Skip to main content
SpringerLink
Log in

Melting heat and viscous dissipation in flow of hybrid nanomaterial: a numerical study via finite difference method

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

Hybrid nanomaterial flowing through Darcy–Forchheimer (D–C) porous medium bounded between two infinite parallel walls is considered in this analysis. The lower wall is fixed and stretchable, while the upper wall moves (squeezes) toward lower one. Cattaneo–Christov (C–C) heat flux is addressed instead of traditional Fourier’s heat flux. Further lower wall is subjected to melting heat. Viscous dissipation accounts heat transport features. Hybrid nanomaterial is constructed through dispersion of both GO (Grapheneoxide) and Cu (Copper) nanoparticles in the water-based liquid. Mathematical formulation in form of PDEs is done. Resulting PDEs are then non-dimensionalized via choosing suitable variables. Numerical technique namely FDM (finite difference method) through FD (forward difference) approximations is executed for these PDEs in order to construct the solutions. Moreover, the velocities and temperature are expressed graphically through involved physical parameters. Velocity of hybrid nanofluid (GO + Cu + Water) enhances with higher estimations of squeezing parameter and Reynolds number while it reduces with an increment in Forchheimer number and porosity parameter. Reduction in temperature of hybrid nanofluid (GO + Cu + Water) is noticed against larger melting parameter while it boosts for higher squeezing parameter and Eckert number.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Choi SUS, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles: the Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA, ASME, FED 231/MD, 66 (1995) 99–105.

  2. 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;78:718–20.

    Article  CAS  Google Scholar 

  3. Sarkar J, Ghosh P, Adil A. A review on hybrid nanofluids: recent research, development and applications. Renew Sustain Energy Rev. 2015;43:164–77.

    Article  CAS  Google Scholar 

  4. Hayat T, Muhammad K, Alsaedi A, Asghar S. Numerical study for melting heat transfer and homogeneous-heterogeneous reactions in flow involving carbon nanotubes. Results Phys. 2018;8:415–21.

    Article  Google Scholar 

  5. Hosseini SR, Ghasemian M, Sheikholeslami M, Shafee A, Li Z. Entropy analysis of nanofluid convection in a heated porous microchannel under MHD field considering solid heat generation. Powder Technol. 2019;344:914–25.

    Article  CAS  Google Scholar 

  6. Dinarvand S, Pop I. Free-convective flow of copper/water nanofluid about a rotating down-pointing cone using Tiwari-Das nanofluid scheme. Adv Powder Technol. 2017;28:900–9.

    Article  CAS  Google Scholar 

  7. Muhammad K, Hayat T, Alsaedi A, Asghar S. Stagnation point flow of basefluid (gasoline oil), nanomaterial (CNTs) and hybrid nanomaterial (CNTs+CuO): A comparative study. Mater Res Express. 2019. https://doi.org/10.1088/2053-1591/ab356e.

    Article  Google Scholar 

  8. Eid MR, Mabood F. Entropy analysis of a hydromagnetic micropolar dusty carbon NTs-kerosene nanofluid with heat generation: Darcy–Forchheimer scheme. J Therm Anal Calorim. 2021;143:2419–36.

    Article  CAS  Google Scholar 

  9. Ahmed F, Khan WA. Efficiency enhancement of an air-conditioner utilizing nanofluids: an experimental study. Energy Rep. 2021;7:575–83.

    Article  Google Scholar 

  10. Nisar Z, Hayat T, Alsaedi A, Ahmad B. Wall properties and convective conditions in MHD radiative peristalsis flow of Eyring-Powell nanofluid. J Therm Anal Calorim. 2021;144:1199–208.

    Article  CAS  Google Scholar 

  11. Souayeh B, Kumar KG, Reddy MG, Rani S, Hdhiri N, Alfannakh H, Rahimi-Gorji M. Slip flow and radiative heat transfer behavior of Titanium alloy and ferromagnetic nanoparticles along with suspension of dusty fluid. J Mol Liq. 2019;290:111223.

    Article  CAS  Google Scholar 

  12. Al-Hossainy AF, Eid MR. Combined experimental thin films, TDDFT-DFT theoretical method, and spin effect on [PEG-H2O/ZrO2+MgO]h hybrid nanofluid flow with higher chemical rate. Surf Interfaces. 2021;23:100971.

