Skip to main content
SpringerLink
Log in

Time-dependent mixed convection flow of Ag–MgO/water hybrid nanofluid over a moving vertical cone with rough surface

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

Abstract

In this paper, an innovative work has been explored on mixed convective hybrid nanofluid flow in the presence of a moving cone with surface roughness. The primary aim of this analysis is to establish the significance of hybrid nanofluid characteristics influencing the wall gradients such as skin friction coefficient and the rate of heat transfer. The hybrid nanofluid comprises water as the base fluid with silver (Ag) nanoparticles and magnesium oxide (MgO) nanoparticles added to it. The flow and heat transfer characteristics governing equations are expressed in terms of nonlinear coupled partial differential equations. The solutions of these equations are attempted numerically by employing the Quasilinearization technique in combination with the implicit finite difference approximation. It is noted that the rate of energy transfer and surface friction are higher for hybrid nanofluid (\(\varphi_{1} = 0.025\), \(\varphi_{2} = 0.025\)) than that for the pure MgO nanofluid (\(\varphi_{1} = 0\), \(\varphi_{2} = 0.05\)) and pure Ag nanofluid (\(\varphi_{1} = 0.05\), \(\varphi_{2} = 0\)), wherein the net volume fraction of 5% of nanoparticles is maintained. For hybrid nanofluid, the Nusselt number rises by 12% and 6% approximately in comparison with that for the pure Ag nanofluid and pure MgO nanofluid, respectively. This result can be attributed to the strong molecular interaction between the hybrid nanoparticles suspended in the water medium. In order to confirm the authentication of the accuracy of the results of the present analysis, the fluid friction and rate of energy transfer are compared with the previous research findings. It is revealed that the present results are in good agreement with those published outcomes.

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
Fig. 14

Similar content being viewed by others

Abbreviations

\(C_{{\text{f}}}\) :

Skin-friction coefficient

\(\left( {C_{{\text{p}}} } \right)_{{\text{f}}} ,\,\left( {C_{{\text{p}}} } \right)_{{{\text{hnf}}}}\) :

Specific heat of the fluid and hybrid nanofluid

Ec :

Eckert number

\(f\) :

Non-dimensional stream function

\(F = f_{{\upeta }}\) :

Non-dimensional velocity

\(g\) :

Acceleration due to gravity

\(G\) :

Non-dimensional temperature

k f :

Thermal conductivity of the fluid

\(k_{{{\text{hnf}}}}\) :

Thermal conductivity of the hybrid nanofluid

m :

Exponent in the power law variation of the mainstream velocity

\(n\) :

Frequency parameter

Nu :

Nusselt number

\(Pr\) :

Prandtl number

Re :

Reynolds number

\(Ri\) :

Richardson number

\(t\) :

Time

\(T\) :

Temperature of the fluid

\(T_{{\text{w}}}\) :

Wall temperature

\(T_{\infty }\) :

Ambient fluid temperature

\(u,\,v\) :

Components of velocity along x and y coordinates, respectively

\(U_{{\text{w}}}\) :

Velocity of the cone surface

\(U_{\text{e}}\) :

Mainstream velocity

\(U_{\infty }\) :

Mainstream velocity constant

\(x,\,y\) :

Cartesian coordinates

α :

Unsteady parameter

β :

Thermal expansion coefficient

γ :

Roughness parameter

ε :

Velocity ratio parameter

θ :

Half angle of the vertical cone

\(\mu _{{\text{f}}} ,\;\mu _{{{\text{hnf}}}}\) :

Dynamic viscosity of the fluid and hybrid nanofluid

\(\nu_{{\text{f}}} ,\;\nu_{{{\text{nf}}}}\) :

Kinematic viscosity of the water and Ag/H2O nanofluid

\(\nu_{{hnf}}\) :

Kinematic viscosity of the hybrid nanofluid

\(\xi ,\;\eta\) :

Transformed variables

\(\rho _{{\text{f}}} ,\;\rho _{{{\text{nf}}}}\) :

Viscosity of the water and Ag/H2O nanofluid

\(\rho _{{{\text{hnf}}}}\) :

Viscosity of the hybrid nanofluid

\(\phi (\tau )\) :

Unsteady function of τ

\(\phi _{1} ,\;\phi _{2}\) :

Solid volume fractions of Ag and MgO nanoparticles, respectively

ψ :

Stream function

\(\xi ,\;\eta\) :

Partial derivatives with respect to ξ, η

\(w,\,\,\infty\) :

Constraints at the surface and away from the surface, respectively

References

  1. Dutta P, Subhashini SV, Ravindran R. Influence of surface mass transfer on mixed convection flows over non-isothermal horizontal flat plates. Appl Math Model. 2009;33:1285–94.

    Article  Google Scholar 

  2. Aydin O, Kaya A. Mixed convection of a viscous dissipating fluid about a vertical flat plate. Appl Math Model. 2007;31:843–53.

    Article  Google Scholar 

  3. Hering RG, Gorsh RJ. Laminar combined convection from a rotating cone. ASME J Heat Transf. 1963;85:29–34.

    Article  Google Scholar 

  4. Kumari M, Pop I, Nath G. Mixed convection along a vertical cone. Int Comm Heat Mass Transf. 1989;16:247–55.

    Article  CAS  Google Scholar 

  5. Takhar HS, Chamkha AJ, Nath G. Unsteady mixed convection flow from a rotating vertical cone with magnetic field. Heat Mass Transf. 2003;39:297–304.

