The current study is based on the mechanism of mixed convection and solar thermal radiation in Walters'-B fluid considering tera-hybrid nano-structures using convective boundary constraints (CBC) and (CHF) constant heat flux. The heat transmission phenomenon of the current study is taken into account under the influence of triple-suspended nanoparticles. The current problem has several potential applications, including improvements in solar thermal energy systems, nanofluids, aerospace, cooling processes, automotive engineering, and numerical modeling methods. A numerical approach, namely Crank-Nicolson, is utilized in the modeling of 3D Walter's B fluid past over a 3D circular cylinder whose radius varies sinusoidally for evaluation of velocity and temperature distributions. For mathematical modeling, the Cartesian coordinate system was used for the current study. Comparative analysis between constant heat flux (CHF) and convective boundary constraints (CBC) was demonstrated graphically against multifarious parameters towards the temperature profile and velocity profiles along the x-axis and in the y-axis. Moreover, comparative analysis for dissimilar parameters was manifested for Nusselt number through tables, and graphically for skin friction co-efficient and Nusselt number and has shown excellent accuracy. It was estimated that by enhancing values of Qsr, C, Hs and Ec, it was addressed that temperature curve increases for CHF and CBC cases.
Citation: Fu Zhang Wang, Muhammad Sohail, Umar Nazir, Emad Mahrous Awwad, Mohamed Sharaf. Utilization of the Crank-Nicolson technique to investigate thermal enhancement in 3D convective Walter-B fluid by inserting tiny nanoparticles on a circular cylinder[J]. AIMS Mathematics, 2024, 9(4): 9059-9090. doi: 10.3934/math.2024441
The current study is based on the mechanism of mixed convection and solar thermal radiation in Walters'-B fluid considering tera-hybrid nano-structures using convective boundary constraints (CBC) and (CHF) constant heat flux. The heat transmission phenomenon of the current study is taken into account under the influence of triple-suspended nanoparticles. The current problem has several potential applications, including improvements in solar thermal energy systems, nanofluids, aerospace, cooling processes, automotive engineering, and numerical modeling methods. A numerical approach, namely Crank-Nicolson, is utilized in the modeling of 3D Walter's B fluid past over a 3D circular cylinder whose radius varies sinusoidally for evaluation of velocity and temperature distributions. For mathematical modeling, the Cartesian coordinate system was used for the current study. Comparative analysis between constant heat flux (CHF) and convective boundary constraints (CBC) was demonstrated graphically against multifarious parameters towards the temperature profile and velocity profiles along the x-axis and in the y-axis. Moreover, comparative analysis for dissimilar parameters was manifested for Nusselt number through tables, and graphically for skin friction co-efficient and Nusselt number and has shown excellent accuracy. It was estimated that by enhancing values of Qsr, C, Hs and Ec, it was addressed that temperature curve increases for CHF and CBC cases.
| [1] | A. Shafiq, Z. Hammouch, H. F. Oztop, Radiative MHD flow of third-grade fluid towards a stretched cylinder, In: 4th International Conference on Computational Mathematics and Engineering Sciences (CMES-2019), Springer International Publishing, 4 (2020), 166−185. https://doi.org/10.1007/978-3-030-39112-6_12 |
