Transient Free Convection Mass Transfer of Second-grade Fluid Flow with Wall Transpiration
DOI:
https://doi.org/10.37934/cfdl.13.11.3552Keywords:
non-Newtonian fluid, second-grade fluid, transient free convective flow, wall transpiration, mass transferAbstract
The study of mass transfer in the non-Newtonian fluid is essential in understanding the engine lubrication, the cooling system of electronic devices, and the manufacturing process of the chemical industry. Optimal performance of the practical applications requires the appropriate conditions. The unsteady transient free convective flow of second-grade fluid with mass transfer and wall transpiration is concerned in the present communication. The behavior of the second-grade fluid under the influence of injection or suction is discussed. Suitable non-dimensional variables are utilized to transform the governing equations into non-dimensional governing equations. A Maple solver “pdsolve” that is using the centered implicit scheme of a finite difference method is utilized to solve the dimensionless governing equations numerically. The effects of wall injection or suction parameter, second-grade fluid viscoelastic parameter, Schmidt number, and modified Grashof number on the velocity and concentration profiles are graphically displayed and analyzed. The results show that with increasing wall suction, viscoelastic parameter, and Schmidt number, the velocity and concentration profiles decrease. Whereas, the velocity profiles show an opposite tendency in situations of wall injection. The wall suction has increased the skin friction and also the rate of mass diffusion in the second-grade fluid.
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Abd-el-Malek, Mina B., Nagwa A. Badran, and Hossam S. Hassan. "Solution of the Rayleigh problem for a power law non-Newtonian conducting fluid via group method." International Journal of Engineering Science 40, no. 14 (2002): 1599-1609. https://doi.org/10.1016/S0020-7225(02)00037-X
Kundu, Pijush K., and Ira M. Cohen. "Fluid mechanics." (2002).
Sun, Le, Guangwei Yang, Yechun Wang, and Dengwei Jing. "Experimental study on high-pressure rheology of water/crude oil emulsion in the presence of methane." Journal of Dispersion Science and Technology 38, no. 6 (2017): 789-795. https://doi.org/10.1080/01932691.2016.1198702
Katritsis, Demosthenes, Lambros Kaiktsis, Andreas Chaniotis, John Pantos, Efstathios P. Efstathopoulos, and Vasilios Marmarelis. "Wall shear stress: theoretical considerations and methods of measurement." Progress in cardiovascular diseases 49, no. 5 (2007): 307-329. https://doi.org/10.1016/j.pcad.2006.11.001
Fatahian, Esmaeel, Naser Kordani, and Hossein Fatahian. "A review on rheology of non-newtonian properties of blood." IIUM Engineering Journal 19, no. 1 (2018): 237-250. https://doi.org/10.31436/iiumej.v19i1.826
Ellahi, R., M. Mubashir Bhatti, and Ioan Pop. "Effects of hall and ion slip on MHD peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct." International journal of numerical methods for heat & fluid flow (2016). https://doi.org/10.1108/HFF-02-2015-0045
Rajput, Govind R., M. D. Shamshuddin, and Sulyman O. Salawu. "Thermosolutal convective non‐Newtonian radiative Casson fluid transport over a vertical plate propagated by Arrhenius kinetics with heat source/sink." Heat Transfer 50, no. 3 (2021): 2829-2848. https://doi.org/10.1002/htj.22008
Shamshuddin, M. D., and C. B. Krishna. "Heat absorption and joule heating effects on transient free convective reactive micro polar fluid flow past a vertical porous plate." Fluid Dynamics & Material Processing 15, no. 3 (2019): 207-231. https://doi.org/10.32604/fdmp.2019.00449
Salawu, S. O., R. A. Kareem, M. D. Shamshuddin, and S. U. Khan. "Double exothermic reaction of viscous dissipative Oldroyd 8-constant fluid and thermal ignition in a channel." Chemical Physics Letters 760 (2020): 138011. https://doi.org/10.1016/j.cplett.2020.138011
Coleman, Bernard D., Hershel Markovitz, and Walter Noll. Viscometric flows of non-Newtonian fluids: theory and experiment. Vol. 5. Springer Science & Business Media, 2012.
