On the motion of non-Newtonian Eyring-Powell fluid conveying tiny gold particles due to generalized surface slip velocity and buoyancy. (English) Zbl 1450.76001
The study deals with the effects of surface slip velocity of a Eyring-Powell fluid within a thin layer on a paraboloid of revolution. Because of the presence of a catalyst on the surface, the quartic autocatalitic reaction with heat transfer takes place in the layer. The situation becomes more complex because of the stretching of the fluid layer at the paraboloid wall.
After non-dimensionalizing the equations describing the flow, the authors obtain a system of nonlinear ordinary differential equations that is solved with shooting techniques by the fourth-order Runge-Kutta integration scheme.
This numerical scheme is successfully tested and used to investigate the dependence of the flow characteristics (such as velocity components, shear stress, temperature distribution, etc.) on the velocity slip parameter.
After non-dimensionalizing the equations describing the flow, the authors obtain a system of nonlinear ordinary differential equations that is solved with shooting techniques by the fourth-order Runge-Kutta integration scheme.
This numerical scheme is successfully tested and used to investigate the dependence of the flow characteristics (such as velocity components, shear stress, temperature distribution, etc.) on the velocity slip parameter.
Reviewer: Aleksey Syromyasov (Saransk)
MSC:
| 76A05 | Non-Newtonian fluids |
| 76T20 | Suspensions |
| 76V05 | Reaction effects in flows |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 80A21 | Radiative heat transfer |
Keywords:
quartic autocatalitic reaction; paraboloid of revolution; nonlinear thermal radiation; shooting method; Runge-Kutta schemeReferences:
| [1] | Anderson, JD, Ludwig Prandtl’s boundary layer, Phys. Today AIP, 58, 42-48, (2005) · doi:10.1063/1.2169443 |
| [2] | Sakiadis, BC, Boundary layer behaviour on continuous solid surfaces, AIChE J., 7, 26-28, (1961) · doi:10.1002/aic.690070108 |
| [3] | Sakiadis, BC, Boundary layer behavior on continuous solid surfaces: II, the boundary layer on a continuous flat surface, AIChE J., 17, 221-225, (1961) · doi:10.1002/aic.690070211 |
| [4] | Boundary layer (2015). https://www.grc.nasa.gov/WWW/k-12/airplane/boundlay.html |
| [5] | Sakiadis, BC, Boundary layer behavior on continuous solid surfaces: the boundary layer on a continuous flat surface, Am. Inst. Chem. Eng. (AIChE), 7, 221-225, (1961) · doi:10.1002/aic.690070211 |
| [6] | Moore, DW, The boundary layer on a spherical gas bubble, J. Fluid Mech., 16, 161, (1963) · Zbl 0112.19003 · doi:10.1017/S0022112063000665 |
| [7] | Murphy, JS, Some effects of surface curvature on laminar boundary-layer flow, J. Aeronaut. Sci., 20, 338-344, (1953) · Zbl 0050.40901 · doi:10.2514/8.2638 |
| [8] | Naramgari, S.; Sulochana, C., MHD flow over a permeable stretching/shrinking sheet of a nanofluid with suction/injection, Alex. Eng. J., 55, 819-827, (2016) · doi:10.1016/j.aej.2016.02.001 |
| [9] | Sowerby, L.; Cooke, J., The flow of fluid along corners and edges, Q. J. Mech. Appl. Math., 6, 50-70, (1953) · Zbl 0051.17004 · doi:10.1093/qjmam/6.1.50 |
| [10] | Sawchuk, SP; Zamir, M., Boundary layer on a circular cylinder in axial flow, Int. J. Heat Fluid Flow, 13, 184-188, (1992) · doi:10.1016/0142-727x(92)90026-6 |
| [11] | Sulochanaa, C.; Ashwinkumara, GP; Sandeep, N., Transpiration effect on stagnation-point flow of a Carreau nanofluid in the presence of thermophoresis and Brownian motion, Alex. Eng. J., 55, 1151-1157, (2016) · doi:10.1016/j.aej.2016.03.031 |
