Numerical Analysis of Boundary Layer Flow and Heat Transfer over a Shrinking Cylinder
DOI:
https://doi.org/10.37934/cfdl.14.5.5667Keywords:
Boundary layer flow, Shrinking cylinder, Heat transfer, Dual solutions, Stability analysisAbstract
The investigation concerning the movement of the viscous fluid and heat transfer rate when the cylinder shrinks is carried out. The role of curvature parameter and effect of cylinder parameter on skin friction and heat transfer rate were studied. The existence of a dual solution is observed and subsequently identifies which solution is stable. By using the similarity transformation, the boundary layer equations are transformed into nonlinear ordinary differential equations which are then solved numerically using bvp4c in MATLAB. The results for the skin friction coefficient, temperature gradient coefficient as well as velocity and temperature profiles are presented graphically. The effects of mass suction parameter and curvature parameter on flow and heat transfer characteristics are also presented. It is found that the dual solution existed when mass suction parameter greater or equal to 2. Cylinder surface diminished the performance of skin friction coefficient and heat transfer rate. The stability analysis result is performed to verify that the upper branch solution is stable and physically meaningful.
References
Wang, C.Y. “Liquid film on an unsteady stretching sheet.” Quarterly of Applied Mathematics 48, (1990): 601-610.
Miklavčič, M., and C. Wang. "Viscous flow due to a shrinking sheet." Quarterly of Applied Mathematics 64, no. 2 (2006): 283-290.
Hayat, T., Z. Abbas, and M. Sajid. "On the analytic solution of magnetohydrodynamic flow of a second grade fluid over a shrinking sheet." (2007): 1165-1171. https://doi.org/10.1115/1.2723820
Wang, C. Y. "Stagnation flow towards a shrinking sheet." International Journal of Non-Linear Mechanics 43, no. 5 (2008): 377-382. https://doi.org/10.1016/j.ijnonlinmec.2007.12.021
Tie-Gang, Fang, Zhang Ji, and Yao Shan-Shan. "Viscous flow over an unsteady shrinking sheet with mass transfer." Chinese Physics Letters 26, no. 1 (2009): 014703. https://doi.org/10.1088/0256-307X/26/1/014703
Ishak, Anuar, Yian Yian Lok, and Ioan Pop. "Stagnation-point flow over a shrinking sheet in a micropolar fluid." Chemical Engineering Communications 197, no. 11 (2010): 1417-1427. https://doi.org/10.1080/00986441003626169
Bhattacharyya, Krishnendu, and G. C. Layek. "Effects of suction/blowing on steady boundary layer stagnation-point flow and heat transfer towards a shrinking sheet with thermal radiation." International Journal of Heat and Mass Transfer 54, no. 1-3 (2011): 302-307. https://doi.org/10.1016/j.ijheatmasstransfer.2010.09.043
Bachok, N., Ishak, A. and Pop, I. “Stagnation-point flow over a stretching/shrinking sheet in a nanofluid.” Nanoscale Research Letters 6, (2011): p. 623. https://doi.org/10.1186/1556-276X-6-623
Bachok, Norfifah, Anuar Ishak, and Ioan Pop. "Boundary layer stagnation-point flow and heat transfer over an exponentially stretching/shrinking sheet in a nanofluid." International Journal of Heat and Mass Transfer 55, no. 25-26 (2012): 8122-8128. https://doi.org/10.1016/j.ijheatmasstransfer.2012.08.051
Bachok, N., Ishak, A. and Pop, I. “Boundary layer stagnation-point flow toward a stretching/shrinking sheet in a nanofluid.” ASME Journal of Heat Transfer 135, (2013): ID 054501. https://doi.org/10.1115/1.4023303
Bhattacharyya, Krishnendu, and Kuppalapalle Vajravelu. "Stagnation-point flow and heat transfer over an exponentially shrinking sheet." Communications in Nonlinear Science and Numerical Simulation 17, no. 7 (2012): 2728-2734. https://doi.org/10.1016/j.cnsns.2011.11.011
Bhattacharyya, Krishnendu. "Boundary layer flow and heat transfer over an exponentially shrinking sheet." Chinese Physics Letters 28, no. 7 (2011): 074701. https://doi.org/10.1088/0256-307X/28/7/074701
Najib, N., Bachok, N., Arifin, N. M. and Ishak, A. “Stagnation point flow and mass transfer with chemical reaction past a stretching/shrinking cylinder.” Scientific Reports 4, (2014): ID 4178. https://doi.org/10.1038/srep04178
