 |
 |
 |
 |
 |
 |
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 ZAINAL1,2, ROSLINDA NAZAR1*,
KOHILAVANI NAGANTHRAN3,4 & 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
Received: 29 December 2020/Accepted: 30 March 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
REFERENCES
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.
*Corresponding author; email: rmn@ukm.edu.my
|
|||
|
