This study presents a numerical investigation of heat and mass transfer in a three-dimensional Williamson hybrid nanofluid composed of cadmium telluride (CdTe) and boron nitride nanotubes (BNNTs) dispersed in RT42 (Rubitherm), which is considered in its fully molten state. The flow is considered to be three-dimensional over a bidirectionally power-law stretching surface of variable thickness, including the effects of thermal radiation, internal heat generation, chemical reaction with activation energy, and Darcy–Forchheimer porous medium resistance. The governing nonlinear partial differential equations are transformed into a system of dimensionless ordinary differential equations using suitable similarity transformations, which, in turn, is solved numerically using shooting techniques through Mathematica functions NDSolve and FindRoot. The numerical method used is validated through comparing some obtained results with previously published limiting case results. The results show that increasing porous medium resistance suppresses fluid velocity while enhancing temperature and concentration distributions due to reduced convective transport. The increase of nanoparticle volume fractions increases the temperature profile and thermal-boundary-layer thickness; however, the accompanying decrease in the reduced Nusselt number indicates a reduction in the local wall heat-transfer rate. Increasing the radiation parameter from 0 to 2 decreased the reduced Nusselt number from 16.1657 to 8.3463, which corresponds to a reduction of approximately 48.4%. The reduced Nusselt number decreased from 17.4351 to 3.6625 upon increasing the Eckert number from 0 to 0.2, a reduction of approximately 78.9%. The primary wall-shear quantity rises by approximately 18.7% when the Forchheimer number increased from 0 to 2. The present study's main contribution is that it simultaneously treats Williamson rheology, BNNTs–CdTe/RT42 HC hybridization, non-Darcy porous resistance, thermal radiation, and Arrhenius kinetics within a single model. The results provide a theoretical basis for evaluating possible hybrid nanofluids in electronic thermal-management systems but not device-level validation.
Citation: Mohammed H. Alharbi, Tarek G. Emam, Essam M. Elsaid. Thermal characteristics of (BNNTs+CdTe/RT42 HC) hybrid phase change nanofluid flow: Cooling electronic devices application[J]. AIMS Mathematics, 2026, 11(9): 29978-30011. doi: 10.3934/math.20261189
This study presents a numerical investigation of heat and mass transfer in a three-dimensional Williamson hybrid nanofluid composed of cadmium telluride (CdTe) and boron nitride nanotubes (BNNTs) dispersed in RT42 (Rubitherm), which is considered in its fully molten state. The flow is considered to be three-dimensional over a bidirectionally power-law stretching surface of variable thickness, including the effects of thermal radiation, internal heat generation, chemical reaction with activation energy, and Darcy–Forchheimer porous medium resistance. The governing nonlinear partial differential equations are transformed into a system of dimensionless ordinary differential equations using suitable similarity transformations, which, in turn, is solved numerically using shooting techniques through Mathematica functions NDSolve and FindRoot. The numerical method used is validated through comparing some obtained results with previously published limiting case results. The results show that increasing porous medium resistance suppresses fluid velocity while enhancing temperature and concentration distributions due to reduced convective transport. The increase of nanoparticle volume fractions increases the temperature profile and thermal-boundary-layer thickness; however, the accompanying decrease in the reduced Nusselt number indicates a reduction in the local wall heat-transfer rate. Increasing the radiation parameter from 0 to 2 decreased the reduced Nusselt number from 16.1657 to 8.3463, which corresponds to a reduction of approximately 48.4%. The reduced Nusselt number decreased from 17.4351 to 3.6625 upon increasing the Eckert number from 0 to 0.2, a reduction of approximately 78.9%. The primary wall-shear quantity rises by approximately 18.7% when the Forchheimer number increased from 0 to 2. The present study's main contribution is that it simultaneously treats Williamson rheology, BNNTs–CdTe/RT42 HC hybridization, non-Darcy porous resistance, thermal radiation, and Arrhenius kinetics within a single model. The results provide a theoretical basis for evaluating possible hybrid nanofluids in electronic thermal-management systems but not device-level validation.
