Abstract
In this research, we examine four models—a rotating cone with a stationary disc, a stationary cone with a revolving disc, a co-rotating cone-disc, and a counter-rotating cone-disc—to determine the role of magnetohydrodynamic (MHD) natural convective flow of hybrid nanofluid and heat transfer in a small gap between cone and disc. An amalgamation of two nanoparticles magnesium oxide \(\left(MgO\right)\) and copper oxide \(\left(CuO\right)\) is used in water \(\left({H}_{2}O\right)\). The computations of the proposed model were limited to Reynolds number 12 with a corresponding conical angle at \(\alpha ={4}^{\circ }\). The temperature of a disc surface varies radially. An innovative aspect of the proposed framework is the convective flow of radiative hybrid nanofluid in the presence of buoyancy force and magnetic field. The governing three-dimensional momentum and energy equations are solved for velocity and temperature fields using befitting similarity transformations. The bvp4c technique has been applied. Graphs demonstrate the effect of dimensionless parameters on flow characteristics. Heat transfer rates are calculated at both the cone and disc surfaces for all four models and found that the co-rotation model produces a higher heat transfer rate at the cone surface. The proposed model has characteristics in solar thermal systems, electronics cooling, energy storage, biomedical, and waste heat recovery. This study has been validated with prior research.
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References
Mooney, M., & Ewart, R. H. (1934). The conicylindrical viscometer. Journal of Applied Physics, 5(11), 350–354. https://doi.org/10.1063/1.1745219
Shevchuk, I. V. (2004). A self-similar solution of Navier-Stokes and energy equations for rotating flows between a cone and a disk. High Temperature, 42(1), 104–110. https://doi.org/10.1023/B:HITE.0000020097.59838.02
Gul, T., Ahmed, Z., Jawad, M., Saeed, A., & Alghamdi, W. (2021). Bio-convectional nanofluid flow due to the thermophoresis and gyrotactic microorganism between the gap of a disk and cone. Brazilian Journal of Physics, 51(3), 687–697. https://doi.org/10.1007/s13538-021-00888-6
Shevchuk, I. V. (2022). An asymptotic expansion method vs a self-similar solution for convective heat transfer in rotating cone-disk systems. Physics of Fluids, 34, 10. https://doi.org/10.1063/5.0120922
Maraj, E. N., Akbar, N. S., Kousar, N., Zehra, I., Muhammad, T. (2023). Thermal enhancement of nano-fluidic transport confined between disk and cone both rotating with distinct angular velocities and heat transfer. International Journal of Numerical Methods for Heat & Fluid Flow. https://doi.org/10.1108/HFF-04-2023-0182
Moatimid, G. M., Mohamed, M. A. A., & Elagamy, K. (2022). A Casson nanofluid flow within the conical gap between rotating surfaces of a cone and a horizontal disc. Scientific Reports, 12(1), 1–21. https://doi.org/10.1038/s41598-022-15094-w
Rooman, M., Shafiq, A., Shah, Z., Vrinceanu, N., Debani, W., & Shutaywi, M. (2022). Statistical modeling for Ree-Eyring nanofluid flow in a conical gap between porous rotating surfaces with entropy generation and Hall Effect. Scientific Reports, 12, 21126. https://doi.org/10.1038/s41598-022-25136-y
Basavarajappa, M., & Bhatta, D. (2022). Study of flow of Buongiorno nanofluid in a conical gap between a cone and a disk. Physics of Fluids, 34, 11. https://doi.org/10.1063/5.0121642
Farooq, U., Waqas, H., Fatima, N., Imran, M., Noreen, S., Bariq, A., & Galal, A. M. (2023). Computational framework of cobalt ferrite and silver-based hybrid nanofluid over a rotating disk and cone: A comparative study. Scientific Reports, 13(1), 5369. https://doi.org/10.1038/s41598-023-32360-7
Srilatha, P., Remidi, S., Nagapavani, M., Singh, H., & Prasannakumara, B. C. (2023). Heat and mass transfer analysis of a fluid flow across the conical gap of a cone-disk apparatus under the thermophoretic particles motion. Energies, 16(2), 952. https://doi.org/10.3390/en16020952
Choi, S. U. S. (1995). Enhancing Thermal Conductivity of Fluid with Nanoparticles. ASME Fluids Engineering Division, 231, 99–105.
