Unsteady magnetohydrodynamic free convection flow of Al2O3–Cu/water nanofluid over a permeable linear stretching sheet through a porous medium with viscous dissipation and heat source/sink

Year 2025, Volume: 11 Issue: 2, 344 - 356, 24.03.2025

Joel Mathews Hymavathi Talla

Abstract

This paper examines the effect of Copper and Aluminium oxide nanoparticles on the MHD water-based flow over a permeable linearly stretching sheet through a porous medium. The objective of the present work is to exhibit the impact of magnetic field, viscous dissipation, thermal radiation, and heat source/sink with the metallic and oxide nanoparticles due to permeable stretching sheet. The significance of a new advanced nanofluid with two kinds of nanoparticle materials (Copper and Aluminium oxide) stems from the fact that in the design of various equipment, such as nuclear power plants, gas turbines, propulsion devices for aircraft, missiles, etc. Similarity variables were used to transform the nonlinear partial differential equations into ordinary differential equations. To solve the obtained ODEs, the MATLAB bvp4c solver is used. The behavior of velocity and temperature profiles is discussed through graphs. Also, the physical quantities, such as Skin friction coefficient and Nusselt number, for both fluids are calculated and presented via tables. We have compared the velocity profiles of nanofluids and pure fluid and observed that Copper and Alumina nanofluids perform more efficiently than the base fluid. Moreover, the numerical results are compared with the existing results and found to have good accuracy with the present results.

Keywords

Heat Source/Sink, Magnetohydrodynamics (MHD), Nanofluids, Permeable Sheet, Thermal Radiation, Viscous-dissipation

