Numerical study of flow behavior and heat transfer of ternary water- based nanofluids in the presence of suction/injection, stretching/ shrinking sheet

Year 2024, Volume: 10 Issue: 4, 1021 - 1043, 29.07.2024

Gul M. Shaikh Abid A. Memon M. Asif Memon Ubaidullah Yashkun Adebowale Martins Obalalu Hasan Köten

Abstract

Research on ternary hybrid nanofluids is driven by the hope that combining various nanoparticles will lead to better heat transfer efficiency, thermal conductivity, as well as other desired properties. The goal of study is to create a nanofluid that performs better than its binary equivalents by deliberately choosing and combining nanoparticles with different sizes, designs, and thermal conductivities. This research delves into the intricacies of stagnation point flow, taking into account suction/injection, a stretching/shrinking sheet, and slip flow boundary conditions. Employing a ternary hybrid nanofluid (THNF) composed of titanium oxide, silver, and zinc oxide provides insights into the velocity field and thermal characteristics. The study leverages the Tiwari Das nanofluid model and boundary flow equations in two dimensions. The governing equations undergo a transformation into a system of ordinary differential equations (ODEs) via a similarity transformation. These ODEs are subsequently tackled using the finite element method. A meticulous parametric study is executed, manipulating the stretching/shrinking parameter, suction/injection parameter, slip flow parameter, and total volume fraction of the ternary nanofluids. The chosen ranges for these parameters are -1 to 0.5, -1 to 1, 0 to 1, and 0.03 to 0.3, respectively. The observed trend reveals a consistent decrease in the percentage change in temperature concerning the ambient temperature with an increase in normalized distance from the stagnation point, whether the sheet is stretching or shrinking. Notably, the temperature decline is more pronounced in the case of a shrinking sheet. Additionally, in instances involving injection, the transformation from a shrinking sheet to a stretching one exerts a more substantial impact on the percentage change in temperature relative to ambient conditions compared to the suction case. The novelty of the work lies in the study’s discovery of correlations for average velocity and average temperature profiles related to the slip flow parameter, suction parameter, and stretching/shrinking parameter, providing a more accurate estimation.

Keywords

Slip Flow Boundary Conditions, Stagnation Point, Stretching/ Shrinking Sheet, Suction/ Injection, Ternary Nanofluid

