Homotopy Analysis Method (HAM) for an Analysis of Unsteady MHD Thin Film Nanofluid Flow over a Moving Flat Surface
Keywords:
Stretching surface, Non-uniform heat source/sink, Magnetohydrodynamics, Nanofluid, Homotopy analysis method.Abstract
The flow and heat transfer properties of a nanofluid in a thin layer over stretched heat have keen applications in several contemporary processes. Indisputably, the thin film's heat transfer rate affects how the coating process is presented as well as the chemical makeup of the final result. The research presented in this article is based on the "Homotopy analysis method," a series solution for an unsteady magnetohydrodynamic thin film's unstable boundary value issue. When there is an uneven heat source or sink present, there is a nanofluid flow over the flat surface. The Homotopy research speeds up the process of ensuring that any strong nonlinearity problem's series solution will converge.
Owing to wide variety of industrial applications, we have investigated impacts of factors such as magnetic field, temperature- and space-dependent and across a stretched sheet in current study with flow property and displayed same visually. Furthermore, it was shown that increasing heat source/sink's non-uniform parameter decreased local Nusselt number while increasing the thermal boundary layer's thickness. The study shows that temperature field, velocity field, Nusselt number, and thin film thickness are all significantly impacted by magnetic field, thermal conductivity, and non-uniform heat source/sink characteristic. Additionally, it is evident that a rise in magnetic field parameter results in an increase in temperature profile, whereas wall friction, fluid's velocity field, and pace at which heat transfer occurs have the opposite impact.
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References
Wang CY. Liquid film on an unsteady stretching surface. Q Appl Math. 1990;48:601–10.
Wang C. Analytic solutions for a liquid film on an unsteady stretching surface. Heat Mass Transf. 2006;42:759–66.
Andersson HI, Aarseth JB, Dandapat BS. Heat transfer in a liquid film on an unsteady stretching surface. Int J Heat Mass Transf. 2000;43:69–74.
Liu IC, Andersson HI. Heat transfer in a liquid film on an unsteady stretching sheet. Int J Therm Sci. 2008;47:766–72.
Myers, T. Application of non-Newtonian models to thin film flow. Phys. Rev. E 2005, 72, 066302.
Marinca, V.; Heris¸anu, N.; Nemes¸, I. Optimal homotopy asymptotic method with application to thin film flow. Open Phys. 2008, 6, 648–653.
Dandapat BS, Santra B, Andersson HI. Thermocapillarity in a liquid film on an unsteady stretching surface. Int J Heat Mass Transf. 2003;46:3009–155.
Dandapat BS, Santra B, Vajravelu K. The effects of variable fluid properties and thermocapillarity on the flow of a thin film on an unsteady stretching surface. Heat Mass Transf. 2007;50:991–6.
Chen CH. Marangoni effects on forced convection of power law liquids in a thin film over a stretching surface. PhysLett A. 2007;370:51–7.
Abel MS, Mahesha N, Tawade J. Heat transfer in a liquid film over an unsteady stretching surface with viscous dissipation in presence of external magnetic field. Appl Math Model. 2009;33:3430–41.
Andersson HI, Aarseth JB, Braud N, Dandapat BS. Flow of a power-law fluid film on an unsteady stretching surface. J Nonnewton Fluid Mech. 1996;62:1–8.
Chen CH. Heat transfer in a power-law fluid film over an unsteady stretching sheet. Heat Mass Transf. 2003;39:791–6.
Chen CH. Effect of viscous dissipation on heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet. J Nonnewton Fluid Mech. 2006;135:128–35.
Noor NFM, Hashim I. Thermocapillarity and magnetic field effects in a thin liquid film on an unsteady stretching surface. Int J Heat Mass Transf. 2010;53:2044–51.
Nadeem S, Awais M. Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity. PhysLett A. 2008;372:4965–72
Nadeem S, Faraz N. Thin film flow of a second grade fluid over a stretching/shrinking sheet with variable temperature-dependent viscosity. Chin PhysLett. 2010;27(3):034704.
Khan Y, Wu Q, Faraz N, Yildirim A. The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet. Comput Math Appl. 2011;61:3391–9.
Khan Y, Faraz N. Thin film flow of an unsteady Maxwell fluid over a shrinking/stretching sheet with variable fluid properties. Int J Numer Meth Heat Fluid Flow. 2018;28(7):1596–612.
Kumar KA, Sandeep N, Sugunamma V, Animasaun IL. Effect of irregular heat source/sink on the radiative thin film flow of MHD hybrid ferrofluid. J Therm Anal Calorim. 2019;1:1–9.
Rehman A, Salleh Z, Gul T, Zaheer Z. The impact of viscous dissipation on the thin film unsteady flow of GO-EG/GO-W nanofluids. Mathematics. 2019;7(7):653.
