A comparative analysis of unsteady and steady Buongiorno's Williamson nanoliquid flow over a wedge with slip effects

doi:10.1016/j.cjche.2020.04.016

Abstract

Abstract: Comparison between unsteady and steady MHD Buongiorno's model Williamson nanoliquid flow through a wedge with slip effects, chemical reaction and radiation is made in this analysis. Thermophoresis and Brownian motion are also considered in this study. Appropriate similarity variables are presented to transmute the governing PDEs into the set of non-linear ODEs. The most widely authenticated finite element method is implemented to analyze these set of ODEs numerically. The behavior of concentration, temperature and velocity sketches for varied values of relevant parameters is numerically calculated and the outcomes are plotted through graphs. The numerical values of dimensionless rates of mass transfer, heat and velocity are also evaluated and depicted through tables. It is noted that with upsurging values of angle of wedge parameter, the distributions of temperature of the liquid intensify in both steady and unsteady cases.

Key words: Finite element method, Chemical reaction, Williamson nanoliquid, Thermophoresis, Thermal radiation, Brownian motion

摘要： Comparison between unsteady and steady MHD Buongiorno's model Williamson nanoliquid flow through a wedge with slip effects, chemical reaction and radiation is made in this analysis. Thermophoresis and Brownian motion are also considered in this study. Appropriate similarity variables are presented to transmute the governing PDEs into the set of non-linear ODEs. The most widely authenticated finite element method is implemented to analyze these set of ODEs numerically. The behavior of concentration, temperature and velocity sketches for varied values of relevant parameters is numerically calculated and the outcomes are plotted through graphs. The numerical values of dimensionless rates of mass transfer, heat and velocity are also evaluated and depicted through tables. It is noted that with upsurging values of angle of wedge parameter, the distributions of temperature of the liquid intensify in both steady and unsteady cases.

关键词: Finite element method, Chemical reaction, Williamson nanoliquid, Thermophoresis, Thermal radiation, Brownian motion

R. Chandra Sekhar Reddy, P. Sudarsana Reddy. A comparative analysis of unsteady and steady Buongiorno's Williamson nanoliquid flow over a wedge with slip effects[J]. Chinese Journal of Chemical Engineering, 2020, 28(7): 1767-1777.

R. Chandra Sekhar Reddy, P. Sudarsana Reddy. A comparative analysis of unsteady and steady Buongiorno's Williamson nanoliquid flow over a wedge with slip effects[J]. 中国化学工程学报, 2020, 28(7): 1767-1777.