    Article  CAS  Google Scholar 

  13. Hayat T, Ahmed B, Abbasi FM, Ahmad B. Mixed Convective Peristaltic flow of carbon nanotubes submerged in water using different thermal Conductivity Models. Comput Methods Programs Biomed. 2016;135:141–50.

    Article  CAS  Google Scholar 

  14. Hajizadeh A, Shah NA, Shah SIA, Animasaun IL, Rahimi-Gorji M, Alarifi IM. Free convection flow of nanofluids between two vertical plates with damped thermal flux. J Mol Liq. 2019;289:110964.

    Article  CAS  Google Scholar 

  15. Kahshan M, Lu D, Rahimi-Gorji M. Hydrodynamical study of flow in a permeable channel: Application to flat plate dialyzer. Int J Hydrog Energy. 2019;44:17041–7.

    Article  CAS  Google Scholar 

  16. Muhammad T, Lu D-C, Mahanthesh B, Eid MR, Ramzan M, Dar A. Significance of Darcy–Forchheimer porous medium in nanofluid through carbon nanotubes. Commun Theor Phys. 2018;70:361.

    Article  CAS  Google Scholar 

  17. Kumar KG, Avinash BS, Rahimi-Gorji M, Alarifi IM. Optical and electrical properties of Ti1-XSnXO2 nanoparticles. J Mol Liq. 2019;293:111556.

    Article  CAS  Google Scholar 

  18. Eid MR. Thermal characteristics of 3D nanofluid flow over a convectively heated riga surface in a Darcy–Forchheimer porous material with linear thermal radiation: an optimal analysis. Arab J Sci Eng. 2020;45:9803–14.

    Article  CAS  Google Scholar 

  19. Seikh AH, Adeyeye O, Omar Z, Raza J, Rahimi-Gorji M, Alharthi N, Khan I. Enactment of implicit two-step Obrechkoff-type block method on unsteady sedimentation analysis of spherical particles in Newtonian fluid media. J Mol Liq. 2019;293:111416.

    Article  CAS  Google Scholar 

  20. Eid MR, Mabood F. Two-phase permeable non-Newtonian cross-nanomaterial flow with Arrhenius energy and entropy generation: Darcy–Forchheimer model. Phys Scr. 2020;95:105209.

    Article  CAS  Google Scholar 

  21. Hayat T, Ahmed B, Alsaedi A. Numerical investigation for peristaltic flow of Carreau-Yasuda magneto-nanofluid with modified Darcy and radiation. J Therm Anal Calorim. 2019;137:1168–77.

    Google Scholar 

  22. Rae B, Shahraki F, Jamailahmad M, Peyghambarzedeh SM. Experimental study on the heat transfer and flow properties of γ-Al2O3/water nanofluid in a double-tube heat exchanger. J Therm Anal Calorim. 2017;127:2561–75.

    Article  Google Scholar 

  23. Turkyilmazoglu M. Single phase nanofluids in fluid mechanics and their hydrodynamic linear stability analysis. Comput Methods Progr Biomed. 2020;187:105171.

    Article  Google Scholar 

  24. Rashidi S, Karimi N, Mahin O, Esfahani JA. A concise review on the role of nanoparticles upon the productivity of solar desalination systems. J Therm Anal Calorim. 2018. https://doi.org/10.1007/s10973-018-7500-8.

    Article  Google Scholar 

  25. Hussain Z. Heat transfer through temperature dependent viscosity hybrid nanofluid subject to homogeneous-heterogeneous reactions and melting condition: A comparative study. Phys Scr. 2020;96:015210.

    Article  Google Scholar 

  26. Turkyilmazoglu M. Thermal management of parabolic pin fin subjected to a uniform oncoming airflow: optimum fin dimensions. J Therm Anal Calorim. 2021;143:3731–9.

    Article  CAS  Google Scholar 

  27. Alsaedi A, Nisar Z, Hayat T, Ahmad B. Analysis of mixed convection and hall current for MHD peristaltic transport of nanofluid with compliant wall. Int Commun Heat Mass Transfer. 2021;121:105121.

    Article  CAS  Google Scholar 

  28. Turkyilmazoglu M. Nanoliquid film flow due to a moving substrate and heat transfer. Eur Phys J Plus. 2020;135:781.

    Article  Google Scholar 

  29. Roberts L. On the melting of a semi-infinite body of ice placed in a hot stream of air. J Fluid Mech. 1958;4:505–28.

    Article  Google Scholar 

  30. Qayyum S, Khan R, Habib H. Simultaneous effects of melting heat transfer and inclined magnetic field flow of tangent hyperbolic fluid over a nonlinear stretching surface with homogeneous–heterogeneous reactions. Int J Mech Sci. 2017;133:1–10.