Benneker, A. H., Alexandre E. Kronberg, and K. R. Westerterp. "Influence of buoyancy forces on the flow of gases through packed beds at elevated pressures." AIChE journal 44, no. 2 (1998): 263-270. https://doi.org/10.1002/aic.690440205
Al-Azawy, Mohammed Ghalib, Saleem Khalefa Kadhim, and Azzam Sabah Hameed. "Newtonian and Non-Newtonian Blood Rheology Inside a Model of Stenosis." CFD Letters 12, no. 11 (2020): 27-36. https://doi.org/10.37934/cfdl.12.11.2736
Ferdows, Mohammad, M. D. Shamshuddin, and Khairy Zaimi. "Dissipative-Radiative Micropolar Fluid Transport in a NonDarcy Porous Medium with Cross-Diffusion Effects." CFD Letters 12, no. 7 (2020): 70-89. https://doi.org/10.37934/cfdl.12.7.7089
Kumar, VS Sampath, N. P. Pai, and B. Devaki. "Analysis of MHD flow and heat transfer of laminar flow between porous disks." Frontiers in Heat and Mass Transfer 16, no. 3 (2021): 1-7. https://doi.org/10.5098/hmt.16.3
Saidin, Norshaza Atika, Mohd Ariff Admon, and Khairy Zaimi. "Unsteady Three-Dimensional Free Convection Flow Near the Stagnation Point Over a General Curved Isothermal Surface in a Nanofluid." CFD Letters 12, no. 6 (2020): 80-92. https://doi.org/10.37934/cfdl.12.6.8092
Ferdows, Mohammad, Mohammed Shamshuddin, and Khairy Zaimi. "Computation of Steady Free Convective Boundary Layer Viscous Fluid Flow and Heat Transfer towards the Moving Flat subjected to Suction/Injection Effects." CFD Letters 13, no. 3 (2021): 16-24. https://doi.org/10.37934/cfdl.13.3.1624
Zokri, Syazwani Mohd, Nur Syamilah Arifin, Abdul Rahman Mohd Kasim, and Mohd Zuki Salleh. "Flow of Jeffrey Fluid over a Horizontal Circular Cylinder with Suspended Nanoparticles and Viscous Dissipation Effect: Buongiorno Model." CFD Letters 12, no. 11 (2020): 1-13. https://doi.org/10.37934/cfdl.12.11.113
Khan, Ansab Azam, Khairy Zaimi, Suliadi Firdaus Sufahani, and Mohammad Ferdows. "MHD Mixed Convection Flow and Heat Transfer of a Dual Stratified Micropolar Fluid Over a Vertical Stretching/Shrinking Sheet With Suction, Chemical Reaction and Heat Source." CFD Letters 12, no. 11 (2020): 106-120. https://doi.org/10.37934/cfdl.12.11.106120
Hamdan, Fakhru Ridhwan, Mohamad Hidayad Ahmad Kamal, Noraihan Afiqah Rawi, Ahmad Qushairi Mohamad, Anati Ali, Mohd Rijal Ilias, and Sharidan Shafie. "g-Jitter Free Convection Flow Near a Three-Dimensional Stagnation-Point Region with Internal Heat Generation." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 67, no. 1 (2020): 119-135.
Khan, Noor Saeed. "Study of two dimensional boundary layer flow of a thin film second grade fluid with variable thermo-physical properties in three dimensions space." Filomat 33, no. 16 (2019): 5387-5405. https://doi.org/10.2298/FIL1916387K
Rehman, Abdul, S. Nadeem, and M. Y. Malik. "Boundary layer stagnation-point flow of a third grade fluid over an exponentially stretching sheet." Brazilian Journal of Chemical Engineering 30, no. 3 (2013): 611-618. https://doi.org/10.1590/S0104-66322013000300018
Hayat, T., M. Hussain, M. Awais, and S. Obaidat. "Melting heat transfer in a boundary layer flow of a second grade fluid under Soret and Dufour effects." International Journal of Numerical Methods for Heat & Fluid Flow (2013). https://doi.org/10.1115/1.4006032
Sadeghy, Kayvan, and Mehdi Sharifi. "Local similarity solution for the flow of a “second-grade” viscoelastic fluid above a moving plate." International Journal of Non-Linear Mechanics 39, no. 8 (2004): 1265-1273. https://doi.org/10.1016/j.ijnonlinmec.2003.08.005
Tan, Wenchang, Feng Xian, and Lan Wei. "An exact solution of unsteady Couette flow of generalized second grade fluid." Chinese Science Bulletin 47, no. 21 (2002): 1783-1785. https://doi.org/10.1007/BF03183841
Mahat, Rahimah, Sharidan Shafie, and Fatihhi Januddi. "Numerical Analysis of Mixed Convection Flow Past a Symmetric Cylinder with Viscous Dissipation in Viscoelastic Nanofluid." CFD Letters 13, no. 2 (2021): 12-28. https://doi.org/10.37934/cfdl.13.2.1228
Aman, Sidra, Zulkhibri Ismail, Mohd Zuki Salleh, and Ilyas Khan. "Flow analysis of second grade fluid with wall suction/injection and convective boundary condition." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 58, no. 1 (2019): 135-143.
