 103115 Search in Google Scholar

28. Hanif H, Jamshed W, Eid MR, Ibrahim RW, Shafie S, Raezah AA, El Din SM. Numerical Crank-Nicolson methodology analysis for hybridity aluminium alloy nanofluid flowing based-water via stretchable horizontal plate with thermal resistive effect. Case Studies in Thermal Engineering. 2023; 42:102707. HanifH JamshedW EidMR IbrahimRW ShafieS RaezahAA El DinSM Numerical Crank-Nicolson methodology analysis for hybridity aluminium alloy nanofluid flowing based-water via stretchable horizontal plate with thermal resistive effect Case Studies in Thermal Engineering. 2023 42 102707 Search in Google Scholar

29. Kai Y, Ahmad S, Takana H, Ali K, Jamshed W, Eid MR, Abd-Elmonem A, El Din SM. Thermal case study and generated vortices by dipole magnetic field in hybridized nanofluid flowing: Alternating direction implicit solution. Results in Physics. 2023; 49:106464. KaiY AhmadS TakanaH AliK JamshedW EidMR Abd-ElmonemA El DinSM Thermal case study and generated vortices by dipole magnetic field in hybridized nanofluid flowing: Alternating direction implicit solution Results in Physics. 2023 49 106464 Search in Google Scholar

30. Ullah I, Ali F, Isa SM, Murtaza S, Jamshed W, Eid MR, Amjad A, Guedri K, Khalifa HA, El Din SM. Electro-magnetic radiative flowing of Williamson-dusty nanofluid along elongating sheet: Nanotechnology application. Arabian Journal of Chemistry. 2023;16(5):104698. UllahI AliF IsaSM MurtazaS JamshedW EidMR AmjadA GuedriK KhalifaHA El DinSM Electro-magnetic radiative flowing of Williamson-dusty nanofluid along elongating sheet: Nanotechnology application Arabian Journal of Chemistry 2023 16 5 104698 Search in Google Scholar

31. Zhang X, Yang D, Katbar NM, Jamshed W, Ullah I, Eid MR, Raizah Z, Ibrahim RW, Khalifa HA, El Din SM. Entropy and thermal case description of monophase magneto nanofluid with thermal jump and Ohmic heating employing finite element methodology. Case Studies in Thermal Engineering. 2023;45:102919. ZhangX YangD KatbarNM JamshedW UllahI EidMR RaizahZ IbrahimRW KhalifaHA El DinSM Entropy and thermal case description of monophase magneto nanofluid with thermal jump and Ohmic heating employing finite element methodology Case Studies in Thermal Engineering. 2023 45 102919 Search in Google Scholar

32. Podlubny I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. elsevier; 1998, 198:1–340. PodlubnyI Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications elsevier 1998 198 1 340 Search in Google Scholar

33. Baleanu D, Fernandez A. On fractional operators and their classifications. Mathematics. 2019;7(9):830. BaleanuD FernandezA On fractional operators and their classifications Mathematics 2019 7 9 830 Search in Google Scholar

34. Wang BO, Tahir M, Imran M, Javaid M, Jung CY. Semi analytical solutions for fractional Oldroyd-B fluid through rotating annulus. IEEE Access. 2019; 7:72482–91. WangBO TahirM ImranM JavaidM JungCY Semi analytical solutions for fractional Oldroyd-B fluid through rotating annulus IEEE Access. 2019 7 72482 91 Search in Google Scholar

35. Ullah Z, Abbas A, El-Zahar ER, Seddek LF, Akgul A, Hassan AM. Significance of thermal density and viscous dissipation on heat and mass transfer of chemically reactive nanofluid flow along stretching sheet under magnetic field. Results in Engineering. 2023; 20:101413. UllahZ AbbasA El-ZaharER SeddekLF AkgulA HassanAM Significance of thermal density and viscous dissipation on heat and mass transfer of chemically reactive nanofluid flow along stretching sheet under magnetic field Results in Engineering. 2023 20 101413 Search in Google Scholar

36. Ahmed N, Baber MZ, Iqbal MS, Annum A, Ali SM, Ali M, Akgül A, El Din SM. Analytical study of reaction diffusion Lengyel-Epstein system by generalized Riccati equation mapping method. Scientific Reports. 2023;13(1):20033. AhmedN BaberMZ IqbalMS AnnumA AliSM AliM AkgülA El DinSM Analytical study of reaction diffusion Lengyel-Epstein system by generalized Riccati equation mapping method Scientific Reports 2023 13 1 20033 Search in Google Scholar

37. Caputo M, Fabrizio M. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications. 2015;1(2):73–85. CaputoM FabrizioM A new definition of fractional derivative without singular kernel Progress in Fractional Differentiation & Applications 2015 1 2 73 85 Search in Google Scholar