| [2] |
H. Vaidya, R. Choudhari, F. Mebarek‐Oudina, I. L. Animasaun, K. V. Prasad, O. D. Makinde, Combined effects of homogeneous and heterogeneous reactions on peristalsis of Ree‐Eyring liquid: Application in hemodynamic flow, Heat Transf., 50 (2021), 2592−2609. https://doi.org/10.1002/htj.21995 doi: 10.1002/htj.21995
|
| [3] |
A. Shafiq, F. Mebarek-Oudina, T. N. Sindhu, G. Rasool, Sensitivity analysis for Walters-B nano liquid flow over a radiative Riga surface by RSM, Sci. Iran., 29 (2022), 1236−1249. https://doi.org/10.24200/sci.2021.58293.5662 doi: 10.24200/sci.2021.58293.5662
|
| [4] |
I. Khan, F. Ali, N. A. Shah, Interaction of magnetic field with heat and mass transfer in free convection flow of a Walters'-B fluid, Eur. Phys. J. Plus, 131 (2016), 77. https://doi.org/10.1140/epjp/i2016-16077-7 doi: 10.1140/epjp/i2016-16077-7
|
| [5] |
T. Hayat, A. Shafiq, M. Mustafa, A. Alsaedi, Boundary-layer flow of Walters' B fluid with Newtonian heating, Z. Naturforsch. A, 70 (2015), 333−341. https://doi.org/10.1515/zna-2014-0280 doi: 10.1515/zna-2014-0280
|
| [6] |
Q. Al-Mdallal, K. A. Abro, I. Khan, Analytical solutions of fractional Walter's B fluid with applications, Complexity, 2018 (2018), 1−10. https://doi.org/10.1155/2018/8131329 doi: 10.1155/2018/8131329
|
| [7] |
A. Tanveer, M. Khan, T. Salahuddin, B. Al Alwan, A. Amari, Dynamics of Walters' B fluid due to periodic wave in a convectively heated channel with internal heat generation, Math. Comput. Simul., 199 (2022), 374−393. https://doi.org/10.1016/j.matcom.2022.03.018 doi: 10.1016/j.matcom.2022.03.018
|
| [8] |
R. Mahat, M. Saqib, I. Khan, S. Shafie, N. A. M. Noor, Thermal radiation effect on Viscoelastic Walters'-B nanofluid flow through a circular cylinder in convective and constant heat flux, Case Stud. Therm. Eng., 39 (2022), 102394. https://doi.org/10.1016/j.csite.2022.102394 doi: 10.1016/j.csite.2022.102394
|
| [9] |
N. A. Shah, K. A. Abro, I. Siddique, Thermography of ferromagnetic Walter's-B fluid thermal stratification, South Afr. J. Chem. Eng., 36 (2021), 118−126. https://doi.org/10.1016/j.sajce.2020.12.004 doi: 10.1016/j.sajce.2020.12.004
|
| [10] |
A. B. Johnson, B. I. Olajuwon, Impact of radiation and heat generation/absorption in a Walters' B fluid through a porous medium with thermal and thermo diffusion in the presence of chemical reaction, Int. J. Model. Simul., 43 (2023), 87−100. https://doi.org/10.1080/02286203.2022.2035948 doi: 10.1080/02286203.2022.2035948
|
| [11] |
P. K. Asifa, T. Anwar, Z. Shah, W. Watthayu, Analysis and modeling of fractional electro-osmotic ramped flow of chemically reactive and heat absorptive/generative Walters' B fluid with ramped heat and mass transfer rates, AIMS Math., 6 (2021), 5942−5976. https://doi.org/10.3934/math.2021352 doi: 10.3934/math.2021352
|
| [12] |
A. Shafiq, A. B. Çolak, T. N. Sindhu, Optimization of bioconvective magnetized Walter's B nanofluid flow towards a cylindrical disk with artificial neural networks, Lubricants, 10 (2022), 209. https://doi.org/10.3390/lubricants10090209 doi: 10.3390/lubricants10090209
|
| [13] |
M. I. Khan, F. Alzahrani, Activation energy and binary chemical reaction effect in nonlinear thermal radiative stagnation point flow of Walter-B nanofluid: Numerical computations, Int. J. Mod. Phys. B, 34 (2020), 2050132. https://doi.org/10.1142/S0217979220501325 doi: 10.1142/S0217979220501325
|
| [14] |