References

• [1] Hiemenz K. Die Grenzschicht an einem in den gleichformigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder. Dinglers Polytech J 1911;326:321324. [German]
• [2] Homann F. Der Einfluss grosser Zähigkeit bei der Strömung um den Zylinder und um die Kugel. J Appl Math Mech (ZAMM) 1936;16:153164. [German] [CrossRef]
• [3] Chiam TC. Stagnation-point flow towards a stretching plate. J Physic Soc Japan 1994;63:24432444. [CrossRef]
• [4] Khashi’ie NS, Arifin NM, Rashidi MM, Hafidzuddin EH, Wahi N. Magnetohydrodynamics (MHD) stagnation point flow past a shrinking/stretching surface with double stratification effect in a porous medium. J Therm Anal Calorim 2020;139:36353648. [CrossRef]
• [5] Choi SUS, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles (No. ANL/MSD/CP-84938; CONF-951135-29). ASME International Mechanical Engineering Congress & Exposition, November 12-17, 1995, San Francisco.
• [6] Lee S, Choi SUS, Li S, Eastman JA. Measuring thermal conductivity of fluids containing oxide nanoparticles. J Heat Transf 1999;121:280289. [CrossRef]
• [7] Keblinski P, Phillpot SR, Choi SUS, Eastman JA. Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids). Int J Heat Mass Transf 2002;45:855863. [CrossRef]
• [8] Kumar MD, Raju CSK, Sajjan K, El-Zahar ER, Shah NA. Linear and quadratic convection on 3D flow with transpiration and hybrid nanoparticles. Int Comm Heat Mass Transf 2022;134:105995. [CrossRef]
• [9] Upadhya SM, Raju SSR, Raju CSK, Shah NA, Chung JD. Importance of entropy generation on casson, micropolar and hybrid magneto-nanofluids in a suspension of cross diffusion. Chinese J Physics 2022;77:10801101. [CrossRef]
• [10] Al-Kouz W, Abderrahmane A, Shamshuddin MD, Younis O, Mohammed S, Bég OA, et al. Heat transfer and entropy generation analysis of water-Fe3O4/CNT hybrid magnetic nanofluid flow in a trapezoidal wavy enclosure containing porous media with the Galerkin finite element method. Eur Physic J Plus 2021;136:1184. [CrossRef]
• [11] Bin Mizan MR, Ferdows M, Shamshuddin MD, Bég OA, Salawu SO, Kadir A. Computation of ferromagnetic/nonmagnetic nanofluid flow over a stretching cylinder with induction and curvature effects. Heat Transf 2021;50:52405266. [CrossRef]
• [12] Rahman M, Ferdows M, Shamshuddin MD, Koulali A, Eid MR. Aiding (opponent) flow of hybrid copper–aluminum oxide nanofluid towards an exponentially extending (lessening) sheet with thermal radiation and heat source (sink) impact. J Petrol Sci Engineer 2022;215:110649. [CrossRef]
• [13] Salawu SO, Shamshuddin MD, Beg OA. Influence of magnetization, variable viscosity and thermal conductivity on Von Karman swirling flow of H2O-FE3O4 and H2O-Mn-ZNFe2O4 ferromagnetic nanofluids from a spinning DISK: Smart spin coating simulation. Mater Sci Engineer B 2022;279:115659.
• [14] Buongiorno J. Convective transport in nanofluids. J Heat Transf 2006;128:240250. [CrossRef]
• [15] Tiwari RK, Das MK. Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int J Heat Mass Transf 2007;50:20022018. [CrossRef]
• [16] Reza-E-Rabbi S, Ahmmed SF, Arifuzzaman SM, Sarkar T, Khan MS. Computational modelling of multiphase fluid flow behaviour over a stretching sheet in the presence of nanoparticles. Engineer Sci Technol 2020;23:605617. [CrossRef]
• [17] Rana BMJ, Arifuzzaman SM, Reza-E-Rabbi S, Ahmed SF, Khan MS. Energy and magnetic flow analysis of Williamson micropolar nanofluid through stretching sheet. Int J Heat Technol 2019;37:487496. [CrossRef]
• [18] Vijatha M. Reddy PBA. Comparative analysis on magnetohydrodynamic flow of non-Newtonian hybrid nanofluid over a stretching cylinder: Entropy generation. J Process Mech Engineer 2022;236:23612371. [CrossRef]
• [19] Nield DA, Kuznetsov AV. The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. Int J Heat Mass Transf 2009;52:57925795. [CrossRef]
• [20] Nield DA, Kuznetsov AV. The Cheng–Minkowycz problem for the double-diffusive natural convective boundary layer flow in a porous medium saturated by a nanofluid. Int J Heat Mass Transf 2011;54:374378. [CrossRef]
• [21] Kuznetsov AV, Nield DA. Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int J Therm Sci 2010;49:243247. [CrossRef]
• [22] Kuznetsov AV, Nield DA. Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate. Int J Therm Sci 2011;50:712717. [CrossRef]
• [23] Bachok N, Ishak A, Pop I. Boundary-layer flow of nanofluids over a moving surface in a flowing fluid. Int J Therm Sci 2010;49:16631668. [CrossRef]
• [24] Bachok N, Ishak A, Pop I. Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet. Int J Heat Mass Transf 2012;55:21022109. [CrossRef]