Lee, S., Choi, S.U.-S., Li, S., & Eastman, J. A. (1999). Measuring thermal conductivity of fluids containing oxide nanoparticles. Journal of Heat Transfer, 121(2), 280–289. https://doi.org/10.1115/1.2825978
Turcu, R., Darabont, A., Nan, A., Aldea, N., Macovei, D., Bica, D., & Biro, L. (2015). New polypyrrole-multiwall carbon nanotubes hybrid materials. Journal of Optoelectronics and Advanced Materials, 2006, 643–647.
HemmatEsfe, M., Wongwises, S., Naderi, A., Asadi, A., Safaei, M. R., Rostamian, H., & Karimipour, A. (2015). Thermal conductivity of Cu/TiO2–water/EG hybrid nanofluid: Experimental data and modeling using artificial neural network and correlation. International Communications in Heat and Mass Transfer, 66, 100–104. https://doi.org/10.1016/j.icheatmasstransfer.2015.05.014
Naveen Kumar, R., Gowda, R. J. P., Gireesha, B. J., & Prasannakumara, B. C. (2021). Non-Newtonian hybrid nanofluid flow over vertically upward/downward moving rotating disk in a Darcy-Forchheimer porous medium. The European Physical Journal Special Topics, 230(5), 1227–1237. https://doi.org/10.1140/epjs/s11734-021-00054-8
Hussain, A., Haider, Q., Rehman, A., Malik, M. Y., Nadeem, S., & Hussain, S. (2021). Heat transport improvement and three-dimensional rotating cone flow of hybrid-based nanofluid. Mathematical Problems in Engineering, 2021, 1–11. https://doi.org/10.1155/2021/6633468
Yıldız, Ç., Arıcı, M., & Karabay, H. (2019). Comparison of a theoretical and experimental thermal conductivity model on the heat transfer performance of Al2O3-SiO2/water hybrid-nanofluid. International Journal of Heat and Mass Transfer, 140, 598–605. https://doi.org/10.1016/j.ijheatmasstransfer.2019.06.028
Muhammad, K., Hayat, T., Alsaedi, A., & Ahmad, B. (2021). Melting heat transfer in squeezing flow of basefluid (water), nanofluid (CNTs + water) and hybrid nanofluid (CNTs + CuO + water). Journal of Thermal Analysis and Calorimetry, 143(2), 1157–1174. https://doi.org/10.1007/s10973-020-09391-7
Khashi’I, E. N. S., MdArifin, N., Pop, I., & Nazar, R. (2022). Melting heat transfer in hybrid nanofluid flow along a moving surface. Journal of Thermal Analysis and Calorimetry, 147(1), 567–578. https://doi.org/10.1007/s10973-020-10238-4
Fallah Najafabadi, M., Talebi Rostami, H., Hosseinzadeh, K., & Ganji, D. D. (2023). Hydrothermal study of nanofluid flow in channel by RBF method with exponential boundary conditions. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 237(6), 2268–2277. https://doi.org/10.1177/09544089221133909
Hosseinzadeh, S., Hosseinzadeh, Kh., Hasibi, A., & Ganji, D. D. (2022). Thermal analysis of moving porous fin wetted by hybrid nanofluid with trapezoidal, concave parabolic and convex cross sections. Case Studies in Thermal Engineering, 30, 101757. https://doi.org/10.1016/j.csite.2022.101757
Najafabadi, M. F., TalebiRostami, H., Hosseinzadeh, Kh., & Ganji, D. D. (2022). Investigation of nanofluid flow in a vertical channel considering polynomial boundary conditions by Akbari-Ganji’s method. Theoretical and Applied Mechanics Letters, 12(4), 100356. https://doi.org/10.1016/j.taml.2022.100356
Zangooee, M. R., Hosseinzadeh, Kh., & Ganji, D. D. (2022). Hydrothermal analysis of hybrid nanofluid flow on a vertical plate by considering slip condition. Theoretical and Applied Mechanics Letters, 12(5), 100357. https://doi.org/10.1016/j.taml.2022.100357
Kármán, T. V. (1921). Über laminare und turbulente Reibung. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1(4), 233–252. https://doi.org/10.1002/zamm.19210010401
Ibrahim, M. (2020). Numerical analysis of time-dependent flow of viscous fluid due to a stretchable rotating disk with heat and mass transfer. Results in Physics, 18, 103242. https://doi.org/10.1016/j.rinp.2020.103242