References

• [1] Sakiadis BC. Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE J 1961;7:26–28. [CrossRef]
• [2] Sakiadis BC. Boundary-layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface. AIChE J 1961;7:221–225. [CrossRef]
• [3] Crane LJ. Flow past a stretching plate. Z Angew Math Phys 1970;21:645–647.
• [4] Gupta PS, Gupta AS. Heat and mass transfer on a stretching sheet with suction or blowing. Can J Chem Eng 1977;55:744–746. [CrossRef]
• [5] Pop I, Tsung-Yen Na. A note on MHD flow over a stretching permeable surface. Mech Res Commun 1998;25:263–269. [CrossRef]
• [6] Kumaran V, Banerjee AK, Vanav Kumar A, Vajravelu K. MHD flow past a stretching permeable sheet. Appl Math Comput 2009;210:26–32. [CrossRef]
• [7] Ali FM, Nazar, Norihan Md Arifin. MHD viscous flow and heat transfer induced by a permeable shrinking sheet with prescribed surface heat flux. WSEAS Trans Math 2010;9:365–375.
• [8] Hayat T, Qasim M, Mesloub S. MHD flow and heat transfer over a permeable stretching sheet with slip conditions. Int J Numer Methods Fluids 2011;66:963–975. [CrossRef]
• [9] Mabood F, Shateyi S. Multiple slip effects on MHD unsteady flow heat and mass transfer impinging on a permeable stretching sheet with radiation. Model Simul Eng 2019;2019:1–11. [CrossRef]
• [10] Ishak A, Nazar R, Pop I. Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature. Nonlinear Anal Real World Appl 2009;10:2909–2913. [CrossRef]
• [11] Choudhary MK, Chaudhary S, Sharma R. Unsteady MHD flow and heat transfer over a stretching permeable surface with suction or injection. Procedia Eng 2015;127:703–710. [CrossRef]
• [12] Hafidzuddin MEH, Nazar RM, Arifin N, Pop I. Unsteady flow and heat transfer over a permeable stretching/shrinking sheet with generalized slip velocity. Int J Numer Methods Heat Fluid Flow 2018;28:1457–1470. [CrossRef]
• [13] Chaudhary S, Chaudhary S, Singh S. Heat transfer in hydromagnetic flow over an unsteady stretching permeable sheet. Int J Math Eng Manag Sci 2019;4:1018–1030. [CrossRef]
• [14] Qasim M, Noreen S. Heat transfer in the boundary layer flow of a Casson fluid over a permeable shrinking sheet with viscous dissipation. Eur Phys J 2014;129:1–8. [CrossRef]
• [15] Chamkha AJ, Aly AM, Mansour MA. Similarity solution for unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction/injection and chemical reaction effects. Chem Eng Commun 2010;197:846–858. [CrossRef]
• [16] Mohana Ramana R, Venkateswara Raju K, Girish Kumar J. Multiple slip and chemical reaction effects on unsteady MHD heat and mass transfer flow over a permeable stretching sheet with radiation. Turk J Comput Math Educ 2021;12:4489–4498.
• [17] Das SK, Choi SU, Yu W, Pradeep T. Nanofluids: Science and Technology. New York: John Wiley & Sons Inc; 2008. pp. 344–345.
• [18] Khan WA, Pop I. Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf 2010;53:2477–2483. [CrossRef]
• [19] 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]
• [20] Elgazery NS. Nanofluids flow over a permeable unsteady stretching surface with a non-uniform heat source/sink in the presence of an inclined magnetic field. J Egypt Math Soc 2019;27:9. [CrossRef]
• [21] Madhu M, Kishan N, Chamkha AJ. Unsteady flow of a Maxwell nanofluid over a stretching surface in the presence of magnetohydrodynamic and thermal radiation effects. Propuls Power Res 2017;6:31–40. [CrossRef]
• [22] Mjankwi MA, Masanja VC, Mureithi EW, MakunguNg’oga J. Unsteady MHD flow of nanofluid with variable properties over a stretching sheet in the presence of thermal radiation and chemical reaction. Int J Math Math Sci 2019;2019:1–14. [CrossRef]
• [23] Khan SA, Nie Y, Ali B. Multiple slip effects on MHD unsteady viscoelastic nanofluid flow over a permeable stretching sheet with radiation using the finite element method. SN Appl Sci 2020;2:66. [CrossRef]
• [24] Khan U, Waini I, Ishak A, Pop I. Unsteady hybrid nanofluid flow over a radially permeable shrinking/stretching surface. J Mol Liq 2021;331:115752. [CrossRef]
