Influence of polymers on drag and heat transfer of nanofluid past stretching surface: A molecular approach

Abstract

This article studies the influence of polymers on drag reduction and heat transfer enhancement of a nanofluid past a uniformly heated permeable vertically stretching surface. Our prime focus is on analyzing the possible effects of polymer inclusion in the nanofluid on drag coefficient, Nusselt number and Sherwood number. Dispersion model is considered to study the behavior of fluid flow and heat transfer in the presence of nanoparticles. Molecular approach is opted to explore polymer addition in the base fluid. An extra stress arises in the momentum equation as an outcome of polymer stretching. The governing boundary layer equations are solved numerically. Dependence of physical quantities of engineering interest on different flow parameters is studied. Reduction in drag coefficient, Nusselt number and Sherwood number is noticed because of polymer additives.

Keywords

polymers / nanofluid, stretching / concentration / drag coefficient / relaxation time / heat flux

References

[1] SreenivasanK R, WhiteC M. The onset of drag reduction by dilute polymer additives, and the maximum drag reduction asymptote [J]. Journal of Fluid Mechanics, 2000, 409: 149-164

[2] ProcacciaI, L’VovV, BenziR. Theory of drag reduction by polymers in wall-bounded turbulence [J]. Reviews of Modren Physics, 2008, 80: 225-247

[3] BenziR, ChingE S C, de AngelisE. Effect of polymer additives on heat transport in turbulent thermal convection [J]. Physical Review Letters, 2010, 104: 024502

[4] AhlersG, Nikolaenko. An effect of a polymer additive on heat transport in turbulent Rayleigh-B’enard convection [J]. Physical Review Letters, 2010, 104034503

[5] GrossmannS, LohseD. Scaling in thermal convection: a unifying theory [J]. Journal of Fluid Mechanics, 2000, 40727-56

[6] SakiadisB C. Boundary-layer behavior on continuous solid surface: I. Boundary-layer equations for two-dimensional and axisymmetric flow [J]. Journal of the American Chemical Society, 1961, 7: 26-28

[7] CraneL J. Flow past a stretching plate [J]. The Journal of Applied Mathematics and Physics (ZAMP), 1970, 21: 645-647

[8] CortellR. Viscous flow and heat transfer over a nonlinearly stretching sheet [J]. Applied Mathematics and Computation, 2007, 2: 864-873

[9] BhattacharyyaK, LayekG C. Chemically reactive solute distribution in MHD boundary layer flow over a permeable stretching sheet with suction or blowing [J]. Chemical Engineering Communications, 2010, 12: 1527-1540

[10] BhattacharyyaK, LayekG C. Slip effect on diffusion of chemically reactive species in boundary layer flow over a vertical stretching sheet with suction or blowing [J]. Chemical Engineering Communications, 2011, 11: 1354-1365

[11] BhattacharyyaK. Effects of radiation and heat source/sink on unsteady MHD boundary layer flow and heat transfer over a shrinking sheet with suction/injection [J]. Frontiers of Chemical Science and Engineering, 2011, 3: 376-384

[12] BhattacharyyaK, ArifM G, PramanikW. MHD boundary layer stagnation-point flow and mass transfer over a permeable shrinking sheet with suction/blowing and chemical reaction [J]. Acta Technica, 2012, 57: 1-15

[13] BhattacharyyaK, MukhopadhyayS, LayekG C. Unsteady MHD boundary layer flow with diffusion and first order chemical reaction over a permeable stretching sheet with suction or blowing [J]. Chemical Engineering Communications, 2013, 3: 379-397

[14] BhattacharyyaK. Heat transfer in unsteady boundary layer stagnation-point flow towards a shrinking sheet [J]. Ain Shams Engineering Journal, 2013, 2: 259-264

[15] SchmidtE, BeckmannW. Das temperatur- und geschwindikeitsfeld von einerwa “rme abgebenden senkrechten platte bei natu” rlicher konvection, II. Die versuche und ihre ergibnisse [J]. Forcsh Ingenieurwes, 1930, 1: 391-406

[16] KuikenH K. An asymptotic solution for large Prandtl number free convection [J]. Journal of Engineering Mathematics, 1968, 2: 355-371

[17] KuikenH K. Free convection at low Prandlt numbers [J]. Journal of Fluid Mechanics, 1969, 39: 785-798

[18] BEJAN A. Convection heat transfer [M]. New York: Wiley, 1984.