• [25] Khan WA, Aziz A. Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux. Int J Therm Sci 2011;50:12071214. [CrossRef]
• [26] Ferdows M, Shamshuddin MD, Salawu SO, Sun S. Thermal cooling performance of convective non-Newtonian nanofluid flowing with variant power-index across moving extending surface. Sci Rep 2022;12:8714. [CrossRef]
• [27] Devi SA, Devi SSU. Numerical investigation of hydromagnetic hybrid Cu–Al2O3/water nanofluid flow over a permeable stretching sheet with suction. Int J Nonlinear Sci Numer Sim 2016;17:249257. [CrossRef]
• [28] Rohsenow WM, Hartnett JP, Ganic EN. Handbook of Heat Transfer Fundamentals. New York: McGraw-Hill; 1985.
• [29] Masad JA, Nayfeh AH. Effects of suction and wall shaping on the fundamental parametric resonance in boundary layers. Physics Fluids A 1992;4:963974. [CrossRef]
• [30] Rosali H, Ishak A, Pop I. Micropolar fluid flow towards a stretching/shrinking sheet in a porous medium with suction. Int Comm Heat Mass Transf 2012;39:826829.
• [31] Crane LJ. Flow past a stretching plate. J Appl Math Physics (ZAMP) 1970;21:645647. [CrossRef]
• [32] Bakr SA, Thumma T, Ahmed SE, Mansour MA, Morsy Z. Effects of wavy porous fins on the flow, thermal fields, and entropy of the magnetic radiative non-Newtonian nanofluid confined inclined enclosures. J Proc Mech Engineer 2022;09544089211072629. [RETRACTED] [CrossRef]
• [33] Dawar A, Wakif A, Thumma T, Shah NA. Towards a new MHD non-homogeneous convective nanofluid flow model for simulating a rotating inclined thin layer of sodium alginate-based Iron oxide exposed to incident solar energy. Int Comm Heat Mass Transf 2022;130:105800. [CrossRef]
• [34] Thumma T, Bég OA, Kadir A. Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet. J Molecular Liquid 2017;232:159173. [CrossRef]
• [35] Thumma T, Mishra SR, Abbas MA, Bhatti MM, Abdelsalam SI. Three-dimensional nanofluid stirring with non-uniform heat source/sink through an elongated sheet. Appl Math Comp 2022;421:126927. [CrossRef]
• [36] Boroomandpour A, Toghraie D, Hashemian M. A comprehensive experimental investigation of thermal conductivity of a ternary hybrid nanofluid containing MWCNTs-titania-zinc oxide/water-ethylene glycol (80: 20) as well as binary and mono nanofluids. Synthetic Metals 2020;268:116501. [CrossRef]
• [37] Dezfulizadeh A, Aghaei A, Joshaghani AH, Najafizadeh MM. An experimental study on dynamic viscosity and thermal conductivity of water-Cu-SiO2-MWCNT ternary hybrid nanofluid and the development of practical correlations. Powder Technol 2021;389:215234. [CrossRef]
• [38] Mohammadfam Y, Heris SZ. Thermophysical characteristics and forced convective heat transfer of ternary doped magnetic nanofluids in a circular tube: An experimental study. Case Stud Therm Engineer 2023;52;103748. [CrossRef]
• [39] Usharani P, Ravindra Reddy B. Thermodynamic analysis of EMHD ternary nanofluid flow with shape factor effects over a shrinking sheet: A non-Fourier heat flux model. Numer Heat Transf Part A Appl 2024;124. [CrossRef]
• [40] Goyal K, Srinivas S. Pulsatile flow of Casson hybrid nanofluid between ternary-hybrid nanofluid and nanofluid in an inclined channel with temperature-dependent viscosity. Numer Heat Transf Part A Appl 2024;130. [CrossRef]
• [41] Uddin MJ, Amirsom NA, Bég OA, Ismail AI. Computation of bio-nano-convection power law slip flow from a needle with blowing effects in a porous medium. Waves in Random and Complex Media, 2022;121. [CrossRef]
• [42] Bég OA, Uddin MJ, Bég TA, Kadir A, Shamshuddin MD, Babaie M. Numerical study of self-similar natural convection mass transfer from a rotating cone in anisotropic porous media with Stefan blowing and Navier slip. Indian J Physic 2020;94:863877. [CrossRef]
• [43] Beg OA, Zohra FT, Uddin MJ, Ismail AIM, Sathasivam S. Energy conservation of nanofluids from a biomagnetic needle in the presence of Stefan blowing: Lie symmetry and numerical simulation. Case Stud Therm Engineer 2021;24:100861. [CrossRef]
• [44] Maxwell JC. VII. On stresses in rarified gases arising from inequalities of temperature. Phil Trans R Soc 1879;170:231256. [CrossRef]
• [45] Wang CY. Stagnation flows with slip: exact solutions of the Navier-Stokes equations. J Appl Math Physics (ZAMP) 2003;1:184189. [CrossRef]
• [46] Paul A, Patgiri B, Sarma N. Darcy-Forchheimer flow of Ag–ZnO–CoFe2O4/H2O Casson ternary hybrid nanofluid induced by a rotatory disk with EMHD. Int J Amb Energy 2024;45:2313697. [CrossRef]