References

[1] S.U.S. Choi, Z.G. Zhang, W. Yu, F.E. Lockwood, E.A. Grulke, Anomalous thermal conductivity enhancement in nano-tube suspensions, Appl. Phys. 79(2001) 2252-2254.
[2] J.A. Eastman, S.U.S. Choi, S. Li, W. Yu, L.J. Thompson, Anomalously increased effective thermal conductivities of ethylene glycol-based nano-liquids containing copper nano-particles, Appl. Phys. 78(2001) 718-720.
[3] M.A. Sheremet, I. Pop, Natural convection in a wavy porous cavity with sinusoidal temperature distributions on both side walls filled with a nanoliquid:Buongiorno's mathematical model, J. Heat Transf. 137(2015), 072601.
[4] M. Ghalambaz, M.A. Sheremet, I. Pop, Free Con. vection in a Parallelogrammic Porous Cavity Filled with a Nanoliquid Using Tiwari and Das Nanoliquid Model, Plos one 2015. https://doi.org/10.1371/journal.pone.0126486.
[5] P. Sudarsana Reddy, Ali J. Chamkha, heat and mass transfer characteristics of Al2o3-water and Ag-water nanoliquid through porous media over a vertical cone with heat generation/absorption, Journal of Porous Media 20(2017) 1-17.
[6] M.A. Sheremet, C. Revnic, I. Pop, Free convection in a porous wavy cavity filled with a nanoliquid using Buongiorno's mathematical model with thermal dispersion effect, Appl. Math. Comput. 299(2017) 1-15.
[7] Z. Hussain, T. Hayat, A. Ahmed, B. Ahmed, Darcy Forhheimer aspects for CNTs nanoliquid past a elongating cylinder using Keller box method, Results in Physics 11(2018) 801-816.
[8] L. Zhixiong, I. Khan, A. Shafee, I. Tlili, T. Asifa, Energy transfer of Jeffery-Hamel nanoliquid flow between non-parallel walls using Maxwell-Garnetts (MG) and brinkman models, Energy Rep. 4(2018) 393-399.
[9] P. Sreedevi, P. Sudarsana Reddy, A.J. Chamkha, Magneto-hydrodynamics heat and mass transfer analysis of single and multi-wall carbon nanotubes over vertical cone with convective boundary condition, Int. J. Mech. Sci. 135(2018) 646-655.
[10] P. Sudarsana Reddy, K. Jyothi, M. Suryanarayana Reddy, Flow and heat transfer analysis of carbon nanotubes based Maxwell nanoliquid flo. w driven by rotating stretchable disks with thermal radiation, J. Braz. Soc. Mech. Sci. Eng. 40(2018) 576. https://doi.org/10.1007/s40430-018-1494-9.
[11] A. Zaib, M.M. Rashidi, A.J. Chamkha, N.F. Mohammad, Impact of nonlinear thermal radiation on stagnation-point flow of a carreau nanoliquid past a nonlinear elongating sheet with binary chemical reaction and activation energy, J. Mech. Eng. Sci. 23(2018) 962-972.
[12] D.S. Bondarenko, M.A. Sheremet, H.F. Oztop, M.E. Ali, Natural convection of Al₂O₃/H₂O nanoliquid in a cavity with a heat-generating element, Heat Line Visualization, International Journal of Heat and Mass Transfer 130(2019) 564-574.
[13] M.M. Bhatti, M.M. Rashidi, Effects of thermo-diffusion and thermal radiation on Williamson nanoliquid over a porous shrinking/elongating sheet, J. Mol. Liq. 221(2016) 567-573.
[14] C. Srinivas Reddy, N. Kishan, M.R. Mohammad, MHD flow and heat transfer characteristics of Williamson nanoliquid over a elongating sheet with variable thickness and variable thermal conductivity, Transactions of A. Razmadze Mathematical Institute 171(2017) 195-211.
[15] M. Khan, M.Y. Malik, T. Salahuddin, K.U. Rehman, M. Naseer, I. Khan, MHD flow of Williamson nanoliquid over a cone and plate with chemically reactive species, J. Mol. Liq. 231(2017) 580-588.
[16] T. Hayat, M.Z. Kiyani, A. Alsaedi, M. Ijaz Khan, I. Ahmad, Mixed convective three-dimensional flow of Williamson nanoliquid subject to chemical reaction, Int. J. Heat Mass Transf. 127(2018) 422-429.
[17] M. Khan, A. Hamid, Influence of non-linear thermal radiation on 2D unsteady flow of a Williamson liquid with heat source/sink, Results in Physics 7(2017) 3968-3975.
[18] A. Hamid, M. Hashim, Khan, impacts of binary chemical reaction with activation energy on unsteady flow of magneto-Williamson nanoliquid, J. Mol. Liq. 262(2018) 435-442.
[19] A. Hamid, M. Hashim, A. Khan, Hafeez, unsteady stagnation-point flow of Williamson liquid generated by elongating/shrinking sheet with Ohmic heating, Int. J. Heat Mass Transf. 126(2018) 933-940.
[20] H. Aamir, H.M. Khan, Unsteady mixed convective flow of Williamson nanoliquid with heat transfer in the presence of variable thermal conductivity and magnetic field, J. Mol. Liq. 260(2018) 436-446.
[21] M. Hamid, M. Usman, Z.H. Khan, R.U. Haq, W. Wang, Numerical study of unsteady MHD flow of Williamson nanoliquid in a permeable channel with heat source/sink and thermal radiation, Eur. Phys. J. Plus 133(2018) 527.
[22] R. Kandasamy, I. Muhaimin, R. Mohammad, Single walled carbon nanotubes on MHD unsteady flow over a porous wedge with thermal radiation with variable stream conditions, Alexandria Engineering Journal 55(2016) 275-285.