| [1] |
B. N. Lakshmi, C. Maheswari, V. S. Bhagavan, S. L. Pala, A. Anjum, U. Khan, et al., Numerical investigation of velocity and thermal slips on MHD hybrid nanofluid flow past a stretching sheet with nth‐order chemical reaction effects, Eng. Rep., 8 (2026), e70760. https://doi.org/10.1002/eng2.70760 doi: 10.1002/eng2.70760
|
| [2] |
S. A. Qureshi, A. Qureshi, S. Shoaib, Numerical treatment of the magnetised dissipative thin-film hybrid nanofluid (S WCNT− MWCNT/H2O) flow and heat transfer over an unsteady stretching sheet with partial slip and convective boundary conditions, Int. J. Ambient Energy, 47 (2026), 2660869. https://doi.org/10.1080/01430750.2026.2660869 doi: 10.1080/01430750.2026.2660869
|
| [3] |
N. H. A. Norzawary, N. Bachok, M. S. Mustafa, S. K. Soid, Velocity and thermal slip of hybrid carbon nanotubes via extendable/shrinkable cylinder: Heat transfer optimization, Z. Angew. Math. Mech., 106 (2026), 70399. https://doi.org/10.1002/zamm.70399 doi: 10.1002/zamm.70399
|
| [4] |
E. O. Fatunmbi, A. T. Adeosun, S. O. Salawu, O. A. Olaiju, Thermal efficiency of MHD micropolar penta-hybrid nanofluid squeezing flow under nonlinear thermal radiation and activation energy effects, Int. J. Thermofluids, 33 (2026), 101626. https://doi.org/10.1016/j.ijft.2026.101626 doi: 10.1016/j.ijft.2026.101626
|
| [5] |
N. S. Akbar, T. Zamir, T. Muhammad, M. Farooq, N. Ullah, S. Shukat, Thermal performance with neural network analysis of Maxwell fluid with hybrid and tri-nanoparticle interactions: A case study, Neural Comput. Applic., 38 (2026), 322. https://doi.org/10.1007/s00521-026-11996-2 doi: 10.1007/s00521-026-11996-2
|
| [6] |
D. A. Kanwal, I. B. Mansir, N. A. Alshehri, Z. Zheng, D. Qaiser, M. A. Fahmy, et al., Heat and mass transfer analysis for bi-dimensional bioconvective MHD nanofluid with varying thermal traits, Int. J. Model. Simul., 46 (2026), 693–707. https://doi.org/10.1080/02286203.2024.2349505 doi: 10.1080/02286203.2024.2349505
|
| [7] |
A. Mishra, Significance of Thompson and Troian slip effects on Fe3O4-CoFe2O4 ethylene glycol-water hybrid nanofluid flow over a permeable plate, Hybrid Adv., 6 (2024), 100262. https://doi.org/10.1016/j.hybadv.2024.100262 doi: 10.1016/j.hybadv.2024.100262
|
| [8] |
A. Mishra, G. Pathak, Thermal-flow characteristics of an Ellis hybrid nanofluid containing polytetrafluoroethylene-SWCNTs over a stretching/shrinking cylinder with slip effect, Nano-Structures Nano-Objects, 43 (2025), 101515. https://doi.org/10.1016/j.nanoso.2025.101515 doi: 10.1016/j.nanoso.2025.101515
|
| [9] |
A. U. Awan, S. Majeed, B. Ali, L. Ali, Significance of nanoparticles aggregation and Coriolis force on the dynamics of Prandtl nanofluid: The case of rotating flow, Chin. J. Phys., 79 (2022), 264–274. https://doi.org/10.1016/j.cjph.2022.07.008 doi: 10.1016/j.cjph.2022.07.008
|
| [10] |
S. Kanwal, S. A. A. Shah, A. Bariq, B. Ali, A. E. Ragab, E. A. Az-Zo'bi, Insight into the dynamics of heat and mass transfer in nanofluid flow with linear/nonlinear mixed convection, thermal radiation, and activation energy effects over the rotating disk, Sci. Reports, 13 (2023), 23031. https://doi.org/10.1038/s41598-023-49988-0 doi: 10.1038/s41598-023-49988-0
|
| [11] |