• [47] Paul A, Patgiri B, Sarma N. Transformer oil‐based Casson ternary hybrid nanofluid flow configured by a porous rotating disk with hall current. J Appl Math Mech (ZAMM) 2024:104:202300704. [CrossRef]
• [48] Paul A, Sarma N, Patgiri B. Numerical assessment of MHD thermo-mass flow of casson ternary hybrid nanofluid around an exponentially stretching cylinder. BioNanoScience 2024;116. [CrossRef]
• [49] Khan U, Ahmed N, Asadullah M, Mohyud-din ST. Effects of viscous dissipation and slip velocity on two-dimensional and axisymmetric squeezing flow of Cu-water and Cu-kerosene nanofluids. Propul Power Res 2015;4:4049. [CrossRef]
• [50] Bég OA, Kabir MN, Uddin MJ, Izani Md Ismail A, Alginahi YM. Numerical investigation of Von Karman swirling bioconvective nanofluid transport from a rotating disk in a porous medium with Stefan blowing and anisotropic slip effects. J Mech Engineer Sci 2021;235:39333951. [CrossRef]
• [51] Latiff NA, Uddin MJ, Ismail AM. Stefan blowing effect on bioconvective flow of nanofluid over a solid rotating stretchable disk. Propul Power Res 2016;5:267278. [CrossRef]
• [52] Tuz Zohra F, Uddin MJ, Basir MF, Ismail AIM. Magnetohydrodynamic bio-nano-convective slip flow with Stefan blowing effects over a rotating disc. J Nanomater Nanoengineer Nanosys 2020;234:8397. [CrossRef]
• [53] Uddin MJ, Kabir MN, Alginahi Y, Bég OA. Numerical solution of bio-nano convection transport from a horizontal plate with blowing and multiple slip effects. J Mech Engineer Sci 2019;233:69106927. [CrossRef]
• [54] Elhag SH, Memon AA, Memon MA, Bhatti K, Jacob K, Alzahrani S, et al. Analysis of forced convection with hybrid Cu-Al2O3 nanofluids injected in a three-dimensional rectangular channel containing three perpendicular rotating blocks with turbulent modeling. J Nanomater 2022;2:127. [CrossRef]
• [55] Memon AA, Khan WA, Muhammad T. Numerical investigation of photovoltaic thermal energy efficiency improvement using the backward step containing Cu-Al2O3 hybrid nanofluid. Alexandria Engineer J 2023;75:391406. [CrossRef]
• [56] Alghamdi M, Memon AA, Muhammad T, Ali M. A numerical investigation of a photovoltaic thermal system contained a trapezoidal channel with transport of silver and titanium oxide using the water as base fluids. Case Stud Therm Engineer 2023;47:103056. [CrossRef]
• [57] Alqarni MM, Memon AA, Memon MA, Mahmoud EE, Fenta A. Numerical investigation of heat transfer and fluid flow characteristics of ternary nanofluids through convergent and divergent channels. Nanoscale Advances 2023;5:68976912. [CrossRef]
• [58] Allehiany FM, Memon AA, Memon MA, Fenta A. Maximizing electrical output and reducing heat-related losses in photovoltaic thermal systems with a thorough examination of flow channel integration and nanofluid cooling. Sci Rep 2023;13:16961. [CrossRef]
• [59] Akram M, Memon AA, Memon MA, Obalalu AM, Khan U. Investigation of a two-dimensional photovoltaic thermal system using hybrid nanofluids and a rotating cylinder. Nanoscale Advances 2023;5:55295542. [CrossRef]
• [60] Memon AA, Memon MA, Haque MM. Numerical investigation of electrical efficiency with the application of hybrid nanofluids for photovoltaic thermal systems contained in a cavity channel. J Math 2023:118. [CrossRef]
• [61] Yashkun U, Zaimi K, Bakar NAA, Ferdows M. Nanofluid stagnation-point flow using Tiwari and Das model over a stretching/shrinking sheet with suction and slip effects. J Adv Res Fluid Mech Therm Sci 2020;70:6276. [CrossRef]
• [62] Mahmood Z, Alhazmi SE, Alhowaity A, Marzouki R, Al-Ansari N, Khan U. MHD mixed convective stagnation point flow of nanofluid past a permeable stretching sheet with nanoparticles aggregation and thermal stratification. Sci Rep 2022;12:16020. [CrossRef]
• [63] Jawad M, Khan Z, Bonyah E, Jan R. Analysis of hybrid nanofluid stagnation point flow over a stretching surface with melting heat transfer. Mathl Problems Engineer 2022:112. [CrossRef]
• [64] Nadeem S, Khan MR, Khan AU. MHD stagnation point flow of viscous nanofluid over a curved surface. Physica Scripta 2019;94:115207. [CrossRef]
• [65] Datta A, Halder P. Field-synergy and nanoparticle’s diameter analysis on circular jet impingement using three oxide–water-based nanofluids. J Therm Engineer 2023;9:179190. [CrossRef]
• [66] Babu MS, Ramana VV, Shankar GR, Raju C. Mixed convective flow of heat and mass transfer of nanofluids over a static wedge with convective boundary conditions. J Therm Engineer 2021;8;1958-1969. [CrossRef]
• [67] Estellé P, Halelfadl S, Maré T. Thermal conductivity of CNT water based nanofluids: Experimental trends and models overview. J Therm Engineer 2015;1:381390. [CrossRef]