| [12] | Animasaun, IL, Melting heat and mass transfer in stagnation point micropolar fluid flow of temperature dependent fluid viscosity and thermal conductivity at constant vortex viscosity, J. Egypt. Math. Soc., 25, 79-85, (2016) · Zbl 1354.76154 · doi:10.1016/j.joems.2016.06.007 |
| [13] | Benazir, AJ; Sivaraj, R.; Rashidi, MM, Comparison between Casson fluid flow in the presence of heat and mass transfer from a vertical cone and flat plate, J. Heat Transf. ASME, 138, 112005, (2016) · doi:10.1115/1.4033971 |
| [14] | McLachlan, RI, The boundary layer on a finite flat plate, Phys. Fluids A, 3, 341-348, (1991) · Zbl 0718.76035 · doi:10.1063/1.858143 |
| [15] | Lakshmi, KB; Kumar, KA; Reddy, JVR; Sugunamma, V., Influence of nonlinear radiation and cross diffusion on MHD flow of Casson and Walters-B nanofluids past a variable thickness sheet, J. Nanofluids, 8, 73-83, (2019) · doi:10.1166/jon.2019.1564 |
| [16] | Kumara, KA; Reddy, JVR; Sugunamma, V.; Sandeep, N., Magnetohydrodynamic Cattaneo-Christov flow past a cone and a wedge with variable heat source/sink, Alex. Eng. J., 57, 435-443, (2018) · doi:10.1016/j.aej.2016.11.013 |
| [17] | Ramadevi, B., Sugunamma, V., Kumar, K.A., Reddy, J.V.R.: MHD flow of Carreau fluid over a variable thickness melting surface subject to Cattaneo-Christov heat flux. Multidiscip. Model. Mater. Struct. (2018). https://doi.org/10.1108/mmms-12-2017-0169 |
| [18] | Kumar, K.A., Reddy, J.V.R., Sugunamma, V., Sandeep, N.: Impact of cross diffusion on MHD viscoelastic fluid flow past a melting surface with exponential heat source. Multidiscip. Model. Mater. Struct. (2018). https://doi.org/10.1108/mmms-12-2017-0151 |
| [19] | Taylor, R.; Coulombe, S.; Otanicar, T.; Phelan, P.; Gunawan, A.; Lv, W.; Tyagi, H., Small particles, big impacts: a review of the diverse applications of nanofluids, J. Appl. Phys., 113, 1, (2013) · doi:10.1063/1.4754271 |
| [20] | Buongiorno, J., Convective transport in nanofluids, J. Heat Transf. Am. Soc. Mech. Eng., 128, 240, (2006) · doi:10.1115/1.2150834 |
| [21] | Haroun, NA; Sibanda, P.; Mondal, S.; Motsa, SS; Rashidi, MM, Heat and mass transfer of nanofluid through an impulsively vertical stretching surface using the spectral relaxation method, Bound. Value Probl., 2015, 161, (2015) · Zbl 1342.35388 · doi:10.1186/s13661-015-0424-3 |
| [22] | Oyelakin, IS; Mondal, S.; Sibanda, P., Unsteady Casson nanofluid flow over a stretching sheet with thermal radiation, convective and slip boundary conditions, Alex. Eng. J., 55, 1025-1035, (2016) · doi:10.1016/j.aej.2016.03.003 |
| [23] | Sithole, HM; Mondal, S.; Sibanda, P.; Motsa, SS, An unsteady MHD Maxwell nanofluid flow with convective boundary conditions using spectral local linearization method, Open Phys., 15, 637-646, (2017) · doi:10.1515/phys-2017-0074 |
| [24] | Koriko, OK; Animasaun, IL; Mahanthesh, B.; Saleem, S.; Sarojamma, G.; Sivaraj, R., Heat transfer in the flow of blood-gold Carreau nanofluid induced by partial slip and buoyancy, Heat Transf. Asian Res., 47, 806-823, (2018) · doi:10.1002/htj.21342 |
| [25] | Powell, RE; Eyring, H., Mechanisms for the relaxation theory of viscosity, Nature, 154, 427-428, (1944) · doi:10.1038/154427a0 |
| [26] | Ziegenhagen, A., The very slow flow of a Powell-Eyring fluid around a sphere, Appl. Sci. Res. Sect. A, 14, 43-56, (1965) · doi:10.1007/bf00382230 |
| [27] | Sirohi, V.; Timol, MG; Kalthia, NL, Powell-Eyring model flow near an accelerated plate, Fluid Dyn. Res., 2, 193-204, (1987) · doi:10.1016/0169-5983(87)90029-3 |