A. Ali, H. Sharif, D. Habib, H. A. Ghazwani, I. Saman, H. Yang, Significance of tri-hybrid nanoparticles in thermal management subject to magnetized squeezing flow of a Boger-micropolar nanofluid between concentring disks, J. Mol. Liq. , 397 (2024), 124141. https://doi.org/10.1016/j.molliq.2024.124141 doi: 10.1016/j.molliq.2024.124141
|
| [12] |
L. Ali, M. G. Murtaza, T. Akter, J. Alam, The effect of electrical conductivity and magnetization on biomagnetic fluid flow containing magnetic particles past a thin needle using lie group analysis, J. Therm. Anal. Calorim., 151 (2026), 9245–9259. https://doi.org/10.1007/s10973-026-15493-5 doi: 10.1007/s10973-026-15493-5
|
| [13] |
Z. Said, A. K. Pandey, A. K. Tiwari, B. Kalidasan, F. Jamil, A. K. Thakur, et al., Nano-enhanced phase change materials Fundamentals and applications, PECS, 104 (2024), 101162. https://doi.org/10.1016/j.pecs.2024.101162 doi: 10.1016/j.pecs.2024.101162
|
| [14] |
S. Chang, X. Li, X. Gao, R. Lin, H. Hu, Y. Shu, Numerical investigation on the heat transfer characteristics and dynamic adaptability of cascaded phase change material (PCM) heat sinks under flight conditions, Energy, 345 (2026), 140206. https://doi.org/10.1016/j.energy.2026.140206 doi: 10.1016/j.energy.2026.140206
|
| [15] |
S. D. Prasetyo, Y. Trisnoaji, Z. Arifin, A. R. Prabowo, Assessment of the performance differences in PV–PCM systems with numerical analysis of different phase change materials and structural designs, Solar Energy Mater. Solar Cells, 295 (2026), 114019. https://doi.org/10.1016/j.solmat.2025.114019 doi: 10.1016/j.solmat.2025.114019
|
| [16] |
D. S. Jayathunga, H. P. Karunathilake, M. Narayana, S. Witharana, Phase change material (PCM) candidates for latent heat thermal energy storage (LHTES) in concentrated solar power (CSP) based thermal applications-a review, Renew. Sust. Energy Rev., 189 (2024), 113904. https://doi.org/10.1016/j.rser.2023.113904 doi: 10.1016/j.rser.2023.113904
|
| [17] |
S. Kasiviswanathan, M. I. Shajahan, R. Bharathiraja, M. Arunprasad, A. C. Benime, Comprehensive overview of phase change materials in electronics, building, and solar applications, Eng. Res. Express, 8 (2026), 032502. https://doi.org/10.1088/2631-8695/ae342a doi: 10.1088/2631-8695/ae342a
|
| [18] |
M. K. Saudi, M. Emam, H. Hassan, H. Sekiguchi, A. S. G. Khalil, Enhancing thermal management of lithium-ion batteries using phase change materials and expanded graphite: An experimental study, J. Energy Storage, 130 (2025), 117427. https://doi.org/10.1016/j.est.2025.117427 doi: 10.1016/j.est.2025.117427
|
| [19] |
R. A. Rachmanto, Z. Arifin, Ubaidillah, W. Endra Juwana, E. Yohana, D. Widhiyanuriyawan, et al., Enhancing thermal performance and energy efficiency in photovoltaic thermal-phase change material systems: a numerical investigation of fin geometry variations, Int. J. Heat Technol., 44 (2026), 201–214. https://doi.org/10.18280/ijht.440117 doi: 10.18280/ijht.440117
|
| [20] |
I. I. Hakim, R. Edriawan, N. Putra, Thermal performance and properties analysis of a building envelope integrated with phase change material for energy conservation in a tropical climate region, AIP Conf. Proc., 2836 (2024), 080003. https://doi.org/10.1063/5.0188417 doi: 10.1063/5.0188417