Dwivedi, Naveen, Arun Kumar Singh, and Ashok Kumar Singh. "Transient free convection of a second‐grade fluid flowing in a vertical cylinder." Heat Transfer 50, no. 2 (2021): 1218-1231. https://doi.org/10.1002/htj.21924
Krishna, M. Veera, N. Ameer Ahamad, and Ali J. Chamkha. "Hall and ion slip impacts on unsteady MHD convective rotating flow of heat generating/absorbing second grade fluid." Alexandria Engineering Journal 60, no. 1 (2021): 845-858. https://doi.org/10.1016/j.aej.2020.10.013
Abdulhameed, M., I. Khan, D. Vieru, and S. Shafie. "Exact solutions for unsteady flow of second grade fluid generated by oscillating wall with transpiration." Applied Mathematics and Mechanics 35, no. 7 (2014): 821-830. https://doi.org/10.1007/s10483-014-1837-9
Hayat, T., Z. Abbas, and M. Sajid. "Heat and mass transfer analysis on the flow of a second grade fluid in the presence of chemical reaction." Physics letters A 372, no. 14 (2008): 2400-2408. https://doi.org/10.1016/j.physleta.2007.10.102
Versteeg, G. F., J. A. M. Kuipers, F. P. H. Van Beckum, and Willibrordus Petrus Maria Van Swaaij. "Mass transfer with complex reversible chemical reactions—I. Single reversible chemical reaction." Chemical Engineering Science 44, no. 10 (1989): 2295-2310. https://doi.org/10.1016/0009-2509(89)85163-2
Gawas, Omkar J., Sahil D. Thool, Anand A. Dubey, and Indrajit N. Yadav. "Vapour Adsorption and Recovery using Fluidized Bed Reactor: A Study." International Research Journal of Engineering and Technology 4 no. 5 (2017): 394-397.
Jang, Jer-Huan, Han-Chieh Chiu, and Wei-Mon Yan. "Wall Transpiration Effects on Developing Mixed Convection Heat Transfer in Inclined Rectangular Ducts." Journal of Marine Science and Technology 18, no. 2 (2010): 11. https://doi.org/10.51400/2709-6998.2324
Ishak, Anuar, Roslinda Nazar, and Ioan Pop. "The effects of transpiration on the boundary layer flow and heat transfer over a vertical slender cylinder." International Journal of Non-Linear Mechanics 42, no. 8 (2007): 1010-1017. https://doi.org/10.1016/j.ijnonlinmec.2007.05.004
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
Chang, Tong-Bou, A. Mehmood, O. Anwar Bég, M. Narahari, M. N. Islam, and F. Ameen. "Numerical study of transient free convective mass transfer in a Walters-B viscoelastic flow with wall suction." Communications in Nonlinear Science and Numerical Simulation 16, no. 1 (2011): 216-225. https://doi.org/10.1016/j.cnsns.2010.02.018
Rashidi, M. M., T. Hayat, and A. Basiri Parsa. "Solving of boundary‐layer equations with transpiration effects, governance on a vertical permeable cylinder using modified differential transform method." Heat Transfer—Asian Research 40, no. 8 (2011): 677-692. https://doi.org/10.1002/htj.20366
Sharma, Rajesh, and Anuar Ishak. "Numerical simulation of transient free convection flow and heat transfer in a porous medium." Mathematical Problems in Engineering 2013 (2013). https://doi.org/10.1155/2013/371971
Memari, A. "Application of Homotopy Perturbation Method to Solve Steady Flow of Walter B Fluid A Vertical Channel In Porous Media." International Journal of Physical and Mathematical Sciences 5, no. 6 (2011): 828-830.
Latifizadeh, Habibolla. "A Novel Approach for Solving Steady Flow of Walter B Fluid in a Vertical Channel with Porous Wall via Sumudu Transform." International Journal of Modern Theoretical Physics 1, no 1 (2012): 23-33.
Ariel, P. D., T. Hayat, and S. Asghar. "The flow of an elastico-viscous fluid past a stretching sheet with partial slip." Acta Mechanica 187, no. 1 (2006): 29-35. https://doi.org/10.1007/s00707-006-0370-3
Mehmood, Obaid Ullah, Norzieha Mustapha, Sharidan Shafie, and Constantin Fetecau. "Simultaneous effects of dissipative heating and partial slip on peristaltic transport of Sisko fluid in asymmetric channel." International Journal of Applied Mechanics 6, no. 01 (2014): 1450008. https://doi.org/10.1142/S1758825114500082
Bariş, Serdar. "Steady three-dimensional flow of a Walter's B'fluid in a vertical channel." Turkish Journal of Engineering and Environmental Sciences 26, no. 5 (2002): 385-394.
Siddiqui, A. M., M. A. Rana, R. Qamar, and S. Irum. "Finite-Difference Analysis for Unsteady Squeezing Flow of a Second Grade Fluid between Circular Plates." Applied Mathematical Sciences 4, no. 51 (2010): 2497-2507.
Sharma, H. G., and M. P. Singh. "Steady Flow of a Visco-elastic Second-grade Fluid between Two Enclosed Rotating Discs with uniform Suction and Injection." (2009): 1-12.
Fadlun, E. A., Roberto Verzicco, Paolo Orlandi, and J. Mohd-Yusof. "Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations." Journal of computational physics 161, no. 1 (2000): 35-60. https://doi.org/10.1006/jcph.2000.6484
Jha, Basant Kumar, and Babatunde Aina. "Role of suction/injection on steady fully developed mixed convection flow in a vertical parallel plate microchannel." Ain Shams Engineering Journal 9, no. 4 (2018): 747-755. https://doi.org/10.1016/j.asej.2016.05.001
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