38. Qayyum M, Afzal S, Saeed ST, Akgül A, Riaz MB. Unsteady hybrid nanofluid (Cu-UO2/blood) with chemical reaction and non-linear thermal radiation through convective boundaries: An application to biomedicine. Heliyon. 2023;9(6):e16578. QayyumM AfzalS SaeedST AkgülA RiazMB Unsteady hybrid nanofluid (Cu-UO2/blood) with chemical reaction and non-linear thermal radiation through convective boundaries: An application to biomedicine Heliyon. 2023 9 6 e16578 Search in Google Scholar

39. Ahmad B, Ahmad MO, Farman M, Akgül A, Riaz MB. A significance of multi slip condition for inclined MHD nano-fluid flow with non linear thermal radiations, Dufuor and Sorrot, and chemically reactive bioconvection effect. South African Journal of Chemical Engineering. 2023;43:135–45. AhmadB AhmadMO FarmanM AkgülA RiazMB A significance of multi slip condition for inclined MHD nano-fluid flow with non linear thermal radiations, Dufuor and Sorrot, and chemically reactive bioconvection effect South African Journal of Chemical Engineering 2023 43 135 45 Search in Google Scholar

40. Riaz S, Sattar M, Abro KA, Ali Q. Thermo-dynamical investigation of constitutive equation for rate type fluid: a semi-analytical approach. International Journal of Modelling and Simulation. 2023;43(3):123–34. RiazS SattarM AbroKA AliQ Thermo-dynamical investigation of constitutive equation for rate type fluid: a semi-analytical approach International Journal of Modelling and Simulation 2023 43 3 123 34 Search in Google Scholar

41. Atangana A, Baleanu D. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. arXiv preprint arXiv:1602.03408. 2016. AtanganaA BaleanuD New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model arXiv preprint arXiv:1602.03408. 2016 Search in Google Scholar

42. Riaz MB, Iftikhar N. A comparative study of heat transfer analysis of MHD Maxwell fluid in view of local and nonlocal differential operators. Chaos, Solitons & Fractals. 2020;132:109556. RiazMB IftikharN A comparative study of heat transfer analysis of MHD Maxwell fluid in view of local and nonlocal differential operators Chaos, Solitons & Fractals. 2020 132 109556 Search in Google Scholar

43. Atangana A. On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation. Applied Mathematics and computation. 2016;273:948–56. AtanganaA On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation Applied Mathematics and computation 2016 273 948 56 Search in Google Scholar

44. Riaz S, Ali Q, Khanam Z, Rezazadeh H, Esfandian H. Modeling and computation of nanofluid for thermo-dynamical analysis between vertical plates. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering. 2023;237(5):1750–60. RiazS AliQ KhanamZ RezazadehH EsfandianH Modeling and computation of nanofluid for thermo-dynamical analysis between vertical plates Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 2023 237 5 1750 60 Search in Google Scholar

45. Riaz S, Amir M, Memon IQ, Ali Q, Abro KA. A comparative study for solidification of nanoparticles suspended in nanofluids through nonlocal kernel approach. Arabian Journal for Science and Engineering. 2023;48(9):11645–63. RiazS AmirM MemonIQ AliQ AbroKA A comparative study for solidification of nanoparticles suspended in nanofluids through nonlocal kernel approach Arabian Journal for Science and Engineering 2023 48 9 11645 63 Search in Google Scholar

46. Riaz S, Ali S, Ali Q, Khan SU, Amir M. Fractional simulations for mixed convection flow of hybrid nanofluids due to inclined channel with chemical reaction and external heat source features. Waves in Random and Complex Media. 2023;1–9. RiazS AliS AliQ KhanSU AmirM Fractional simulations for mixed convection flow of hybrid nanofluids due to inclined channel with chemical reaction and external heat source features Waves in Random and Complex Media. 2023 1 9 Search in Google Scholar

47. Ali Q, Yassen MF, Asiri SA, Pasha AA, Abro KA. Role of viscoelasticity on thermoelectromechanical system subjected to annular regions of cylinders in the existence of a uniform inclined magnetic field. The European Physical Journal Plus. 2022;137(7):1–0. AliQ YassenMF AsiriSA PashaAA AbroKA Role of viscoelasticity on thermoelectromechanical system subjected to annular regions of cylinders in the existence of a uniform inclined magnetic field The European Physical Journal Plus 2022 137 7 1 0 Search in Google Scholar

48. Stehfest H. Algorithm 368: Numerical inversion of Laplace transforms [D5]. Communications of the ACM. 1970;13(1):47–9. StehfestH Algorithm 368: Numerical inversion of Laplace transforms [D5] Communications of the ACM 1970 13 1 47 9 Search in Google Scholar

49. Tzou DY. Macro-to microscale heat transfer: the lagging behavior. John Wiley & Sons; 2014. TzouDY Macro-to microscale heat transfer: the lagging behavior John Wiley & Sons 2014 Search in Google Scholar