    Article  Google Scholar 

  31. Qi R, Wang Z, Ren J, Wu Y. Numerical investigation on heat transfer characteristics during melting of lauric acid in a slender rectangular cavity with flow boundary condition. Int J Heat Mass Transfer. 2020;157:119927.

    Article  Google Scholar 

  32. Ho CJ, Gao JY. An experimental study on melting heat transfer of paraffin dispersed with AlO nanoparticles in a vertical enclosure. Int J Heat Mass Transfer. 2013;62:2–8.

    Article  CAS  Google Scholar 

  33. Das K. Radiation and melting effects on MHD boundary layer flow over a moving surface. Ain Shams Eng J. 2014;5:1207–14.

    Article  Google Scholar 

  34. Hayat T, Muhammad K, Alsaedi A. Melting effect in MHD stagnation point flow of Jeffrey nanomaterial. Phys Scr. 2019. https://doi.org/10.1088/1402-4896/ab210e.

    Article  Google Scholar 

  35. Motahar S. Experimental study and ANN-based prediction of melting heat transfer in a uniform heat flux PCM enclosure. J Energy. 2020;30:101535.

    Google Scholar 

  36. Hayat T, Muhammad K, Alsaedi A, Ahmad B. Melting effect in squeezing flow of third-garde fluid with non-Fourier heat flux model. Phys Scr. 2019. https://doi.org/10.1088/1402-4896/ab1c2c.

    Article  Google Scholar 

  37. Ibrahim W. Magnetohydrodynamic (MHD) boundary layer stagnation point flow and heat transfer of a nanofluid past a stretching sheet with melting. Propuls Power Res. 2017;6:214–22.

    Article  Google Scholar 

  38. Hayat T, Muhammad K, Alsaedi A, Asghar S. Thermodynamics by melting in flow of an Oldroyd-B material. J Braz Soc Mech Sci Eng. 2018;40:530.

    Article  Google Scholar 

  39. Khan MdS, Alam M, Tzirtzilakis E, Ferdows M. Finite difference simulation of MHD radiative flow of a nanofluid past a stretching sheet with stability analysis. Int J Adv Thermofluid Res. 2016;2:15–30.

    Google Scholar 

  40. Ahmad S, Hayat T, Alsaedi A. Numerical analysis of entropy generation in viscous nanofluid stretched flow. Int Commun Heat Mass Transfer. 2020;117:104772.

    Article  CAS  Google Scholar 

  41. Bisht A, Sharma R. Non-similar solution of Sisko nanofluid flow with variable thermal conductivity: a finite difference approach. Int J Numer Meth Heat Fluid Flow. 2020;31:345–66.

    Article  Google Scholar 

  42. Davydov O, Safarpoor M. A meshless finite difference method for elliptic interface problems based on pivoted QR decomposition. Appl Numer Math. 2021;161:489–509.

    Article  Google Scholar 

  43. Benito JJ, García A, Gavete L, Negreanu M, Ureña F, Vargas AM. Solving Monge–Ampère equation in 2D and 3D by generalized finite difference method. Eng Anal Bound Elem. 2021;124:52–63.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University, Islamabad, 44000, Pakistan

    T. Hayat & Khursheed Muhammad

  2. Pakistan Academy of Sciences (PAS), G-5/2, Islamabad, Pakistan

    T. Hayat

  3. Nonlinear Dynamics Research Centre (NRDC), Ajman University, Ajman, UAE

    S. Momani

  4. Department of Mathematics, Faculty of Science, University of Jordan, Amman, 11942, Jordan

    S. Momani

Authors
  1. T. Hayat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Khursheed Muhammad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Momani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Khursheed Muhammad.

Ethics declarations

Conflict of interest

It is declared that there is no conflict of interest among the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hayat, T., Muhammad, K. & Momani, S. Melting heat and viscous dissipation in flow of hybrid nanomaterial: a numerical study via finite difference method. J Therm Anal Calorim 147, 6393–6401 (2022). https://doi.org/10.1007/s10973-021-10944-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-021-10944-7

Keywords

Search

Navigation