C. K. Damala, V. Bhumarapu, O. D. Makinde, Radiative MHD Walter's liquid-B flow past a semi-infinite vertical plate in the presence of viscous dissipation with a heat source, Eng. T., 69 (2021), 373−401. https://doi.org/10.24423/EngTrans.1370.20211215 doi: 10.24423/EngTrans.1370.20211215
|
| [15] |
G. P. Vanitha, U. S. Mahabaleshwar, Z. Liu, X. Yang, B. Sundén, Magnetohydrodynamic Marangoni boundary layer flow of nanoparticles with thermal radiation and heat transfer in a porous sheet, Case Stud. Therm. Eng., 44 (2023), 102815. https://doi.org/10.1016/j.csite.2023.102815 doi: 10.1016/j.csite.2023.102815
|
| [16] |
H. Waqas, M. Alghamdi, T. Muhammad, M. A. Khan, Bioconvection transport of magnetized Walter's B nanofluid across a cylindrical disk with nonlinear radiative heat transfer, Case Stud. Therm. Eng., 26 (2021), 101097. https://doi.org/10.1016/j.csite.2021.101097 doi: 10.1016/j.csite.2021.101097
|
| [17] |
O. D. Makinde, M. G. Reddy, K. V. Reddy, Effects of thermal radiation on MHD peristaltic motion of Walters-B fluid with heat source and slip conditions, J. Appl. Fluid Mech., 10 (2017), 1105−1112. https://doi.org/10.18869/acadpub.jafm.73.241.27082 doi: 10.18869/acadpub.jafm.73.241.27082
|
| [18] |
M. V. Krishna, Hall and ion slip effects on MHD laminar flow of an elastico‐viscous (Walter's‐B) fluid, Heat Transf., 49 (2020), 2311−2329. https://doi.org/10.1002/htj.21722 doi: 10.1002/htj.21722
|
| [19] | G. Chakraborty, P. R. Sengupta, MHD flow of unsteady viscoelastic (Walters liquid B') conducting fluid between two porous concentric circular cylinders, In: Proceedings of the National Academy of Sciences, Section A: Physical Sciences, India, 64 (1994). |
| [20] |
P. Y. Huang, J. Feng, Wall effects on the flow of viscoelastic fluids around a circular cylinder, J. Non-Newton. Fluid, 60 (1995), 179−198. https://doi.org/10.1016/0377-0257(95)01394-2 doi: 10.1016/0377-0257(95)01394-2
|
| [21] |
G. M. Moatimid, M. H. Zekry, Nonlinear stability of electro-visco-elastic Walters' B type in porous media, Microsyst. Technol., 26 (2020), 2013−2027. https://doi.org/10.1007/s00542-020-04752-6 doi: 10.1007/s00542-020-04752-6
|
| [22] | A. R. M. Kasim, N. F. Mohammad, S. Shafie, Effect of heat generation on free convection boundary layer flow of a viscoelastic fluid past a horizontal circular cylinder with constant surface heat flux, In: AIP Conference Proceedings, American Institute of Physics, 1450 (2012), 286−292. |
| [23] |
S. Nadeem, N. S. Akbar, Influence of heat and chemical reactions on Walter's B fluid model for blood flow through a tapered artery, J. Taiwan Inst. Chem. Eng., 42 (2011), 67−75. https://doi.org/10.1016/j.jtice.2010.03.012 doi: 10.1016/j.jtice.2010.03.012
|
| [24] |
R. P. Bharti, R. P. Chhabra, V. Eswaran, Steady flow of power law fluids across a circular cylinder, Can. J. Chem. Eng., 84 (2006), 406−421. https://doi.org/10.1002/cjce.5450840402 doi: 10.1002/cjce.5450840402
|
| [25] |
R. Naz, S. Tariq, H. Alsulami, Inquiry of entropy generation in stratified Walters' B nanofluid with swimming gyrotactic microorganisms, Alex. Eng. J., 59 (2020), 247−261. https://doi.org/10.1016/j.aej.2019.12.037 doi: 10.1016/j.aej.2019.12.037
|
| [26] |
M. I. Khan, M. Tamoor, T. Hayat, A. Alsaedi, MHD boundary layer thermal slip flow by nonlinearly stretching cylinder with suction/blowing and radiation, Results Phys., 7 (2017), 1207−1211. https://doi.org/10.1016/j.rinp.2017.03.009 doi: 10.1016/j.rinp.2017.03.009
|
| [27] |