[23] U. Imran, S. Shafie, I. Khan, MHD mixed convection flow of Casson liquid over a moving wedge saturated in a porous medium in the presence of chemical reaction and convective boundary conditions, J. Sci. Technol. 9(2017) 131-139.
[24] M. Khan, M. Azam, A.S. Alshomrani, Unsteady slip flow of Carreau nanoliquid over a wedge with nonlinear radiation and new mass flux condition, Results in Physics 7(2017) 2261-2270.
[25] M. Khan, M. Azam, A.S. Alshomrani, Effects of melting and heat generation/absorption on unsteady Falkner-Skan flow of Carreau nanoliquid over a wedge, Int. J. Heat Mass Transf. 110(2017) 437-446.
[26] N. Sandeep, M. Gnaneswara Reddy, Heat transfer of nonlinear radiative magneto hydrodynamic cu-water nanoliquid flow over two different geometries, J. Mol. Liq. 225(2017) 87-94.
[27] H. A. El-Dawy, G. Rama Subba Reddy, Unsteady Flow of a Nanoliquid Over a Shrinking/Elongating Porous Wedge Sheet in the Presence of Solar Radiation, Journal of Nanoliquids 7(2018) 1208-1216.
[28] A. Mahdy, A.J. Chamkha, Unsteady MHD boundary layer flow of tangent hyperbolic two-phase nanoliquid of moving stretched porous wedge, International Journal of Numerical Methods for Heat & Liquid Flow Int. J. Heat Mass Transf. Liq. Flow 28(11) (2018) 2567-2580, https://doi.org/10.1108/HFF-12-2017-0499.
[29] L. Zhixiong, M. Sheikholeslami, M. Samandari, A. Shafee, Nanoliquid unsteady heat transfer in a porous energy storage enclosure in existence of Lorentz forces, Int. J. Heat Mass Transf. 127(2018) 914-926.
[30] W.A. Khan, I. Haq, M. Ali, M. Shahzad, M. Khan, M. Irfan, Significance of static-moving wedge for unsteady Falkner-Skan forced convective flow of MHD cross liquid, J. Braz. Soc. Mech. Sci. Eng. 40(2018) 470-482.
[31] M. Azam, A. Shakoor, H.F. Rasool, M. Khan, Numerical simulation for solar energy aspects on unsteady convective flow of MHD cross nanoliquid:A revised approach, Int. J. Heat Mass Transf. 131(2019) 495-505.
[32] I.S. Awaludi, A. Ishak, I. Pop, On the stability of MHD boundary layer flow over a elongating/shrinking wedge, Sci. Rep. 8(2018) 13622-13629.
[33] W. Ibrahim, T. Ayele, Magnetohydrodynamic (MHD) boundary layer flow past a wedge with heat transfer and viscous effects of nanoliquid embedded in porous media, Math. Probl. Eng. 25(2019) 1-12.
[34] A. Hamid, M. Hashim, Khan, numerical simulation for heat transfer performance in unsteady flow of Williamson liquid driven by a wedge-geometry, Results in Physics 9(2018) 479-485.
[35] M. Hashim, A. Khan, Hamid, numerical investigation on time-dependent flow of Williamson nanoliquid along with heat and mass transfer characteristics past a wedge geometry, Int. J. Heat Mass Transf. 118(2018) 480-491.
[36] T. Hayat, S. Ayub, A. Tanveer, A. Alsaedi, Numerical simulation for MHD Williamson fluid utilizing modified Darcy's law, Results in Physics 10(2018) 751-759.
[37] T. Hayat, A. Saleem, A. Tanveer, F. Alsaadi, Numerical analysis for peristalsis of Williamson nanofluid in presence of an endoscope, Int. J. Heat Mass Transf. 114(2017) 395-401.
[38] M. Khan, M.Y. Malik, T. Salahuddin, A. Hussian, Heat and mass transfer of Williamson nanofluid flow yield by an inclined Lorentz force over a nonlinear stretching sheet, Results in Physics 8(2018) 862-868.
[39] T. Salahuddin, M.Y. Malik, A. Hussain, M. Awais, S. Bilal, Mixed convection boundary layer flow of Williamson fluid with slip conditions over a stretching cylinder by using Keller box method, IJNSNS 18(2017) 9-17.
[40] M. Khan, T. Salahuddin, M. Yousaf, F. Khan, A. Hussain, Variable diffusion and conductivity change in 3D rotating Williamson fluid flow along with magnetic field and activation energy, International Journal of Numerical Methods for Heat & Fluid Flow 30(5) (2019) 2467-2484.
[41] P. Sudarsan Reddy, D.R.V. Prasada Rao, Thermo-diffusion and diffusion -thermo effects on convective heat and mass transfer through a porous medium in a circular cylindrical annulus with quadratic density temperature variation-Finite element study, Journal of Applied Liquid Mechanics 5(2012) 139-144.
[42] P. Sreedevi, P. Sudarsana Reddy, Ali J. Chamkha, Heat and mass transfer analysis of nanoliquid over linear and non-linear elongating surface with thermal radiation and chemical reaction, Powder Technol. 315(2017) 194-204.
[43] K. Jyothi, P. Sudarsana Reddy, M. Suryanarayana Reddy, Influence of magnetic field and thermal radiation on convective flow of SWCNTs-water and MWCNTs-water nanoliquid between rotating stretchable disks with convective boundary conditions, Powder Technol. 331(2018) 326-337.
[44] P. Sudarsana Reddy, A.J. Chamkha, Heat and mass transfer characteristics of MHD three-dimensional flow over a elongating sheet filled with water-based alumina nanoliquid, International Journal of Numerical Methods for Heat and Liquid Flow 28(2018) 532-546.