• [25] Muntazir RM, Mushtaq M, Shahzadi S, Jabeen K. MHD nanofluid flow around a permeable stretching sheet with thermal radiation and viscous dissipation. Proc Inst Mech Eng Part C J Mech Eng Sci 2022;236:137–152. [CrossRef]
• [26] Adnan UK, Ahmed N, Tauseef S, Mohyud Din, Alsulami MD, Khan I. A novel analysis of heat transfer in the nanofluid composed by nanodiamond and silver nanomaterials: numerical investigation. Sci Rep 2022;12:1284. [CrossRef]
• [27] Khan AA, Zaimi K, Ying TY. Unsteady MHD stagnation point flow of Al₂O₃-Cu/H₂O hybrid nanofluid past a convectively heated permeable stretching/shrinking sheet with suction/injection. J Adv Res Fluid Mech Therm Sci 2022;96:96–114. [CrossRef]
• [28] Kumar VG, Rehman KU, Kumar RVMSSK, Shatanawi W. Unsteady magnetohydrodynamic nanofluid flow over a permeable exponentially surface manifested with non-uniform heat source/sink effects. Waves Random Complex Media 2022;1–19. [CrossRef]
• [29] Oyelakin IS, Mondal S, Sibanda P. Unsteady MHD three-dimensional Casson nanofluid flow over a porous linear stretching sheet with slip condition. Front Heat Mass Transf 2017;8:1–9. [CrossRef]
• [30] Hymavathi T, Mathews J, Kumar RVMSSK. Heat transfer and inclined magnetic field effects on unsteady free convection flow of MoS₂ and MgO–water-based nanofluids over a porous stretching sheet. Int J Ambient Energy 2022;43:5855–5863. [CrossRef]
• [31] Kumar RVMSS, Varma SVK. Multiple slips and thermal radiation effects on MHD boundary layer flow of a nanofluid through a porous medium over a nonlinear permeable sheet with heat source and chemical reaction. J Nanofluids 2017;6:48–58. [CrossRef]
• [32] Khashi’ie NS, Waini I, Arifin NM, Pop I. Unsteady squeezing flow of Cu-Al₂O₃/water hybrid nanofluid in a horizontal channel with a magnetic field. Sci Rep 2021;11:14128. [CrossRef]
• [33] Shahzad U, Mushtaq M, Farid S, Jabeen K, Muntazir RM. A numerical approach for an unsteady tangent hyperbolic nanofluid flow past a wedge in the presence of suction/injection. Math Probl Eng 2021;2021:1–15. [CrossRef]
• [34] Shuaib M, Ali A, Khan MA, Ali A. Numerical investigation of an unsteady nanofluid flow with magnetic and suction effects to the moving upper plate. Adv Mech Eng 2020;12:1–13. [CrossRef]
• [35] Ahamed SM, Mondal S, Sibanda P. Unsteady mixed convection flow through a permeable stretching flat surface with partial slip effects through MHD nanofluid using the spectral relaxation method. Open Phys 2017;15:323–334. [CrossRef]
• [36] Eastman JA, Choi SUS, Li S, Yu W, Thompson LJ. Anomalously increased effective thermal conductivities of ethylene glycol–based nanofluids containing copper nanoparticles. Appl Phys Lett 2001;78:718–720. [CrossRef]
• [37] Patel HE, Das SK, Sundararajan T, Sreekumaran NA, George B, Pradeep T. Thermal conductivities of naked and monolayer protected metal nanoparticle-based nanofluids: manifestation of anomalous enhancement and chemical effects. Appl Phys Lett 2003;83:2931–2933. [CrossRef]
• [38] Choi SUS, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles. Am Soc Mech Eng 1995;66:99–105.
• [39] Vassallo P, Kumar R, D’Amico S. Pool boiling heat transfer experiments in silica–water nanofluids. Int J Heat Mass Transfer 2004;47:407–411. [CrossRef]
• [40] Li X, Zhu D, Wang X. Evaluation on dispersion behavior of the aqueous copper nano-suspensions. J Colloid Interface Sci 2007;310:456–463. [CrossRef]
• [41] Chon CH, Kihm KD, Lee SP, Choi SUS. Empirical correlation finding the role of temperature and particle size for nanofluid (Al₂O₃) thermal conductivity enhancement. Appl Phys Lett 2005;87:153107. [CrossRef]
• [42] Das SK, Putra N, Thiesen P, Roetzel W. Temperature dependence of thermal conductivity enhancement for nanofluids. J Heat Transf 2003;125:567–574. [CrossRef]
• [43] Olabi AG, Wilberforce T, Sayed ET, Elsaid K, Atiqure Rahman SM, Abdelkareem MA. Geometrical effect coupled with nanofluid on heat transfer enhancement in heat exchangers. Int J Thermofluids 2021;10:100072. [CrossRef]
• [44] Yashawantha KM, Asif A, Babu RG, Ramis MK. Rheological behavior and thermal conductivity of graphite–ethylene glycol nanofluid. J Test Eval 2021;49:2906–2927. [CrossRef]