Turkyilmazoglu, M. (2016). Flow and heat simultaneously induced by two stretchable rotating disks. Physics of Fluids, 28, 4. https://doi.org/10.1063/1.4945651
Bhattacharyya, A., Seth, G. S., Kumar, R., & Chamkha, A. J. (2020). Simulation of Cattaneo-Christov heat flux on the flow of single and multi-walled carbon nanotubes between two stretchable coaxial rotating disks. Journal of Thermal Analysis and Calorimetry, 139(3), 1655–1670. https://doi.org/10.1007/s10973-019-08644-4
Hussain, A., Hassan, A., Arshad, M., Rehman, A., Matoog, R. T., & Abdeljawad, T. (2021). Numerical simulation and thermal enhancement of multi-based nanofluid over an embrittled cone. Case Studies in Thermal Engineering, 28, 101614. https://doi.org/10.1016/j.csite.2021.101614
Hussain, A., Haider, Q., Rehman, A., Ahmad, H., Baili, J., Aljahdaly, N. H., & Hassan, A. (2021). A thermal conductivity model for hybrid heat and mass transfer investigation of single and multi-wall carbon nano-tubes flow induced by a spinning body. Case Studies in Thermal Engineering, 28, 101449. https://doi.org/10.1016/j.csite.2021.101449
Faghiri, S., Akbari, S., Shafii, M. B., & Hosseinzadeh, Kh. (2022). Hydrothermal analysis of non-Newtonian fluid flow (blood) through the circular tube under prescribed non-uniform wall heat flux. Theoretical and Applied Mechanics Letters, 12(4), 100360. https://doi.org/10.1016/j.taml.2022.100360
Attar, M. A., Roshani, M., Hosseinzadeh, Kh., & Ganji, D. D. (2022). Analytical solution of fractional differential equations by Akbari–Ganji’s method. Partial Differential Equations in Applied Mathematics, 6, 100450. https://doi.org/10.1016/j.padiff.2022.100450
Akbari, S., Faghiri, S., Poureslami, P., Hosseinzadeh, K., & Behshad Shafii, M. (2022). Analytical solution of non-Fourier heat conduction in a 3-D hollow sphere under time-space varying boundary conditions. Heliyon, 8(12), e12496. https://doi.org/10.1016/j.heliyon.2022.e12496
Alfvén, H. (1942). Existence of electromagnetic-hydrodynamic waves. Nature, 150(3805), 405–406. https://doi.org/10.1038/150405d0
Tassaddiq, A., Khan, S., Bilal, M., Gul, T., Mukhtar, S., Shah, Z., & Bonyah, E. (2020). Heat and mass transfer together with hybrid nanofluid flow over a rotating disk. AIP Advances, 10(5), 055317. https://doi.org/10.1063/5.0010181
Sharma, K., Vijay, N., Mabood, F., & Badruddin, I. A. (2022). Numerical simulation of heat and mass transfer in magnetic nanofluid flow by a rotating disk with variable fluid properties. International Communications in Heat and Mass Transfer, 133, 105977. https://doi.org/10.1016/j.icheatmasstransfer.2022.105977
Hosseinzadeh, Kh., Mardani, M. R., Paikar, M., Hasibi, A., Tavangar, T., Nimafar, M., & Shafii, M. B. (2023). Investigation of second grade viscoelastic non-Newtonian nanofluid flow on the curve stretching surface in presence of MHD. Results in Engineering, 17, 100838. https://doi.org/10.1016/j.rineng.2022.100838
Alrabaiah, H., Bilal, M., Khan, M. A., Muhammad, T., & Legas, E. Y. (2022). Parametric estimation of gyrotactic microorganism hybrid nanofluid flow between the conical gap of spinning disk-cone apparatus. Scientific Reports, 12(1), 1–14. https://doi.org/10.1038/s41598-021-03077-2
Usman, M., Gul, T., Khan, A., Alsubie, A., & Ullah, M. Z. (2021). Electromagnetic couple stress film flow of hybrid nanofluid over an unsteady rotating disc. International Communications in Heat and Mass Transfer, 127, 105562. https://doi.org/10.1016/j.icheatmasstransfer.2021.105562
Ramzan, M., Riasat, S., Kadry, S., Kuntha, P., Nam, Y., & Howari, F. (2020). Numerical analysis of carbon nanotube-based nanofluid unsteady flow amid two rotating disks with hall current coatings and homogeneous–heterogeneous reactions. Coatings, 10(1), 48. https://doi.org/10.3390/coatings10010048