Y. M. Chu, N. Khan, M. I. Khan, K. Al-Khaled, N. Abbas, S. U. Khan, et al., Thermophoresis particle deposition analysis for nonlinear thermally developed flow of Magneto-Walter's B nanofluid with buoyancy forces, Alex. Eng. J., 60 (2021), 1851−1860. https://doi.org/10.1016/j.aej.2020.11.033 doi: 10.1016/j.aej.2020.11.033
|
| [28] |
F. Alzahrani, M. I. Khan, Significance of heat conduction in binary reactive flow of Walter's B fluid with radiative flux and activation energy, Mod. Phys. Lett. B, 35 (2021), 2140024. https://doi.org/10.1142/S0217984921400248 doi: 10.1142/S0217984921400248
|
| [29] |
C. Ragavan, S. Munirathinam, M. Govindaraju, A. K. Abdul-Hakeem, B. Ganga, Elastic deformation and inclined magnetic field on entropy generation forwalter's liquid B fluid over a stretching sheet, J. Appl. Math. Comput. Mech., 18 (2019). https://doi.org/10.17512/jamcm.2019.2.08 doi: 10.17512/jamcm.2019.2.08
|
| [30] | A. R. M. Kasim, Free and mixed convective boundary layer flow of a viscoelastic fluid past a horizontal circular cylinder, Universiti Teknologi Malaysia, 2011. |
| [31] |
L. Ahmad, S. Javed, M. I. Khan, M. R. Khan, E. R. El-Zahar, A. A. A. Mousa, Non-axisymmetric Homann stagnation-point flow of unsteady Walter's B nanofluid over a vertical cylindrical disk, P. I. Mech. Eng. E-J. Pro., 2021. https://doi.org/10.1177/09544089211064480 doi: 10.1177/09544089211064480
|
| [32] |
T. Hayat, Y. Wang, A. M. Siddiqui, K. Hutter, S. Asghar, Peristaltic transport of a third-order fluid in a circular cylindrical tube, Math. Mod. Meth. Appl. S., 12 (2002), 1691−1706. https://doi.org/10.1142/S0218202502002288 doi: 10.1142/S0218202502002288
|
| [33] |
B. J. Akinbo, Influence of convective boundary condition on heat and mass transfer in a Walters' B fluid over a vertical stretching surface with thermal-diffusion effect, J. Therm. Eng., 7 (2021), 1784−1796. https://doi.org/10.18186/thermal.1026001 doi: 10.18186/thermal.1026001
|
| [34] | I. Khan, F. Ali, S. Shafie, M. Qasim, Unsteady free convection flow in a Walters-B fluid and heat transfer analysis, B. Malays. Math. Sci. Soc., 37 (2014), 437−448. |
| [35] |
D. Qaiser, Z. Zheng, M. R. Khan, Numerical assessment of mixed convection flow of Walters-B nanofluid over a stretching surface with Newtonian heating and mass transfer, Therm. Sci. Eng. Prog., 22 (2021), 100801. https://doi.org/10.1016/j.tsep.2020.100801 doi: 10.1016/j.tsep.2020.100801
|
| [36] |
K. Gangadhar, R. E. Nayak, M. V. S. Rao, T. Kannan, Nodal/Saddle stagnation point slip flow of an aqueous convectional magnesium oxide-gold hybrid nanofluid with viscous dissipation, Arab. J. Sci. Eng., 46 (2021), 2701−2710. https://doi.org/10.1007/s13369-020-05195-x doi: 10.1007/s13369-020-05195-x
|
| [37] |
K. Gangadhar, M. A. Kumari, A. J. Chamkha, EMHD flow of radiative second-grade nanofluid over a Riga Plate due to convective heating: Revised Buongiorno's nanofluid model, Arab. J. Sci. Eng., 47 (2022), 8093−8103. https://doi.org/10.1007/s13369-021-06092-7 doi: 10.1007/s13369-021-06092-7
|
| [38] |
K. Gangadhar, M. A. Kumari, M. V. S. Rao, A. J. Chamkha, Oldroyd-B nanoliquid flow through a triple stratified medium submerged with gyrotactic bioconvection and nonlinear radiations, Arab. J. Sci. Eng., 47 (2022), 8863–8875. https://doi.org/10.1007/s13369-021-06412-x doi: 10.1007/s13369-021-06412-x
|
| [39] |
G. Kotha, V. R. Kolipaula, M. V. S. Rao, S. Penki, A. J. Chamkha, Internal heat generation on bioconvection of an MHD nanofluid flow due to gyrotactic microorganisms, Eur. Phys. J. Plus, 135 (2020), 1−19. https://doi.org/10.1140/epjp/s13360-020-00606-2 doi: 10.1140/epjp/s13360-020-00606-2
|
| [40] |