Merkin, J. H. "On dual solutions occurring in mixed convection in a porous medium." Journal of engineering Mathematics 20, no. 2 (1986): 171-179. https://doi.org/10.1007/BF00042775
Weidman, P. D., D. G. Kubitschek, and A. M. J. Davis. "The effect of transpiration on self-similar boundary layer flow over moving surfaces." International journal of engineering science 44, no. 11-12 (2006): 730-737. https://doi.org/10.1016/j.ijengsci.2006.04.005
Merrill, Keith, Matthew Beauchesne, Joseph Previte, Joseph Paullet, and Patrick Weidman. "Final steady flow near a stagnation point on a vertical surface in a porous medium." International journal of heat and mass transfer 49, no. 23-24 (2006): 4681-4686. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2006.02.056
Ishak, A. “Flow and heat transfer over a shrinking sheet: a stability analysis.” International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering 8, no. 5, (2014): 905-909. https://doi.org/10.5281/zenodo.1092443
Yasin, M. H. M., Ishak, A. and Pop, I. “MHD stagnation-point flow and heat transfer with effects of viscous dissipation, Joule heating and partial velocity slip.” Scientific Reports 5, (2015): ID 17848. https://doi.org/10.1038/srep17848
Dzulkifli, Nor Fadhilah, Norfifah Bachok, Nor Azizah Yacob, Ioan Pop, Norihan Arifin, and Haliza Rosali. "Stability Solution of Unsteady Stagnation-Point Flow and Heat Transfer over a Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect." CFD Letters 14, no. 1 (2022): 66-86. https://doi.org/10.37934/cfdl.14.1.6686
Abu Bakar, Shahirah, Norihan Md Arifin, Fadzilah Md Ali, Norfifah Bachok, Roslinda Nazar, and Ioan Pop. "A stability analysis on mixed convection boundary layer flow along a permeable vertical cylinder in a porous medium filled with a nanofluid and thermal radiation." Applied Sciences 8, no. 4 (2018): 483. https://doi.org/10.3390/app8040483
Khashi’ie, Najiyah Safwa, Iskandar Waini, Nurul Amira Zainal, Khairum Hamzah, and Abdul Rahman Mohd Kasim. "Hybrid nanofluid flow past a shrinking cylinder with prescribed surface heat flux." Symmetry 12, no. 9 (2020): 1493. https://doi.org/10.3390/sym12091493
Waini, I., Ishak, A. and Pop, I. “Hybrid nanofluid flow on a shrinking cylinder with prescribed surface heat flux.” International Journal of Numerical Methods for Heat & Fluid Flow 31, no. 6 (2020): 1987-2004. https://doi.org/10.1108/HFF-07-2020-0470
Waini, Iskandar, Anuar Ishak, and Ioan Pop. "Hybrid nanofluid flow towards a stagnation point on a stretching/shrinking cylinder." Scientific Reports 10, no. 1 (2020): 1-12. https://doi.org/10.1038/s41598-020-66126-2
Zeeshan, Ahmad, Obaid Ullah Mehmood, Fazle Mabood, and Faris Alzahrani. "Numerical analysis of hydromagnetic transport of Casson nanofluid over permeable linearly stretched cylinder with Arrhenius activation energy." International Communications in Heat and Mass Transfer 130 (2022): 105736. https://doi.org/10.1016/j.icheatmasstransfer.2021.105736
Uddin, Ziya, and Manoj Kumar. "Hall and ion-slip effect on MHD boundary layer flow of a micro polar fluid past a wedge." Scientia Iranica 20, no. 3 (2013): 467-476. https://doi.org/10.1016/j.scient.2013.02.013
Mabood, Fazle, Sami Ullah Khan, and Iskander Tlili. "Numerical simulations for swimming of gyrotactic microorganisms with Williamson nanofluid featuring Wu’s slip, activation energy and variable thermal conductivity." Applied Nanoscience (2020): 1-14. https://doi.org/10.1007/s13204-020-01548-y
Bhatti, M. M., M. B. Arain, A. Zeeshan, R. Ellahi, and M. H. Doranehgard. "Swimming of Gyrotactic Microorganism in MHD Williamson nanofluid flow between rotating circular plates embedded in porous medium: Application of thermal energy storage." Journal of Energy Storage 45 (2022): 103511. https://doi.org/10.1016/j.est.2021.103511
Wahid, Nur Syahirah, Norihan Md Arifin, Najiyah Safwa Khashi'ie, Ioan Pop, Norfifah Bachok, and Mohd Ezad Hafidz Hafidzuddin. "Flow and heat transfer of hybrid nanofluid induced by an exponentially stretching/shrinking curved surface." Case Studies in Thermal Engineering 25 (2021): 100982.https://doi.org/10.1016/j.csite.2021.100982