Punith Gowda, R. J., Naveen Kumar, R., Aldalbahi, A., Issakhov, A., Prasannakumara, B. C., Rahimi-Gorji, M., & Rahaman, M. (2021). Thermophoretic particle deposition in time-dependent flow of hybrid nanofluid over rotating and vertically upward/ downward moving disk. Surfaces and Interfaces, 22, 100864. https://doi.org/10.1016/j.surfin.2020.100864
Reddy, M. G., Kumar, N., Prasannakumara, B. C., Rudraswamy, N. G., & Kumar, K. G. (2021). Magnetohydrodynamic flow and heat transfer of a hybrid nanofluid over a rotating disk by considering Arrhenius energy. Communications in Theoretical Physics, 73(4), 045002. https://doi.org/10.1088/1572-9494/abdaa5
Jayadevamurthy, P. G. R., Rangaswamy, N. k., Prasannakumara, B. C., & Nisar, K. S. (2024). Emphasis on unsteady dynamics of bioconvective hybrid nanofluid flow over an upward–downward moving rotating disk. Numerical Methods for Partial Differential Equations, 40(1), e22680. https://doi.org/10.1002/num.22680
Zangooee, M. R., Hosseinzadeh, Kh., & Ganji, D. D. (2023). Hydrothermal analysis of Ag and CuO hybrid NPs suspended in mixture of water 20%+EG 80% between two concentric cylinders. Case Studies in Thermal Engineering, 50, 103398. https://doi.org/10.1016/j.csite.2023.103398
Talebi Rostami, H., Fallah Najafabadi, M., Hosseinzadeh, K., & Ganji, D. D. (2022). Investigation of mixture-based dusty hybrid nanofluid flow in porous media affected by magnetic field using RBF method. International Journal of Ambient Energy, 43(1), 6425–6435. https://doi.org/10.1080/01430750.2021.2023041
Mahanthesh, B., Gireesha, B. J., & Gorla, R. S. R. (2017). Unsteady three-dimensional MHD flow of a nano Eyring-Powell fluid past a convectively heated stretching sheet in the presence of thermal radiation, viscous dissipation and Joule heating. Journal of the Association of Arab Universities for Basic and Applied Sciences, 23,75–84. https://doi.org/10.1016/j.jaubas.2016.05.004
Ibrahim, W., & Gamachu, D. (2022). Entropy generation in radiative magneto-hydrodynamic mixed convective flow of viscoelastic hybrid nanofluid over a spinning disk. Heliyon, 8(12), e11854. https://doi.org/10.1016/j.heliyon.2022.e11854
Ramzan, M., Kumam, P., Lone, S. A., Seangwattana, T., Saeed, A., & Galal, A. M. (2023). A theoretical analysis of the ternary hybrid nanofluid flows over a non-isothermal and non-isosolutal multiple geometries. Heliyon, 9(4), e14875. https://doi.org/10.1016/j.heliyon.2023.e14875
Mahesh, A., Varma, S. V. K., Raju, C. S. K., Babu, M. J., Vajravelu, K., & Al-Kouz, W. (2021). Significance of non-Fourier heat flux and radiation on PEG – water based hybrid nanofluid flow among revolving disks with chemical reaction and entropy generation optimization. International Communications in Heat and Mass Transfer, 127, 105572. https://doi.org/10.1016/j.icheatmasstransfer.2021.105572
Sreedevi, P., & Reddy, P. S. (2019). Effect of SWCNTs and MWCNTs Maxwell MHD nanofluid flow between two stretchable rotating disks under convective boundary conditions. Heat Transfer—Asian Research, 48(8), 4105–4132. https://doi.org/10.1002/htj.21584
Ahmed, J., Khan, M., & Ahmad, L. (2019). Transient thin-film spin-coating flow of chemically reactive and radiative Maxwell nanofluid over a rotating disk. Applied Physics A, 125(3), 1–17. https://doi.org/10.1007/s00339-019-2424-0
Rana, P., & Gupta, G. (2022). FEM solution to quadratic convective and radiative flow of Ag-MgO/H2O hybrid nanofluid over a rotating cone with Hall current: Optimization using Response Surface Methodology. Mathematics and Computers in Simulation, 201, 121–140. https://doi.org/10.1016/j.matcom.2022.05.012
Gulzar, M. M., Aslam, A., Waqas, M., Javed, M. A., & Hosseinzadeh, K. (2020). A nonlinear mathematical analysis for magneto-hyperbolic-tangent liquid featuring simultaneous aspects of magnetic field, heat source and thermal stratification. Applied Nanoscience, 10(12), 4513–4518. https://doi.org/10.1007/s13204-020-01483-y