K. Gangadhar, K. B. Lakshmi, T. Kannan, A. J. Chamkha, Bioconvective magnetized oldroyd-B nanofluid flow in the presence of Joule heating with gyrotactic microorganisms, Wave. Random Complex, 2022, 1−21. https://doi.org/10.1080/17455030.2022.2050441 doi: 10.1080/17455030.2022.2050441
|
| [41] |
K. Gangadhar, A. J. Chamkha, Entropy minimization on magnetized Boussinesq couple stress fluid with non-uniform heat generation, Phys. Scripta, 96 (2021), 095205. https://doi.org/10.1088/1402-4896/ac03de doi: 10.1088/1402-4896/ac03de
|
| [42] | K. Gangadhar, K. B. Lakshmi, S. El-Sapa, M. V. S. Rao, A. J. Chamkha, Thermal energy transport of radioactive nanofluid flow submerged with microorganisms with zero mass flux condition, Wave. Random Complex, 2022, 1−23. https://doi.org/10.1080/17455030.2022.2072536 |
| [43] |
K. Gangadhar, E. M. Victoria, A. J. Chamkha, Hydrothermal features in the swirling flow of radiated graphene-Fe3O4 hybrid nanofluids through a rotating cylinder with exponential space-dependent heat generation, Wave. Random Complex, 2022, 1−24. https://doi.org/10.1080/17455030.2022.2100004 doi: 10.1080/17455030.2022.2100004
|
| [44] |
K. Gangadhar, M. Prameela, A. J. Chamkha, Exponential space-dependent heat generation on Powell-Eyring hybrid nanoliquid under nonlinear thermal radiation, Indian J. Phys., 97 (2023), 2461–2473. https://doi.org/10.1007/s12648-022-02585-9 doi: 10.1007/s12648-022-02585-9
|
| [45] |
K. Gangadhar, P. M. Seshakumari, M. V. S. Rao, A. J. Chamkha, Biconvective transport of magnetized couple stress fluid over a radiative paraboloid of revolution, P. I. Mech. Eng. E-J. Pro., 236 (2022), 1661−1670. https://doi.org/10.1177/09544089211072715 doi: 10.1177/09544089211072715
|
| [46] |
K. Gangadhar, R. E. Nayak, M. V. S. Rao, A. J. Chamkha, Nonlinear radiations in chemically reactive Walter's B nanoliquid flow through a rotating cone, P. I. Mech. Eng. E-J. Pro., 237 (2023), 731−739. https://doi.org/10.1177/09544089221105932 doi: 10.1177/09544089221105932
|
| [47] |
D. N. Bhargavi, K. Gangadhar, A. J. Chamkha, Graphene-gold/PDMS Maxwell hybrid nanofluidic flow in a squeezed channel with linear and irregular radiations, P. I. Mech. Eng. E-J. Pro., 2022. https://doi.org/10.1177/09544089221139696 doi: 10.1177/09544089221139696
|
| [48] |
H. Hanif, W. Jamshed, M. R. Eid, S. Shafie, R. W. Ibrahim, N. A. A. M. Nasir, et al., Thermal description and entropy evaluation of magnetized hybrid nanofluid with variable viscosity via Crank-Nicolson method, Case Stud. Therm. Eng., 47 (2023), 103132. https://doi.org/10.1016/j.csite.2023.103132 doi: 10.1016/j.csite.2023.103132
|
| [49] |
H. Hanif, W. Jamshed, M. R. Eid, R. W. Ibrahim, S. Shafie, A. A. Raezah, et al., Numerical Crank-Nicolson methodology analysis for hybridity aluminium alloy nanofluid flowing based-water via stretchable horizontal plate with thermal resistive effect, Case Stud. Therm. Eng., 42 (2023), 102707. https://doi.org/10.1016/j.csite.2023.102707 doi: 10.1016/j.csite.2023.102707
|
| [50] |
M. D. Shamshuddin, A. Saeed, S. R. Mishra, R. Katta, M. R. Eid, Homotopic simulation of MHD bioconvective flow of water-based hybrid nanofluid over a thermal convective exponential stretching surface, Int. J. Numer. Method. H., 34 (2024), 31−53. https://doi.org/10.1108/HFF-03-2023-0128 doi: 10.1108/HFF-03-2023-0128
|
| [51] |
Y. Li, M. Imtiaz, W. Jamshed, S. Rehman, M. R. Eid, N. A. A. M. Nasir, et al., Nonlinear thermal radiation and the slip effect on a 3D bioconvection flow of the Casson nanofluid in a rotating frame via a homotopy analysis mechanism, Nanotechnol. Rev., 12 (2023), 20230161. https://doi.org/10.1515/ntrev-2023-0161 doi: 10.1515/ntrev-2023-0161