|
| [21] |
A. Srinu, K. S. Reddy, N. Amar, Radiation and inclined magnetic field effects on Williamson fluid flow above a stretching sheet in the existence of velocity, thermal, and concentration slips, PDE Appl. Math., 9 (2024), 100611. https://doi.org/10.1016/j.padiff.2023.100611 doi: 10.1016/j.padiff.2023.100611
|
| [22] |
S. T. Abbas, I. H. Qureshi, M. Sohail, M. J. Khan, Numerical investigation of williamson nanofluid heat transfer over a stretching sheet employing buongiorno model and bvp4c boundary layer solution, PDE Appl. Math., 18 (2026), 101362. https://doi.org/10.1016/j.padiff.2026.101362 doi: 10.1016/j.padiff.2026.101362
|
| [23] | B. G. Negash, H. Dessie, E. Haile, T. Walelign, Magnetohydrodynamic analysis of unsteady williamson nanofluid flow over a permeable inclined stretching sheet with cattaneo-christov double-diffusion effects, preprint paper, 2026. https://doi.org/10.21203/rs.3.rs-9411000/v1 |
| [24] |
R. A. Oderinu, T. A. Oyeyinka, S. Alao, F. J. Ayanbukola, B. A. Sanusi, Mixed convection and permeability effects on magnetohydrodynamic williamson fluid flow over an inclined stretchy surface with radiation influence, Eng. Rep., 7 (2025), e70078. https://doi.org/10.1002/eng2.70078 doi: 10.1002/eng2.70078
|
| [25] |
P. Priyadharshini, V. Karpagam, P. Gayathri, Numerical and ANN optimization analysis for Williamson fluid flow across a porous surface, Neural Comput. Appl., 38 (2026), 333. https://doi.org/10.1007/s00521-026-12073-4 doi: 10.1007/s00521-026-12073-4
|
| [26] |
M. Madhu, N. S. Shashikumar, K. Thriveni, B. J. Gireesha, B. Mahanthesh, Irreversibility analysis of the MHD Williamson fluid flow through a microchannel with thermal radiation, Waves Random Compl. Med., 35 (2025), 10105–10127. https://doi.org/10.1080/17455030.2022.2111473 doi: 10.1080/17455030.2022.2111473
|
| [27] |
M. Hasnain, H. Sezer, J. H. Mason, Mathematical modeling of heat and mass transfer in metal hydride hydrogen storage systems: A comprehensive review, Renew. Sust. Energy Rev., 226 (2026), 116294. https://doi.org/10.1016/j.rser.2025.116294 doi: 10.1016/j.rser.2025.116294
|
| [28] |
Y. Jin, X. Yang, Q. Zeng, H. Deng, X. Gao, H. Xu, Research on heat and mass transfer of PEMEC anode flow channel based on topology optimization, Fuel, 404 (2026), 136144. https://doi.org/10.1016/j.fuel.2025.136144 doi: 10.1016/j.fuel.2025.136144
|
| [29] |
K. Zhang, D. Yang, L. Wang, C. Gu, K. Wang, Macro-micro simulation of heat and mass transfer, grain growth during ultrasonic vibration-assisted wire-arc directed energy deposition, Int. J. Heat Mass Transfer, 256 (2026), 128038. https://doi.org/10.1016/j.ijheatmasstransfer.2025.128038 doi: 10.1016/j.ijheatmasstransfer.2025.128038
|
| [30] |
M. Sharifi, Effects of various instabilities on heat and mass transfer characteristics and their analysis in practical multidiffusive flow systems: A comprehensive review, Int. Commun. Heat Mass Transfer, 162 (2025), 108685. https://doi.org/10.1016/j.icheatmasstransfer.2025.108685 doi: 10.1016/j.icheatmasstransfer.2025.108685
|
| [31] |