• [45] Das PK, Dash SK, Ganguly R, Santra AK, Venkatesan EP, Rajhi AA, Saboor S, et al. Effect of particle loading and temperature on the rheological behavior of Al₂O₃ and TiO₂ nanofluids. Energy Sources Part A Recover Util Environ Eff 2022;44:7062–7079. [CrossRef]
• [46] Saleh B, Sundar LS, Aly AA, Venkata Ramana E, Sharma KV, Afzal A, et al. The combined effect of Al₂O₃ nanofluid and coiled wire inserts in a flat-plate solar collector on heat transfer, thermal efficiency, and environmental CO₂ characteristics. Arab J Sci Eng 2022;47:9187–9214. [CrossRef]
• [47] Taghikhani MA. Magnetic field effect on the heat transfer in a nanofluid-filled lid-driven cavity with Joule heating. J Therm Eng 2020;6:521–543. [CrossRef]
• [48] Thameem Basha H, Sivaraj R. Heat and mass transfer in stagnation point flow of cross nanofluid over a permeable extending/contracting surface: a stability analysis. J Therm Eng 2022;8:38–51. [CrossRef]
• [49] Pattnaik PK, Syed SA, Mishra S, Swarnalata J, Sachindar Kumar R, Muduli K. Flow of viscous nanofluids across a nonlinear stretching sheet. J Therm Eng 2023;9:593–601. [CrossRef]
• [50] Paul A, Mani Nath J, Das TK. An investigation of the MHD Cu-Al₂O₃/H₂O hybrid-nanofluid in a porous medium across a vertically stretching cylinder incorporating thermal stratification impact. J Therm Eng 2023;9:799–810. [CrossRef]
• [51] Rama Subba Reddy G, Ibrahim S. Free convection on a vertical stretching surface with suction and blowing. Appl Sci Res 1994;52:247–257. [CrossRef]
• [52] Rashidi MM, Rostami B, Freidoonimehr N, Abbasbandy S. Free convective heat and mass transfer for MHD fluid flow over a permeable vertical stretching sheet in the presence of radiation and buoyancy effects. Ain Shams Eng J 2014;5:901–912. [CrossRef]
• [53] Afify AA, Uddin MJ, Ferdows M. Scaling group transformation for MHD boundary layer flow over a permeable stretching sheet in the presence of slip flow with Newtonian heating effects. Appl Math Mech 2014;35:1375–1386. [CrossRef]
• [54] Hasan M, Karim E, Samad A. MHD free convection flow past an inclined stretching sheet considering viscous dissipation and radiation. Open J Fluid Dyn 2017;7:152–168. [CrossRef]
• [55] Freidoonimehr N, Rashidi MM, Mahmud S. Unsteady MHD free convective flow past a permeable stretching vertical surface in a nanofluid. Int J Therm Sci 2015;7:136–145. [CrossRef]
• [56] Lim YJ, Mohamad AQ, Rawi NA, Ling DCC, Zin NAM, Shafie S. Analysis of quadratic thermal radiation on Carreau fluid past a melting stretchable cylinder. Res Square 2023 Jan 05. [Preprint] [CrossRef]
• [57] Wong KFV, Leon OD. Applications of nanofluids: current and future. Adv Mech Eng 2010;2:519659. [CrossRef]
• [58] Barai D, Bhanvase BA. Future prospects of industrial applications of nanofluids. In: Bhanvase BA, Barai D, Zyla G, Said Z, eds.Towards Nanofluids For Large-Scale Industrial Applications. Amsterdam: Elsevier; 2024. pp. 429–446. [CrossRef]
• [59] Gupta S, Kumar D, Singh J. Magnetohydrodynamic three-dimensional boundary layer flow and heat transfer of water-driven copper and alumina nanoparticles induced by convective conditions. Int J Mod Phys B 2019;33:1950307. [CrossRef]
• [60] Das K, Sarkar A, Kumar PK. Cu-water nanofluid flow induced by a vertical stretching sheet in the presence of a magnetic field with convective heat transfer. Propuls Power Res 2017;6:206–213. [CrossRef]
• [61] Oztop HF, Abu-Nada E. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int J Heat Fluid Flow 2008;29:1326–1336. [CrossRef]
• [62] Ascher UM, Mattheij RMM, Russell RD. Numerical solution of boundary value problems for ordinary differential equations. Philadelphia: SIAM; 1995. [CrossRef]
• [63] Shampine LF, Reichelt MW, Kierzenka J. Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c. Available at: https://classes.engineering.wustl.edu/che512/bvp_paper.pdf. Accessed Feb 26, 2025.
• [64] Alrihieli H, Alrehili M, Megahed AM. Radiative MHD nanofluid flow due to a linearly stretching sheet with convective heating and viscous dissipation. Mathematics 2022;10:4743. [CrossRef]