|
| [52] |
I. Ullah, W. A. Khan, W. Jamshed, A. Abd-Elmonem, N. S. E. Abdalla, R. W. Ibrahim, et al., Heat generation (absorption) in 3D bioconvection flow of Casson nanofluid via a convective heated stretchable surface, J. Mol. Liq., 392 (2023), 123503. https://doi.org/10.1016/j.molliq.2023.123503 doi: 10.1016/j.molliq.2023.123503
|
| [53] |
J. Bouslimi, A. A. Alkathiri, T. M. Althagafi, W. Jamshed, M. R. Eid, Thermal properties, flow and comparison between Cu and Ag nanoparticles suspended in sodium alginate as Sutterby nanofluids in solar collector, Case Stud. Therm. Eng., 39 (2022), 102358. https://doi.org/10.1016/j.csite.2022.102358 doi: 10.1016/j.csite.2022.102358
|
| [54] |
A. D. Aldabesh, I. Tlili, Thermal enhancement and bioconvective analysis due to chemical reactive flow viscoelastic nanomaterial with modified heat theories: Bio-fuels cell applications, Case Stud. Therm. Eng., 52 (2023), 103768. https://doi.org/10.1016/j.csite.2023.103768 doi: 10.1016/j.csite.2023.103768
|
| [55] |
Q. H. Le, K. Smida, Z. Abdelmalek, I. Tlili, Removal of heavy metals by polymers from wastewater in the industry: A molecular dynamics approach, Eng. Anal. Bound. Elem., 155 (2023), 1035−1042. https://doi.org/10.1016/j.enganabound.2023.07.034 doi: 10.1016/j.enganabound.2023.07.034
|
| [56] |
R. Sajjad, M. Hussain, S. U. Khan, A. Rehman, M. J. Khan, I. Tlili, et al., CFD analysis for different nanofluids in fin prolonged heat exchanger for waste heat recovery, South Afr. J. Chem. Eng., 47 (2024), 9−14. https://doi.org/10.1016/j.sajce.2023.10.005 doi: 10.1016/j.sajce.2023.10.005
|
| [57] |
Z. Hussain, Z. U. Rehman, T. Abbas, K. Smida, Q. H. Le, Z. Abdelmalek, et al., Analysis of bifurcation and chaos in the traveling wave solution in optical fibers using the Radhakrishnan-Kundu-Lakshmanan equation, Results Phys., 55 (2023), 107145. https://doi.org/10.1016/j.rinp.2023.107145 doi: 10.1016/j.rinp.2023.107145
|
| [58] |
M. M. Bhatti, O. A. Bég, S. Kuharat, Electromagnetohydrodynamic (EMHD) convective transport of a reactive dissipative carreau fluid with thermal ignition in a non-Darcian vertical duct, Numer. Heat Tr. A-Appl., 2023, 1−31. https://doi.org/10.1080/10407782.2023.2284333 doi: 10.1080/10407782.2023.2284333
|
| [59] |
M. M. Bhatti, S. Jun, C. M. Khalique, A. Shahid, L. Fasheng, M. S. Mohamed, Lie group analysis and robust computational approach to examine mass transport process using Jeffrey fluid model, Appl. Math. Comput., 421 (2022), 126936. https://doi.org/10.1016/j.amc.2022.126936 doi: 10.1016/j.amc.2022.126936
|
| [60] |
K. Smida, M. U. Sohail, I. Tlili, A. Javed, Numerical thermal study of ternary nanofluid influenced by thermal radiation towards convectively heated sinusoidal cylinder, Heliyon, 9 (2023). https://doi.org/10.1016/j.heliyon.2023.e20057 doi: 10.1016/j.heliyon.2023.e20057
|
| [61] |
I. Tlili, T. A. Alkanhal, A. Rebey, M. B. Henda, A. Sa'ed, Nanofluid bioconvective transport for non-Newtonian material in bidirectional oscillating regime with nonlinear radiation and external heat source: Applications to storage and renewable energy, J. Energy Storage, 68 (2023), 107839. https://doi.org/10.1016/j.est.2023.107839 doi: 10.1016/j.est.2023.107839
|
| [62] |
C. Li, I. Tlili, Novel study of perovskite materials and the use of biomaterials to further solar cell application in the built environment: A molecular dynamic study, Eng. Anal. Bound. Elem., 155 (2023), 425−431. https://doi.org/10.1016/j.enganabound.2023.06.018 doi: 10.1016/j.enganabound.2023.06.018