Alipour, N., Jafari, B., & Hosseinzadeh, K. (2023). Optimization of wavy trapezoidal porous cavity containing mixture hybrid nanofluid (water/ethylene glycol Go–Al2O3) by response surface method. Scientific Reports, 13(1), 1–24. https://doi.org/10.1038/s41598-023-28916-2
Mahboobtosi, M., Hosseinzadeh, Kh., & Ganji, D. D. (2023). Entropy generation analysis and hydrothermal optimization of ternary hybrid nanofluid flow suspended in polymer over curved stretching surface. International Journal of Thermofluids, 20, 100507. https://doi.org/10.1016/j.ijft.2023.100507
Turkyilmazoglu, M. (2020). On the fluid flow and heat transfer between a cone and a disk both stationary or rotating. Mathematics and Computers in Simulation, 177, 329–340. https://doi.org/10.1016/j.matcom.2020.04.004
Wang, F., Rani, S. P., Sarada, K., Gowda, R. P., Zahran, H. Y., & Mahmoud, E. E. (2022). The effects of nanoparticle aggregation and radiation on the flow of nanofluid between the gap of a disk and cone. Case Studies in Thermal Engineering, 33, 101930. https://doi.org/10.1016/j.csite.2022.101930
Sulochana, C., Aparna, S. R., & Sandeep, N. (2020). Magnetohydrodynamic MgO/CuO-water hybrid nanofluid flow driven by two distinct geometries. Heat Transfer, 49(6), 3663–3682. https://doi.org/10.1002/htj.21794
Khan, U., Shafiq, A., Zaib, A., & Baleanu, D. (2020). Hybrid nanofluid on mixed convective radiative flow from an irregular variably thick moving surface with convex and concave effects. Case Studies in Thermal Engineering, 21, 100660. https://doi.org/10.1016/j.csite.2020.100660
Khashi’ie, N. S., Arifin, N. M., Pop, I., & Wahid, N. S. (2020). Flow and heat transfer of hybrid nanofluid over a permeable shrinking cylinder with Joule heating: A comparative analysis. Alexandria Engineering Journal, 59(3), 1787–1798. https://doi.org/10.1016/j.aej.2020.04.048
Wahid, N. S., Arifin, N. M., Khashi’ie, N. S., Pop, I., Bachok, N., & Hafidzuddin, M. E. H. (2021). Flow and heat transfer of hybrid nanofluid induced by an exponentially stretching/shrinking curved surface. Case Studies in Thermal Engineering, 25, 100982. https://doi.org/10.1016/j.csite.2021.100982
Olver, P. J. (1993). Applications of Lie groups to differential equations (Vol. 107). Springer Science & Business Media
Shevchuk, I. V. (2009). Convective heat and mass transfer in rotating disk systems (Vol. 45). Berlin: Springer. https://doi.org/10.1007/978-3-642-00718-7
Gul, T., Kashifullah, Bilal, M., Alghamdi, W., Asjad, M. I., Abdeljawad, T. (2021). Hybrid nanofluid flow within the conical gap between the cone and the surface of a rotating disk. Scientific Reports, 11(1), 1180. https://doi.org/10.1038/s41598-020-80750-y
Gul, T., Gul, R., Noman, W., Saeed, A., Mukhtar, S., Alghamdi, W., & Alrabaiah, H. (2020). CNTs-nanofluid flow in a rotating system between the gap of a disk and cone. Physica Scripta, 95(12), 125202. https://doi.org/10.1088/1402-4896/abbf1e
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Geetika received funding provided by CSIR-UGC through grant no.- 09/1313(0001)/2020-EMR-I.
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Geetika Saini: data curation, conceptualization, investigation, validation, writing manuscript, edited and submitted the manuscript; Hanumagowda B.N: data curation, formal analysis, supervision. All authors have reviewed and approved the final manuscript.
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Saini, G., Hanumagowda, B.N. Natural Convective Heat Transfer Analysis of Electrically Conducting Hybrid Nanofluid in a Small Gap Between Rotating Cone and Disc. BioNanoSci. (2024). https://doi.org/10.1007/s12668-024-01308-0
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DOI: https://doi.org/10.1007/s12668-024-01308-0