| [28] | Malek, J.: Some Frequently Used Models for Non-Newtonian Fluids. Mathematical Institute Charles University, Prague (2011) |
| [29] | Hayat, T.; Farooq, M.; Alsaedi, A.; Iqbal, Z., Melting heat transfer in the stagnation point flow of Powell-Eyring fluid, J. Thermophys. Heat Transf., 27, 761-766, (2013) · doi:10.2514/1.T4059 |
| [30] | Khan, NA; Aziz, S.; Khan, NA, MHD flow of Powell-Eyring fluid over a rotating disk, J. Taiwan Inst. Chem. Eng., 45, 2859-2867, (2014) · doi:10.1016/j.jtice.2014.08.018 |
| [31] | Nadeem, S.; Saleem, S., Mixed convection flow of Erying-Powell fluid along a rotating cone, Results Phys., 4, 54-62, (2014) · doi:10.1016/j.rinp.2014.03.004 |
| [32] | Malik, MY; Khan, I.; Hussain, A.; Salahuddin, T., Mixed convection flow of MHD Eyring-Powell nanofluid over a stretching sheet: a numerical study, AIP Adv., 5, 117118, (2015) · doi:10.1063/1.4935639 |
| [33] | Sugunamma, V.; Sandeep, N.; Ramana Reddy, JV; Mohan Krishna, P., Influence of non uniform heat source/sink on Powell-Erying fluid past an inclined stretching sheet with suction/injection, Math. Theory Model., 6, 51-60, (2016) |
| [34] | Agbaje, TM; Mondal, S.; Motsa, SS; Sibanda, P., A numerical study of unsteady non-Newtonian Powell-Eyring nanofluid flow over a shrinking sheet with heat generation and thermal radiation, Alex. Eng. J., 56, 81-91, (2017) · doi:10.1016/j.aej.2016.09.006 |
| [35] | Abegunrin, O.A., Animasaun, I.L., Sandeep, N.: Insight into the boundary layer flow of non-Newtonian Eyring-Powell fluid due to catalytic surface reaction on an upper horizontal surface of a paraboloid of revolution. Alex. Eng. J. (2017). https://doi.org/10.1016/j.aej.2017.05.018 |
| [36] | Chaudhary, MA; Merkin, JH, A simple isothermal model for homogeneous-heterogeneous reactions in boundary layer flow. I Equal diffusivities, Fluid Dyn. Res., 16, 311-333, (1995) · Zbl 1052.80505 · doi:10.1016/0169-5983(95)00015-6 |
| [37] | Animasaun, IL; Raju, CSK; Sandeep, N., Unequal diffusivities case of homogeneous-heterogeneous reactions within viscoelastic fluid flow in the presence of induced magnetic-field, and nonlinears thermal radiation, Alex. Eng. J., 55, 1595-1606, (2016) · doi:10.1016/j.aej.2016.01.018 |
| [38] | Makinde, OD; Animasaun, IL, Bioconvection in MHD nanofluidflow with nonlinear thermal radiation and quartic autocatalysis chemical reaction past an upper surface of a paraboloid of revolution, Int. J. Therm. Sci., 109, 159-171, (2016) · doi:10.1016/j.ijthermalsci.2016.06.003 |
| [39] | Imtiaz, M.; Hayat, T.; Alsaedi, A., MHD convective flow of Jeffry fluid due to a curved stretching surface with homogeneous-heterogeneous reactions, PLoS ONE, 11, e0161641, (2016) · doi:10.1371/journal.pone.0161641 |
| [40] | Koriko, OK; Animasaun, IL, New similarity solution of micropolar fluid flow problem over an uhspr in the presence of quartic kind of autocatalytic chemical reaction, Front. Heat Mass Transf., 8, 1-13, (2017) · doi:10.5098/hmt.8.26 |
| [41] | Lee, LL, Boundary layer over a thin Needle, Phys. Fluids, 10, 820, (1967) · Zbl 0158.23204 · doi:10.1063/1.1762194 |
| [42] | Davis, RT; Werle, MJ, Numerical solutions for laminar incompressible flow past a paraboloid of revolution, AIAA J., 10, 1224-1230, (1972) · Zbl 0251.76016 · doi:10.2514/3.50354 |
| [43] | Fang, T.; Zhang, JI; Zhong, Y., Boundary layer flow over a stretching sheet with variable thickness, Appl. Math. Comput., 218, 7241-7252, (2012) · Zbl 1426.76124 |
| [44] | Animasaun, IL, 47nm alumina-water nanofluid flow within boundary layer formed on upper horizontal surface of paraboloid of revolution in the presence of quartic autocatalysis chemical reaction, Alex. Eng. J., 55, 2375-2389, (2016) · doi:10.1016/j.aej.2016.04.030 |