|
| [63] |
Q. H. Le, F. Neila, K. Smida, Z. Li, Z. Abdelmalek, I. Tlili, pH-responsive anticancer drug delivery systems: Insights into the enhanced adsorption and release of DOX drugs using graphene oxide as a nanocarrier, Eng. Anal. Bound. Elem., 157 (2023), 157−165. https://doi.org/10.1016/j.enganabound.2023.09.008 doi: 10.1016/j.enganabound.2023.09.008
|
| [64] |
A. Abd-Elmonem, S. Kanwal, M. Imtiaz, K. Ali, S. Ahmad, W. Jamshed, et al., Case study of heat generation/absorption and activation energy on MHD hybrid nanofluid (GO-MoS2/water) flow owing to a rotatfing disk, Case Stud. Therm. Eng., 51 (2023), 103632. https://doi.org/10.1016/j.csite.2023.103632 doi: 10.1016/j.csite.2023.103632
|
| [65] |
M. R. Eid, W. Jamshed, A. Abd-Elmonem, A. F. Al-Hossainy, N. Almutlaq, A. Amjad, et al., Energy bandgap and thermal characteristics of non-Darcian MHD rotating hybridity nanofluid thin film flow: Nanotechnology application, Nanotechnol. Rev., 12 (2023), 20230159. https://doi.org/10.1515/ntrev-2023-0159 doi: 10.1515/ntrev-2023-0159
|
| [66] |
N. Ullah, S. Nadeem, A. U. Khan, R. U. Haq, I. Tlili, Influence of metallic nanoparticles in water driven along a wavy circular cylinder, Chinese J. Phys., 63 (2020), 168−185. https://doi.org/10.1016/j.cjph.2019.11.012 doi: 10.1016/j.cjph.2019.11.012
|
| [67] |
Z. Raizah, A. Saeed, M. Bilal, A. M. Galal, E. Bonyah, Parametric simulation of stagnation points flows of motile microorganism hybrid nanofluid across a circular cylinder with sinusoidal radius, Open Phys., 21 (2023), 20220205. https://doi.org/10.1515/phys-2022-0205 doi: 10.1515/phys-2022-0205
|
| [68] |
M. Gholinia, K. Hosseinzadeh, D. D. Ganji, Investigation of different base fluids suspend by CNTs hybrid nanoparticle over a vertical circular cylinder with sinusoidal radius, Case Stud. Therm. Eng., 21 (2020), 100666. https://doi.org/10.1016/j.csite.2020.100666 doi: 10.1016/j.csite.2020.100666
|
| [69] |
S. Dinarvand, R. Hosseini, E. Damangir, I. Pop, Series solutions for steady three-dimensional stagnation point flow of a nanofluid past a circular cylinder with sinusoidal radius variation, Meccanica, 48 (2013), 643−652. https://doi.org/10.1007/s11012-012-9621-7 doi: 10.1007/s11012-012-9621-7
|
| [70] |
P. Sunthrayuth, A. Alderremy, S. Aly, R. Shah, A. Akgül, Exact analysis of electro-osmotic flow of Walters'-B fluid with non-singular kernel, Pramana, 95 (2021), 1−10. https://doi.org/10.1007/s12043-021-02224-8 doi: 10.1007/s12043-021-02224-8
|
| [71] |
U. O. Mehmood, N. Mustapha, S. Shafie, Nonlinear peristaltic flow of Walter's B fluid in an asymmetric channel with heat transfer and chemical reactions, Therm. Sci., 18 (2014), 1095−1107. https://doi.org/10.2298/TSCI110921096M doi: 10.2298/TSCI110921096M
|
| [72] |
M. Arif, P. Kumam, W. Kumam, I. Khan, M. Ramzan, A fractional model of Casson fluid with ramped wall temperature: engineering applications of engine oil, Comput. Math. Method., 3 (2021), e1162. https://doi.org/10.1002/cmm4.1162 doi: 10.1002/cmm4.1162
|
| [73] |
M. H. Esfe, F. Zabihi, H. Rostamian, S. Esfandeh, Experimental investigation and model development of the non-Newtonian behavior of CuO-MWCNT-10w40 hybrid nano-lubricant for lubrication purposes, J. Mol. Liq., 249 (2018), 677−687. https://doi.org/10.1016/j.molliq.2017.11.020 doi: 10.1016/j.molliq.2017.11.020
|
| [74] |