Noor NFM, Abdulaziz O, Hashim I. MHD flow and heat transfer in a thin liquid film on an unsteady stretching sheet by the homotopy analysis method. Int J Numer Meth Fluids. 2010;63:357–73.
Yan Zhang, Min Zhang, Shujuan Qi, "Heat and Mass Transfer in a Thin Liquid Film over an Unsteady Stretching Surface in the Presence of Thermosolutal Capillarity and Variable Magnetic Field", Mathematical Problems in Engineering, vol. 2016, Article ID 8521580, 12 pages, 2016. https://doi.org/10.1155/2016/8521580.
Choi, S. U. S., 1995, “Enhancing Thermal Conductivity of Fluids With Nanoparticles,” Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, CA, FED231/MD66, pp. 99–105.
Choi, S. U. S., Zhang, Z. G., Yu, W., Lockwood, F. E., and Grulke, E. A., 2001, “Anomalously Thermal Conductivity Enhancement in Nanotube Suspension,” Appl. Phys. Lett., 79(14), pp. 2252–2254
Narayana M, Sibanda P. Laminar flow of a nanoliquid film over an unsteady stretching sheet. Int J Heat Mass Transf. 2012;55:7552–600.
Xu H, Pop I, You XC. Flow and heat transfer in a nano-liquid film over an unsteady stretching surface. Int J Heat Mass Transf. 2013;60:646–52.
Aziz RC, Hashim I, Abbasbandy S. Flow and heat transfer in a nanofluid thin film over an unsteady stretching sheet. SainsMalaysiana. 2018;47(7):1599–605.
Khan ZH, Qasim M, Lopez RJ. Heat and mass transfer in nanofluid thin film over an unsteady stretching sheet using buongiorno’s model. EurPhys J Plus. 2016;131(16):1–11.
Giri SS, Das K, Kundu PK. Inclined magnetic field effects on unsteady nanofluid flow and heat transfer in a finite thin film with non-uniform heat source/sink. Multidiscip Model Mater Struct. 2019;15(1):265–82.
Jawad M, Shah Z, Islam S, Khan W, Khan AZ. Nanofluid thin film flow of Sisko fluid and variable heat transfer over an unsteady stretching surface with external magnetic field. J Algorithms Comput Technol. 2018;13:1–16.
S. Maity, Y. Ghatani , B. S. Dandapat, Thermocapillary Flow of a Thin Nanoliquid Film Over an Unsteady Stretching Sheet, J. Heat Transfer. Apr 2016, 138(4): 042401 (8 pages)
Liao SJ. Proposed homotopy analysis techniques for the solution of nonlinear problems. Ph.D. Dissertation, Shanghai Jiao Tong University (1992).
Wang C, Pop I. Analysis of the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method. J Nonnewton Fluid Mech. 2006;138:161–72.
I-Chung Liu, Ahmed M. Megahed, "Homotopy Perturbation Method for Thin Film Flow and Heat Transfer over an Unsteady Stretching Sheet with Internal Heating and Variable Heat Flux", Journal of Applied Mathematics, vol. 2012, Article ID 418527, 12 pages, 2012.
I-C. Liu and A. M. Megahed , Numerical Study for the Flow and Heat Transfer in a Thin Liquid Film Over an Unsteady Stretching Sheet with Variable Fluid Properties in the Presence of Thermal Radiation, Journal of Mechanics, Volume 28, Issue 2 June 2012 , pp. 291-297.
Shah Z, Bonyah E, Islam S, Khan W, Ishaq M. Radiative MHD thin film flow of Williamson fluid over an unsteady permeable stretching sheet. Heliyon. 2018;4:e00825. doi: 10.1016/j.heliyon.2018.e00825.
Patel H.R. Effects of cross diffusion and heat generation on mixed convective MHD flow of Casson fluid through porous medium with non-linear thermal radiation. Heliyon. 2019;5
Ullah, A.; Shah, Z.; Kumam, P.; Ayaz, M.; Islam, S.; Jameel, M. Viscoelastic MHD Nanofluid Thin Film Flow over an Unsteady Vertical Stretching Sheet with Entropy Generation. Processes 2019, 7, 262.
R.C. Aziz, I. Hashim and S.Abbasbandy, Flow and Heat Transfer in a Nanofluid Thin Film over an Unsteady Stretching Sheet, SainsMalaysiana 47(7)(2018): 1599–1605
Liao SJ. Beyond perturbation: introduction to the homotopy analysis method. Boca Raton: Chapman & Hall; 2004.
Liao SJ. On the homotopy analysis method for nonlinear problems. Appl Math Comput. 2004;147:449–513.
Liao SJ. Homotopy analysis method in nonlinear differential equations. Berlin: Springer; 2012.
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