[19] KhairK R, BejanA. Mass transfer to natural convection boundary-layer flow driven by heat transfer [J]. ASME Journal of Heat Transfer, 1985, 107: 979-981

[20] ChoiS U S. Enhancing thermal conductivity of fluids with nanoparticles [J]. ASME International Journal of Mechanical Engineering, 1995, 66: 99-105

[21] MasudaH, EbataA, TeramaeK, et al. . Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles [J]. Netsu Bussei, 1993, 7: 227-233

[22] BuongiornoJ. Convective transport in nanofluids [J]. Journal of Heat Transfer, 2006, 3: 240-250

[23] NieldD A, KuznetsovA V. The Cheng-Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid [J]. International Journal of Heat Mass Transfer, 2009, 52: 5792-5795

[24] KuznetsovA V, NieldD A. Natural convective boundarylayer flow of a nanofluid past a vertical plate [J]. Internbational Journal of Thermal Sciences, 2010, 2: 243-247

[25] KhanW A, PopI. Boundary-layer flow of a nanofluid past a stretching sheet [J]. International Journal of Heat and Mass Transfer, 2010, 53: 2477-2483

[26] ChangsungS K. Nonequilibrium molecular dynamics approach for nanoelectromechanical systems: Nanofluidics and its applications [J]. Journal of Fluids Engineering, 2007, 129(9): 1140-1146

[27] IbrahimW, ShankerB. Boundary-layer flow and heat transfer of nanofluid over a vertical plate with convective surface boundary condition [J]. Journal of Fluids Engineering, 2012, 134(8): 081203

[28] JabeenK, MushtaqM, AkramR M. Suction and injection impacts on Casson nanofluid with gyrotactic microorganisms over a moving wedge [J]. Journal of Fluids Engineering, 2021, 1441011204

[29] TurkyilmazogluM. Suspension of dust particles over a stretchable rotating disk and two-phase heat transfer [J]. The International Journal of Multiphase Flow, 2020, 127: 103260

[30] WahidN S, ArifinN D, TurkyilmazogluM, et al. . MHD hybrid Cu-Al₂O₃/water nanofluid flow with thermal radiation and partial slip past a permeable stretching surface: Analytical solution [J]. Journal of Nano Research, 2020, 6475-91

[31] AminJ, MustafaT, RoşcaA V, et al. . Complete theory of the elastic wall jet: A new flow geometry with revisited two-phase nanofluids [J]. European Journal of Mechanics, B/Fluids, 2021, 8625-36

[32] ArulmozhiS, SukkiramathiK, SantraS S, et al. . Heat and Mass transfer analysis of radiative and chemical reactive effects on MHD Nanofluid over an infinite moving vertical plate [J]. Results in Engineering, 2022, 14: 100394

[33] TawadeJ V, GuledC N, NoeiaghdamS, et al. . Effects of thermophoresis and Brownian motion for thermal and chemically reacting Casson nanofluid flow over a linearly stretching sheet [J]. Results in Engineering, 2022, 15100448

[34] KhanM S, MeiS, ShabnamF, et al. . Numerical simulation of a time-dependent electroviscous and hybrid nanofluid with Darcy-Forchheimer effect between squeezing plates [J]. Nanomaterials, 2022, 12876

[35] AhlersG, GrossmannS, LohseD. Heat transfer and large-scale dynamics in turbulent Rayleigh-B’enard convection [J]. Reviews of Modren Physics, 2009, 81503-537

[36] ZhouQ, StevensR J A, SugiyamaK. Prandtl-Blasius temperature and velocity boundary layer profiles in turbulent Rayleigh-B’enard convection [J]. Journal of Fluid Mechanics, 2010, 664: 297-312

[37] LANDAU L D, LIFSHITZ E M. Fluid mechanics [M]. Oxford: Pergamon Press, 1987.

[38] SCHLICHTING H, GERSTEN K. Boundary-layer theory [M]. 8th ed. Springer, 2004.

[39] BenziR, ChingE S C, ChuV W S. Heat transpor by laminar boundary layer flow with polymers [J]. Journal of Fluid Mechanics, 2012, 696: 330-344

[40] XieY C, HuangS D, FunfschillingD, et al. . Effects of polymer additives in the bulk of turbulent thermal convection [J]. Journal of Fluid Mechanics, 2015, 784: R3

[41] BenziR, ChingE S C, YuW C K, et al. . Heat transport modification by finitely extensible polymers in laminar boundary layer flow [J]. Journal of Fluid Mechanics, 2016, 788337-357

[42] BenziR, ChingE S C, AngelisE D. Turbulent Rayleigh-Benard convection with polymers: Understanding how heat flux is modified [J]. Physical Reviews E, 2016, 94063110

[43] ChengJ P, ZhangH N, CaiW H, et al. . Effect of polymer additives on heat transport and large-scale circulation in turbulent Rayleigh-Bénard convection [J]. Physical Reviews Journal, 2017, 96013111

[44] ChengJ P, QuJ G, ZhangH N, et al. . Steady laminar plume generated from a heated line in polymer solutions [J]. Physics of Fluids, 2019, 31103101

[45] ATHAR M, AHMAD A. Behavior of fluid flow and heat transfer induced by a stretching surface in the presence of polymers [J]. Physica Scripta, 2021: 095203. DOI: https://doi.org/10.1088/1402-4896/ac0376.

[46] BIRD R B, HASSAGER O, ARMSTRONG R C et al. Dynamics of polymeric liquids [M]. Wiley-Interscience, 1987.