T. Sajid, A. A. Gari, W. Jamshed, M. R. Eid, N. Islam, K. Irshad, et al., Case study of autocatalysis reactions on tetra hybrid binary nanofluid flow via Riga wedge: Biofuel thermal application, Case Stud. Therm. Eng., 47 (2023), 103058. https://doi.org/10.1016/j.csite.2023.103058 doi: 10.1016/j.csite.2023.103058
|
| [75] |
Z. A. Qureshi, S. Bilal, I. A. Shah, A. Akgül, R. Jarrar, H. Shanak, et al., Computational analysis of the morphological aspects of triadic hybridized magnetic nanoparticles suspended in liquid streamed in coaxially swirled disks, Nanomaterials, 12 (2022), 671. https://doi.org/10.3390/nano12040671 doi: 10.3390/nano12040671
|
| [76] |
A. Hussain, M. Arshad, A. Hassan, A. Rehman, H. Ahmad, J. Baili, et al., Heat transport investigation of engine oil based rotating nanomaterial liquid flow in the existence of partial slip effect, Case Stud. Therm. Eng., 28 (2021), 101500. https://doi.org/10.1016/j.csite.2021.101500 doi: 10.1016/j.csite.2021.101500
|
| [77] |
F. A. Soomro, R. U. Haq, M. Hamid, Brownian motion and thermophoretic effects on non-Newtonian nanofluid flow via Crank-Nicolson scheme, Arch. Appl. Mech., 91 (2021), 3303−3313. https://doi.org/10.1007/s00419-021-01966-6 doi: 10.1007/s00419-021-01966-6
|
| [78] |
M. Ghani, Y. Norasia, I. Anggriani, M. Tafrikan, Z. Zulaikha, Numerical results of Crank-Nicolson scheme on unsteady nano fluid under the effect of Prandtl, Mixed Convection, and Magnetohydrodynamics, Int. J. Comput. Sci. Appl. Math., 8 (2022), 71−78. https://doi.org/10.12962/j24775401.v8i2.14155 doi: 10.12962/j24775401.v8i2.14155
|
| [79] |
F. Waseem, M. Sohail, N. Ilyas, E. M. Awwad, M. Sharaf, M. J. Khan, et al., Entropy analysis of MHD hybrid nanoparticles with OHAM considering viscous dissipation and thermal radiation, Sci. Rep., 14 (2024), 1096. https://doi.org/10.1038/s41598-023-50865-z doi: 10.1038/s41598-023-50865-z
|
| [80] |
F. Wang, J. Zhang, S. Algarni, M. N. Khan, T. Alqahtani, S. Ahmad, Numerical simulation of hybrid Casson nanofluid flow by the influence of magnetic dipole and gyrotactic microorganism, Wave. Random Complex, 2022, 1−16. https://doi.org/10.1080/17455030.2022.2032866 doi: 10.1080/17455030.2022.2032866
|
| [81] |
F. Wang, M. Awais, R. Parveen, M. K. Alam, S. Rehman, N. A. Shah, Melting rheology of three-dimensional Maxwell nanofluid (Graphene-Engine-Oil) flow with slip condition past a stretching surface through Darcy-Forchheimer medium, Results Phys., 51 (2023), 106647. https://doi.org/10.1016/j.rinp.2023.106647 doi: 10.1016/j.rinp.2023.106647
|
| [82] |
S. Li, M. Sohail, U. Nazir, E. Sherif, A. Hassan, Statistical investigations and morphological aspects of cross-rheological material suspended in transportation of alumina, silica, titanium, and ethylene glycol via the Galerkin algorithm, Nanotechnol. Rev., 12 (2023), 20230169. https://doi.org/10.1515/ntrev-2023-0169 doi: 10.1515/ntrev-2023-0169
|
| [83] |
F. Wang, Z. Iqbal, J. Zhang, M. A. Abdelmohimen, A. H. Almaliki, A. M. Galal, Bidirectional stretching features on the flow and heat transport of Burgers nanofluid subject to modified heat and mass fluxes, Wave. Random Complex, 2022, 1−18. https://doi.org/10.1080/17455030.2022.2055203 doi: 10.1080/17455030.2022.2055203
|
Figures(19) / Tables(2)
Fu Zhang Wang, Muhammad Sohail, Umar Nazir, Emad Mahrous Awwad, Mohamed Sharaf. Utilization of the Crank-Nicolson technique to investigate thermal enhancement in 3D convective Walter-B fluid by inserting tiny nanoparticles on a circular cylinder[J]. AIMS Mathematics, 2024, 9(4): 9059-9090. doi: 10.3934/math.2024441
DownLoad: