Sains Malaysiana 50(12)(2021): 3753-3764

http://doi.org/10.17576/jsm-2021-5012-24

Unsteady Transport Phenomena of Hybrid Al₂O₃-Cu/H₂O Nanofluid Past a Shrinking Slender Cylinder

(Fenomenon Angkutan Tak Mantap Nanobendalir Hibrid Al₂O₃-Cu/H₂O terhadap Silinder Langsing Mengecut)

NURUL AMIRA ZAINAL^1,2, ROSLINDA NAZAR¹*, KOHILAVANI NAGANTHRAN^3,4 & IOAN POP⁵

¹Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

²Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka,76100 Melaka, Malaysia

³Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

⁴Center for Data Analytics, Consultancy and Services, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

⁵Department of Mathematics, Babeş-Bolyai University, R-400084 Cluj-Napoca, Romania

Diserahkan: 29 Disember 2020/Diterima: 30 Mac 2021

ABSTRACT

Theoretical investigations of unsteady boundary layer flow gain interest due to its relatability to practical settings. Thus, this study proposes a unique mathematical model of the unsteady flow and heat transfer in hybrid nanofluid past a permeable shrinking slender cylinder. The suitable form of similarity transformations is adapted to simplify the complex partial differential equations into a solvable form of ordinary differential equations. A built-in bvp4c function in MATLAB software is exercised to elucidate the numerical analysis for certain concerning parameters, including the unsteadiness and curvature parameters. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The present analysis further observed dual solutions that exist in the system of equations. Notable findings showed that by increasing the nanoparticles volume fraction, the skin friction coefficient increases in accordance with the heat transfer rate. In contrast, the decline of the unsteadiness parameter demonstrates a downward trend toward the heat transfer performance.

Keywords: Dual solutions; hybrid nanofluid; shrinking cylinder; unsteady flow

ABSTRAK

Kajian teori aliran lapisan sempadan tak mantap telah menarik minat ramai kerana kaitannya dengan tetapan praktikal. Oleh itu, kajian ini mencadangkan suatu model matematik yang unik untuk mengkaji aliran tak mantap dan pemindahan haba dalam nanobendalir hibrid melewati silinder langsing telap mengecut. Bentuk penjelmaan keserupaan yang sesuai digunakan untuk menurunkan persamaan pembezaan separa yang kompleks kepada bentuk persamaan pembezaan biasa yang boleh diselesaikan. Fungsi bvp4c terbina dalam perisian MATLAB digunakan untuk menjelaskan analisis berangka bagi parameter yang bersangkutan termasuk parameter ketakmantapan dan kelengkungan. Prosedur bvp4c adalah sangat sesuai dan cekap dalam memperoleh lebih daripada satu penyelesaian dengan ramalan yang mencukupi. Analisis kajian ini mendapati yang penyelesaian dual wujud dalam sistem persamaan. Hasil keputusan kajian menunjukkan bahawa dengan meningkatkan pecahan isi padu nanozarah, pekali geseran kulit meningkat sesuai dengan kadar pemindahan haba. Sebaliknya, penurunan parameter ketakmantapan menunjukkan trend penurunan prestasi pemindahan haba.

Kata kunci: Aliran tak mantap; nanobendalir hibrid; penyelesaian dual; silinder mengecut

RUJUKAN

Abbas, Z., Rasool, S. & Rashidi, M.M. 2015. Heat transfer analysis due to an unsteady stretching/shrinking cylinder with partial slip condition and suction. Ain Shams Engineering Journal 6(3): 939-945.

Almaneea, A. 2020. Experimental and numerical investigation of fluid flow and heat transfer in circular micro-channel. Sains Malaysiana 49(10): 2599-2608.

Altan, T., Oh, S., Gegel, H. & Park, M. 1983. Metal Forming: Theory and Applications. Ohio: American Society of Metals. pp. 386-387.

Arifin, N.M., Nazar, R. & Pop, I. 2011. Non-isobaric Marangoni boundary layer flow for Cu, Al₂O₃ and TiO₂ nanoparticles in a water-based fluid. Meccanica 46: 833-843.

Awaludin, I.S., Ahmad, R. & Ishak, A. 2020. On the stability of the flow over a shrinking cylinder with prescribed surface heat flux. Propulsion and Power Research 9: 181-187.

Bachok, N. & Ishak, A. 2010. Flow and heat transfer over a stretching cylinder with prescribed surface heat flux. Malaysian Journal of Mathematical Sciences 4(2): 159-169.

Benson, R.S., Garg, R.D. & Woollatt, D. 1964. A numerical solution of unsteady flow problems.  International Journal of Mechanical Sciences 6(1): 117-144.

Butt, A.S. & Ali, A. 2014. Entropy analysis of magnetohydrodynamic flow and heat transfer due to a stretching cylinder. Journal of the Taiwan Institute of Chemical Engineers 45(3): 780-786.

Choi, S.U.S. & Eastman, J.A. 1995. Enhancing thermal conductivity of fluids with nanoparticles. In  American Society of Mechanical Engineers, Fluids Engineering Division. United States. pp. 99-103.

Das, P.K. 2017. A review based on the effect and mechanism of thermal conductivity of normal nanofluids and hybrid nanofluids. Journal of Molecular Liquids 240: 420-446.

Devi, S.S.U. & Devi, S.P.A. 2017. Heat transfer enhancement of Cu-Al₂O₃/water hybrid nanofluid flow over a stretching sheet. Journal of the Nigerian Mathematical Society 36(2): 419-433.

Devi, S.P.A. & Devi, S.S.U. 2016a. Numerical investigation of hydromagnetic hybrid Cu-Al₂O₃/water nanofluid flow over a permeable stretching sheet with suction. International Journal of Nonlinear Sciences and Numerical Simulation 17(5): 249-257.

Devi, S.S.U. & Devi, S.P.A. 2016b. Numerical investigation of three-dimensional hybrid Cu-Al₂O₃/water nanofluid flow over a stretching sheet with effecting Lorentz force subject to Newtonian heating. Canadian Journal of Physics 94(5): 490-496.

Fang, T.G., Zhang, J., Zhong, Y.F. & Tao, H. 2011. Unsteady viscous flow over an expanding stretching cylinder. Chinese Physics Letters 28(12): 124707.

Fisher, E.G. 1976. Extrusion of Plastics. New York: John Wiley.

Ganesan, P. & Loganathan, P. 2003. Magnetic field effect on a moving vertical cylinder with constant heat flux. Heat and Mass Transfer 39: 381-386.

Ghalambaz, M., Roşca, N.C., Roşca, A.V. & Pop, I. 2020. Mixed convection and stability analysis of stagnation-point boundary layer flow and heat transfer of hybrid nanofluids over a vertical plate. International Journal of Numerical Methods for Heat & Fluid Flow 30(7): 3737-3754.

Hamzah, M.H., Sidik, N.A.C., Ken, T.L., Mamat, R. & Najafi, G. 2017. Factors affecting the performance of hybrid nanofluids: A comprehensive review. International Journal of Heat and Mass Transfer 115: 630-646.

Hosseinzadeh, K., Asadi, A., Mogharrebi, A.R., Ermia Azari, M. & Ganji, D.D. 2020. Investigation of mixture fluid suspended by hybrid nanoparticles over vertical cylinder by considering shape factor effect. Journal of Thermal Analysis and Calorimetry 143: 1081-1095.

Jahan, S., Sakidin, H., Nazar, R. & Pop, I. 2018. Unsteady flow and heat transfer past a permeable stretching/shrinking sheet in a nanofluid: A revised model with stability and regression analyses. Journal of Molecular Liquids 261: 550-564.

Jamil, F. & Ali, H.M. 2020. Applications of Hybrid Nanofluids in Different Fields, in Hybrid Nanofluids for Convection Heat Transfer. Massachusetts: Academic Press.

Kamal, F., Zaimi, K., Ishak, A. & Pop, I. 2019. Stability analysis of MHD stagnation-point flow towards a permeable stretching/shrinking sheet in a nanofluid with chemical reactions effect. Sains Malaysiana 48(1): 243-250.

Karwe, M.V. & Jaluria, Y. 1991. Numerical simulation of thermal transport associated with a continuously moving flat sheet in materials processing. Journal of Heat Transfer 113(3): 612-619.

Khashi’ie, N.S., Arifin, N.M., Pop, I., Nazar, R., Hafidzuddin, E.H. & Wahi, N. 2020a. Thermal Marangoni flow past a permeable stretching/shrinking sheet in a hybrid Cu-Al₂O₃/water nanofluid. Sains Malaysiana 49(1): 211-222.

Khashi’ie, N.S., Waini, I., Zainal, N.A., Hamzah, K. & Mohd Kasim, A.R. 2020b. Hybrid nanofluid flow past a shrinking cylinder with prescribed surface heat flux. Symmetry 12(9): 1493.

Khashi’ie, N.S., Hafidzuddin, E.H., Arifin, N.M. & Wahi, N. 2020c. Stagnation point flow of hybrid nanofluid over a permeable vertical stretching/shrinking cylinder with thermal stratification effect. Letters 12(2): 80-94.

Khashi’ie, N.S., Arifin, N.M., Pop, I. & Wahid, N.S. 2020d. 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.

Khashi'ie, N.S., Arifin, N.M. & Pop, I. 2020e. Unsteady axisymmetric flow and heat transfer of a hybrid nanofluid over a permeable stretching/shrinking disc. International Journal of Numerical Methods for Heat & Fluid Flow 31(6): 2005-2021.

Khashi’ie, N.S., Arifin, N.M., Hafidzuddin, E.H. & Wahi, N. 2019. Thermally stratified flow of Cu-Al₂O₃/water hybrid nanofluid past a permeable stretching/shrinking circular cylinder. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 63(1): 154-163.

Maskeen, M.M., Zeeshan, A., Mehmood, O.U. & Hassan, M. 2019. Heat transfer enhancement in hydromagnetic alumina-copper/water hybrid nanofluid flow over a stretching cylinder. Journal of Thermal Analysis and Calorimetry 138(2): 1127-1136.

McCroskey, W.J. 1977. Some current research in unsteady fluid dynamics. Journal of Fluids Engineering 99(1): 8-39.

Merkin, J.H., Najib, N., Bachok, N., Ishak, A. & Pop, I. 2017. Stagnation-point flow and heat transfer over an exponentially stretching/shrinking cylinder. Journal of the Taiwan Institute of Chemical Engineers 74: 65-72.

Najib, N., Bachok, N., Arifin, N. & Ishak, A. 2014. Stagnation point flow and mass transfer with chemical reaction past a stretching/shrinking cylinder. Scientific Reports 4: 4178.

Nadeem, S., Abbas, N. & Malik, M.Y. 2020. Inspection of hybrid-based nanofluid flow over a curved surface. Computer Methods and Programs in Biomedicine 189: 105193.

Naganthran, K., Hashim, I. & Nazar, R. 2020. Triple solutions of Carreau thin film flow with thermocapillarity and injection on an unsteady stretching sheet. Energies 13(12): 3177.

Oztop, H.F. & Abu-Nada, E. 2008. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal of Heat and Fluid Flow 29(5): 1326-1336.

Rangi, R.R. & Ahmad, N. 2012. Boundary layer flow past a stretching cylinder and heat transfer with variable thermal conductivity. Applied Mathematics 3(3): 205-209.

Roşca, N.C., Roşca, A.V., Pop, I. & Merkin, J.H. 2020. Nanofluid flow by a permeable stretching/shrinking cylinder. Heat and Mass Transfer 56(2): 547-557.

Salleh, M.Z. & Nazar, R. 2010. Aliran lapisan sempadan olakan bebas terhadap silinder bulat mengufuk dengan pemanasan Newtonan. Sains Malaysiana 39(4): 671-676.

Sarkar, J., Ghosh, P. & Adil, A. 2015. A review on hybrid nanofluids: Recent research, development and applications. Renewable and Sustainable Energy Reviews 43(C): 164-177.

Sears, W.R. & Telionis, D.P. 1975. Boundary-layer separation in unsteady flow. Journal on Applied Mathematics 28(1): 215-235.

Shah, T.R. & Ali, H.M. 2019. Applications of hybrid nanofluids in solar energy, practical limitations and challenges: A critical review. Solar Energy 183: 173-203.

Shampine, L.F., Gladwell, I. & Thompson, S. 2003. Solving ODEs with MATLAB. Cambridge: Cambridge University Press.

Smith, F.T. 1986. Steady and unsteady boundary layer separation. Annual Review of Fluid Mechanics 18: 197-220.

Suresh, S., Venkitaraj, K.P., Selvakumar, P. & Chandrasekar, M. 2011a. Synthesis of Al₂O₃-Cu/water hybrid nanofluids using two step method and its thermo physical properties. Colloids and Surfaces A: Physicochemical and Engineering Aspects 388(1-3): 41-48.

Suresh, S., Venkitaraj, K.P. & Selvakumar, P. 2011b. Synthesis, characterisation of Al₂O₃-Cu nanocomposite powder and water-based nanofluids. Advanced Materials Research 328-330: 1560-1567.

Tabassum, G.D., Mehmood, A., Usman, M. & Dar, A. 2020. Multiple solutions for an unsteady stretching cylinder. Journal of Applied Mechanics and Technical Physics 61: 439-446.

Takabi, B. & Salehi, S. 2014. Augmentation of the heat transfer performance of a sinusoidal corrugated enclosure by employing hybrid nanofluid. Advances in Mechanical Engineering 6: 147059.

Tiwari, R.K. & Das, M.K. 2007. Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. International Journal of Heat and Mass Transfer 50(9-10): 2002-2018.

Vajravelu, K. & Mukhopadhyay, S. 2016. Fluid Flow, Heat and Mass Transfer at Bodies of Different Shapes: Numerical Solutions. Massachusetts: Academic Press.

Vajravelu, K., Prasad, K.V. & Santhi, S.R. 2012. Axisymmetric magneto-hydrodynamic (MHD) flow and heat transfer at a non-isothermal stretching cylinder. Applied Mathematics and Computation 219: 3993-4005.

Waini, I., Ishak, A. & Pop, I. 2020a. Hybrid nanofluid flow towards a stagnation point on a stretching/shrinking cylinder. Scientific Reports 10(9296): 1-12.

Waini, I., Ishak, A. & Pop, I. 2020b. Hybrid nanofluid flow on a shrinking cylinder with prescribed surface heat flux. International Journal of Numerical Methods for Heat and Fluid Flow 31(6): 1987-2004.

Waini, I., Ishak, A. & Pop, I. 2019. Unsteady flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid. International Journal of Heat and Mass Transfer 136: 288-297.

Wang, C.Y. 1988. Fluid flow due to a stretching cylinder. Physics of Fluids 31: 466-468.

White, F.M. 1991. Viscous Fluid Flow. 2nd ed. New York: McGraw-Hill.

Yang, L., Ji, W., Mao, M. & Huang, J.N. 2020. An updated review on the properties, fabrication and application of hybrid-nanofluids along with their environmental effects. Journal of Cleaner Production 257(4): 120408.

Zaimi, K., Ishak, A. & Pop, I. 2017. Unsteady flow of a nanofluid past a permeable shrinking cylinder using Buongiorno’s model. Sains Malaysiana 46(9): 1667-1674.

Zainal, N.A., Nazar, R., Naganthran, K. & Pop, I. 2020a. MHD flow and heat transfer of hybrid nanofluid over a permeable moving surface in the presence of thermal radiation. International Journal of Numerical Methods for Heat and Fluid Flow 31(3): 858-879.

Zainal, N.A., Nazar, R., Naganthran, K. & Pop, I. 2020b. Unsteady stagnation point flow of hybrid nanofluid past a convectively heated stretching/shrinking sheet with velocity slip. Mathematics 8(10): 1649.

Zainal, N.A., Nazar, R., Naganthran, K. & Pop, I. 2020c. Unsteady three-dimensional MHD non-axisymmetric Homann stagnation point flow of a hybrid nanofluid with stability analysis. Mathematics 8(5): 784.

*Pengarang untuk surat-menyurat; email: rmn@ukm.edu.my