| [45] | Ajayi, T. M.; Omowaye, A. J.; Animasaun, I. L., Viscous Dissipation Effects on the Motion of Casson Fluid over an Upper Horizontal Thermally Stratified Melting Surface of a Paraboloid of Revolution: Boundary Layer Analysis, Journal of Applied Mathematics, 2017, 1-13, (2017) · Zbl 1437.76053 · doi:10.1155/2017/1697135 |
| [46] | Abegunrin, OA; Okhuevbie, SO; Animasaun, IL, Comparison between the flow of two non-Newtonian fluids over an upper horizontal surface of paraboloid of revolution: boundary layer analysis, Alex. Eng. J., 55, 1915-1929, (2016) · doi:10.1016/j.aej.2016.08.002 |
| [47] | Steff, J.F.: Rheological Methods in Food Process Engineering, 2nd edn. Freeman Press, East Lansing (1996) |
| [48] | Ara, A.; Khan, NA; Khan, H.; Sultan, F., Radiation effect on boundary layer flow of an Erying-Powell fluid over an exponentially shrinking sheet, Ain Shams Eng. J., 5, 1337-1342, (2014) · doi:10.1016/j.asej.2014.06.002 |
| [49] | Lynch, DT, Chaotic behavior of reaction systems: mixed cubic and quadratic autocatalysis, Chem. Eng. Sci., 47, 4435-4444, (1992) · doi:10.1016/0009-2509(92)85121-Q |
| [50] | Mintsa, H.A., Nguyen, C.T., Roy, G.: New temperature dependent thermal conductivity data of water based nanofluids. In: Proceedings of the 5th IASME/WSEAS int. conference on heat transfer, thermal engineering and environment, vol 290, Athens, Greece, pp. 25-27 (2007) |
| [51] | Michaelides, EE, Transport properties of nanofluids. A critical review, J. Non Equilib. Thermodyn., 38, 1-79, (2013) · Zbl 1267.80009 · doi:10.1515/jnetdy-2012-0023 |
| [52] | Wang, X.; Xu, X.; Choi, SUS, Thermal conductivity of nanoparticle-fluid mixture, J. Thermophys. Heat Transf., 13, 474-480, (1999) · doi:10.2514/2.6486 |
| [53] | Motsa, S.S., Haroun, N.A., Sibanda, P., Mondal, S.: On unsteady MHD mixed convection in a nanofluid due to a stretching/shrinking surface with suction/injection using the spectral relaxation method. Bound. Value Probl. 24 (2015). https://doi.org/10.1186/s13661-015-0289-5 · Zbl 1315.35168 |
| [54] | Hatami, M.; Hatami, J.; Ganji, DD, Computer simulation of MHD blood conveying gold nanoparticles as a third grade non-Newtonian nanofluid in a hollow porous vessel, Comput. Methods Programs Biomed., 113, 632-641, (2014) · doi:10.1016/j.cmpb.2013.11.001 |
| [55] | Thompson, PA; Troian, SM, A general boundary condition for liquid flow at solid surfaces, Nature, 389, 360-362, (1997) · doi:10.1038/38686 |
| [56] | Aziz, AA, A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Commun. Nonlinear Sci. Numer. Simul., 14, 1064-1068, (2009) · doi:10.1016/j.cnsns.2008.05.003 |
| [57] | Grosan, T.; Revnic, C.; Pop, I., Blasius problem with generalized surface slip velocity, J. Appl. Fluid Mech., 9, 1641-1644, (2016) |
| [58] | Na, T.Y.: Computational Methods in Engineering Boundary Value Problems, p. 1979. Academic Press, New York (2009) |
| [59] | Aljoufi, MD; Ebaid, A., Effect of a convective boundary condition on boundary layer slip flow and heat transfer over a stretching sheet in view of the exact solution, J. Theor. Appl. Mech., 46, 85-95, (2016) · doi:10.1515/jtam-2016-0022 |
| [60] | Koriko, OK; Animasaun, IL; Gnaneswara Reddy, M.; Sandeep, N., Scrutinization of thermal stratification, nonlinear thermal radiation and quartic autocatalytic chemical reaction effects on the flow of three-dimensional Eyring-Powell alumina-water nanofluid, Multidiscip. Model. Mater. Struct., 14, 261-283, (2018) · doi:10.1108/MMMS-08-2017-0077 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