A. Atia, S. Benarrache, H. M. Regue, M. Teggar, S. Bouabdallah, N. H. Hamza, et al., Heat and mass transfer enhancement with latent heat thermal storage for improving the solar still performance: A comprehensive review, Appl. Therm. Eng., 279 (2025), 128061. https://doi.org/10.1016/j.applthermaleng.2025.128061 doi: 10.1016/j.applthermaleng.2025.128061
|
| [32] |
M. A. Fahmy, A new boundary element formulation for modeling and simulation of three‐temperature distributions in carbon nanotube fiber reinforced composites with inclusions, Math. Meth. Appl. Sci., 49 (2026), 7550–7565. https://doi.org/10.1002/mma.7312 doi: 10.1002/mma.7312
|
| [33] |
M. A. Fahmy, M. Toujani, A. E. Abouelregal, A boundary element framework for fractional dual-phase-lag modeling of nanoparticle-assisted photothermal heat transfer in skin tissue, Results Eng., 29 (2026), 109417. https://doi.org/10.1016/j.rineng.2026.109417 doi: 10.1016/j.rineng.2026.109417
|
| [34] |
J. H. Merkin, N. C. Roșca, A. V. Roșca, I. Pop, MHD mixed convection flow over a permeable vertical flat plate embedded in a Darcy–Forchheimer porous medium, Transp. Porous Med., 1511 (2024), 2511–2528. https://doi.org/10.1007/s11242-024-02124-6 doi: 10.1007/s11242-024-02124-6
|
| [35] |
H. C. Nagari, M. D. Firdi, E. H. Rikitu, Investigation of thermal radiation and joule heating effects on variable viscosity Casson nanofluid flow over a stretching sheet in Darcy–Forchheimer porous medium, Numer. Heat Transfer Part A, 87 (2026), 2382929. https://doi.org/10.1080/10407782.2024.2382929 doi: 10.1080/10407782.2024.2382929
|
| [36] |
Q. Raza, X. Wang, Analyzing heat transfer behavior in two-dimensional Darcy–Forchheimer porous medium using magnetized nanoparticles, Numer. Heat Transfer Part B, 86 (2025), 4314–4334. https://doi.org/10.1080/10407790.2024.2380034 doi: 10.1080/10407790.2024.2380034
|
| [37] |
Q. Raza, X. Wang, A. J. Chamkha, Bio-convection of ternary magnetized nanoparticles thermal conductivity in chemical reaction and activation energy flow with Darcy Forchheimer permeable across a double porous medium, Numer. Heat Transfer Part A, 87 (2026), 2316210. https://doi.org/10.1080/10407782.2024.2316210 doi: 10.1080/10407782.2024.2316210
|
| [38] |
S. N. Safiullah, P. De, Thermal radiation, heat generation/absorption effect on bioconvective Sisko nanofluids over Darcy Forchheimer porous medium with regression analysis, Numer. Heat Transfer Part B., 87 (2026), 2390099. https://doi.org/10.1080/10407790.2024.2390099 doi: 10.1080/10407790.2024.2390099
|
| [39] |
L. Ahmad, S. Islam, A. M. Alqahtani, M. Sarfraz, Swirling motion of temperature-dependent chemical reactions and Arrhenius activation energy in Cross fluid, Int. Commun. Heat Mass Transfer, 159 (2024), 108082. https://doi.org/10.1016/j.icheatmasstransfer.2024.108082 doi: 10.1016/j.icheatmasstransfer.2024.108082
|
| [40] |
T. Muhammad, F. Haider, Time-dependent flow of Reiner–Rivlin nanofluid over a stretching sheet with Arrhenius activation energy and binary chemical reaction, Multidiscip. Model. Mater. Struct., 21 (2025), 1–18. https://doi.org/10.1108/MMMS-05-2024-0123 doi: 10.1108/MMMS-05-2024-0123
|
| [41] |
M. I. U. Rehman, H. Chen, F. Z. Duraihem, M. Hussien, A. Hamid, H. Qi, Darcy-Forchheimer aspect on unsteady bioconvection flow of Reiner-Philippoff nanofluid along a wedge with swimming microorganisms and Arrhenius activation energy, Numer. Heat Transfer Part A, 87 (2026), 2314221. https://doi.org/10.1080/10407782.2024.2314221 doi: 10.1080/10407782.2024.2314221