Shamshuddin, M. D., Fazle Mabood, and O. Anwar Bég. "Thermomagnetic reactive ethylene glycol-metallic nanofluid transport from a convectively heated porous surface with Ohmic dissipation, heat source, thermophoresis and Brownian motion effects." International Journal of Modelling and Simulation (2021): 1-15. https://doi.org/10.1080/02286203.2021.1977531
Uddin, Ziya, Korimerla Sai Vishwak, and Souad Harmand. "Numerical duality of MHD stagnation point flow and heat transfer of nanofluid past a shrinking/stretching sheet: Metaheuristic approach." Chinese Journal of Physics 73 (2021): 442-461. https://doi.org/10.1016/j.cjph.2021.07.018
Zeeshan, A., M. B. Arain, M. M. Bhatti, F. Alzahrani, and O. Anwar Bég. "Radiative bioconvection nanofluid squeezing flow between rotating circular plates: Semi-numerical study with the DTM-Padé approach." Modern Physics Letters B 36, no. 03 (2022): 2150552. https://doi.org/10.1142/S0217984921505527
Uddin, Ziya, and Souad Harmand. "Natural convection heat transfer of nanofluids along a vertical plate embedded in porous medium." Nanoscale research letters 8, no. 1 (2013): 1-19. https://doi.org/10.1186/1556-276X-8-64
Uddin, Z., R. Asthana, M. Kumar Awasthi, and S. Gupta. "Steady MHD flow of nano-fluids over a rotating porous disk in the presence of heat generation/absorption: a numerical study using PSO." J. Appl. Fluid Mech 10, no. 3 (2017): 871-879. https://doi.org/10.18869/ACADPUB.JAFM.73.240.26650
Uddin, Ziya, Manoj Kumar, and Souad Harmand. "Influence of thermal radiation and heat generation/absorption on MHD heat transfer flow of a micropolar fluid past a wedge considering hall and ion slip currents." Thermal Science 18, no. 2 (2014): 489-502. https://doi.org/10.2298/TSCI110712085U
Mabood, F., Khan, W. A. and Ismail, A. I. M. “Analytical investigation for free convective flow of non-newtonian nanofluids flow in porous media with gyrotactic microorganisms.” Journal of Porous Media 18, no. 7 (2015), 653-663. https://doi.org/10.1615/JPorMedia.v18.i7.10
Uddin, Ziya, Rishi Asthana, Mukesh Kumar Awasthi, and Hamdy Hassan. "A metaheuristic approach for the comparative study of MHD flow of nano liquids in a semi-porous channel." International Journal for Computational Methods in Engineering Science and Mechanics 22, no. 3 (2021): 244-251. https://doi.org/10.1080/15502287.2021.1916700
Arain, M. B., Bhatti, M. M., Zeeshan, A., Saeed, T., & Hobiny, A. “Analysis of arrhenius kinetics on multiphase flow between a pair of rotating circular plates.” Mathematical Problems in Engineering, (2020), ID 2749105. https://doi.org/10.1155/2020/2749105
Arain, Muhammad Bilal, Muhammad Mubashir Bhatti, Ahmad Zeeshan, and Faris Saeed Alzahrani. "Bioconvection reiner-rivlin nanofluid flow between rotating circular plates with induced magnetic effects, activation energy and squeezing phenomena." Mathematics 9, no. 17 (2021): 2139. https://doi.org/10.3390/math9172139
Azam, M., T. Xu, F. Mabood, and M. Khan. "Non-linear radiative bioconvection flow of cross nano-material with gyrotatic microorganisms and activation energy." International Communications in Heat and Mass Transfer 127 (2021): 105530. https://doi.org/10.1016/j.icheatmasstransfer.2021.10553
Shehzad, S. A., F. Mabood, A. Rauf, Mohsen Izadi, and F. M. Abbasi. "Rheological features of non-Newtonian nanofluids flows induced by stretchable rotating disk." Physica Scripta 96, no. 3 (2021): 035210. https://doi.org/10.1088/1402-4896/abd652
Najib, N., Bachok, N. and Arifin, N. M. “Stability of Dual Solutions in Boundary Layer Flow and Heat Transfer over an Exponentially Shrinking Cylinder.” Indian Journal of Science and Technology 9, no. 48 (2016): 6pp. doi: 10.17485/ijst/2016/v9i48/97740
Harris, S.D., Ingham, D.B. and Pop, I. “Mixed Convection Boundary-Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium: Brinkman Model with Slip.” Transport Porous Media 77, (2009): 267–285. doi:10.1007/s11242-008-9309-6