|
| [42] |
M. M. Ghazy, Kh. S. Mekheimer, A. M. Megahed, R. E. Aboelkhair, Iirreversibility and controlled entropy generation for squeezing sutterby nanofluid flow with joule heating and arrhenius activation energy, Z. Angew. Math. Mech., 106 (2026), e70412. https://doi.org/10.1002/zamm.70412 doi: 10.1002/zamm.70412
|
| [43] |
A. K. Gautam, A. K. Verma, K. Bhattacharyya, S. Mukhopadhyay, A. J. Chamkha, Impacts of activation energy and binary chemical reaction on MHD flow of Williamson nanofluid in Darcy–Forchheimer porous medium: A case of expanding sheet of variable thickness, Waves Random Compl Med., 34 (2021), 3528–3549. https://doi.org/10.1080/17455030.2021.1979274 doi: 10.1080/17455030.2021.1979274
|
| [44] |
M. Taj, T. Salahuddin, A three dimensional frictional flow study of Williamson fluid with chemical reaction, Mater. Sci. Eng. : B, 291 (2023), 116305. https://doi.org/10.1016/j.mseb.2023.116305 doi: 10.1016/j.mseb.2023.116305
|
| [45] |
M. Taj, T. Salahuddin, A brief flow analysis of Williamson fluid near a radiated irregular vertical surface with binary chemical reaction, Waves Random Compl. Med., 36 (2026), 3604–3618. https://doi.org/10.1080/17455030.2023.2178835 doi: 10.1080/17455030.2023.2178835
|
| [46] |
S. M. R. S. Naqvi, H. Waqas, S. Yasmin, D. Liu, T. Muhammad, S. M. Eldin, et al., Numerical simulations of hybrid nanofluid flow with thermal radiation and entropy generation effects, Case Stud. Therm. Eng., 40 (2022), 102479. https://doi.org/10.1016/j.csite.2022.102479 doi: 10.1016/j.csite.2022.102479
|
| [47] |
Z. Qin, C. Ji, Z. Low, S. Dubey, F. H. Choo, F. Duan, Effect of fin location on the latent heat storage: A numerical study, Energy Proced., 143 (2017), 320–326. https://doi.org/10.1016/j.egypro.2017.12.691 doi: 10.1016/j.egypro.2017.12.691
|
| [48] |
P. N. S. Teja, S. K. Gugulothu, P. D. S. Reddy, A. Ashraf, B. Deepanraj, P. T. Arasu, Numerical study on the thermal enhancement of phase change material with the addition of nanoparticles and changing the orientation of the enclosure, J. Nanomater., 2022 (2022), 6428469. https://doi.org/10.1155/2022/6428469 doi: 10.1155/2022/6428469
|
| [49] |
E. M. Elsaid, M. S. Abdel‐Wahed, Thermal evaluation of MHD boundary‐layer flow of hybridity nanofluid via a 3D sinusoidal cylinder, Z. Angew. Math. Mech., 104 (2024), e202300186. https://doi.org/10.1002/zamm.202300186 doi: 10.1002/zamm.202300186
|
| [50] |
T. Hayat, A. Aziz, T. Muhammad, A. Alsaedi, On magnetohydrodynamic three-dimensional flow of nanofluid over a convectively heated nonlinear stretching surface, Int. J. Heat Mass Transfer, 100 (2016), 566–572. https://doi.org/10.1016/j.ijheatmasstransfer.2016.04.113 doi: 10.1016/j.ijheatmasstransfer.2016.04.113
|
| [51] |
A. A. Al Qarni, E. M. Elsaid, M. R. Eid, A. H. Abdel-Aty, A. J. Alqarni, M. S. Abdel-wahed, Heat transfer evaluation of (CaTe+SiC) hybrid nanofluid flow based RT42 HC (Rubitherm) phase change material: Cooling photovoltaic panels application, Modern Phys. Lett. B, 39 (2025), 2450440. https://doi.org/10.1142/S0217984924504402 doi: 10.1142/S0217984924504402
|