    Article  Google Scholar 

  6. Pop I, Grosan T, Kumari M. Mixed convection along a vertical cone for fluids of any Prandtl number: case of constant wall temperature. Int J Num Methods Heat Fluid Flow. 2003;13:815–29.

    Article  Google Scholar 

  7. Ravindran R, Roy S, Momoniat E. Effects of injection (suction) on a steady mixed convection boundary layer flow over a vertical cone. Int J Num Methods Heat Fluid Flow. 2009;19:432–44.

    Article  CAS  Google Scholar 

  8. Pullepu B, Sambath P, Viswanathan KK. Effects of chemical reactions on unsteady free convective and mass transfer flow from a vertical cone with heat generation/absorption in the presence of VWT/VWC. Math Probl Eng. 2014;2014:1–20.

    Article  Google Scholar 

  9. Patil PM, Pop I. Effects of surface mass transfer on unsteady mixed convection flow over a vertical cone with chemical reaction. Heat mass Transf. 2011;47:1453–64.

    Article  CAS  Google Scholar 

  10. Rosali H, Ishak A, Nazar R, Pop I. Mixed convection boundary layer flow past a vertical cone embedded in a porous medium subjected to a convective boundary condition. Propuls Power Res. 2016;5:118–22.

    Article  Google Scholar 

  11. Patil PM, Shashikant A, Hiremath PS. Diffusion of liquid hydrogen and oxygen in nonlinear mixed convection nanofluid flow over vertical cone. Int J Hydrogen Energy. 2019;44:17061–71.

    Article  CAS  Google Scholar 

  12. Patil PM, Chamkha AJ. Unsteady combined heat and mass transfer from a moving vertical plate in a parallel free stream. Int J Energy Techn. 2010;2(9):1–13.

    CAS  Google Scholar 

  13. Roy S, Anilkumar D. Unsteady mixed convection from a moving vertical slender cylinder. J Heat Transf. 2006;128:368–73.

    Article  Google Scholar 

  14. Patil PM, Roy S, Pop I. Unsteady mixed convection flow over a vertical stretching sheet in a parallel free stream with variable wall temperature. Int J Heat Mass Transf. 2010;53:4741–8.

    Article  Google Scholar 

  15. Rehman S, Rehman SU, Khan A, Khan Z. The effect of flow distribution on heat and mass transfer of MHD thin liquid film flow over an unsteady stretching sheet in the presence of variational physical properties with mixed convection. Phys A. 2020;551:124120.

    Article  Google Scholar 

  16. Mahdy A, Chamkha AJ, Nabwey HA. Entropy analysis and unsteady MHD mixed convection stagnation-point flow of Casson nanofluid around a rotating sphere. Alex Eng J. 2020;59:1693–703.

    Article  Google Scholar 

  17. Ali R, Hasan N. Steady and unsteady flow regimes in two-dimensional mixed convective flow of air past a heated square cylinder. Int J Mech Sci. 2020;175:105533.

    Article  Google Scholar 

  18. Hang Xu. Modelling unsteady mixed convection of a nanofluid suspended with multiple kinds of nanoparticles between two rotating disks by generalized hybrid model. Int Comm Heat Mass Transf. 2019;108:104275.

    Article  Google Scholar 

  19. Cimpean DS, Sheremet MA, Pop I. Mixed convection of hybrid nanofluid in a porous trapezoidal chamber. Int Comm Heat Mass Transf. 2020;116:104627.

    Article  CAS  Google Scholar 

  20. Rostami MN, Dinarvand S, Pop I. Dual solutions for mixed convective stagnation-point flow of an aqueous silica-alumina hybrid nanofluid. Chin J Phys. 2018;56:2465–78.

    Article  CAS  Google Scholar 

  21. Benkhedda M, Boufendi T, Touahri S. Laminar mixed convective heat transfer enhancement by using Ag-TiO2-water hybrid Nanofluid in a heated horizontal annulus. Heat mass Transf. 2018;54:2799–814.

    Article  CAS  Google Scholar 

  22. Nisar KS, Khan U, Zaib A, Khan I, Baleanu D. Numerical simulation of mixed convection squeezing flow of a hybrid nanofluid containing magnetized ferroparticles in 50%:50% of ethylene glycol-water mixture base fluids between two disks with the presence of a non-linear thermal radiation heat flux. Front Chem. 2020;8:792.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Khan U, Zaib A, Kasmaei HD, Malaver M. Mixed convective in an axisymmetric magneto flow owing to MoS2-GO hybrid nanoliquids in H2O based liquid through an upright cylinder with shape factor. Preprints. 2020. https://doi.org/10.20944/preprints202003.0301.v1.

    Article  Google Scholar 

  24. Hanif H, Khan I, Shafie S. Heat transfer exaggeration and entropy analysis in magneto-hybrid nanofluid flow over a vertical cone: a numerical study. J Therm Anal Calorim. 2020;141:2001–17.

    Article  CAS  Google Scholar 

  25. Esfe MH, Rostamian SH, Alirezaie A. An applicable study on the thermal conductivity of SWCNT-MgO hybrid nanofluid and price-performance analysis for energy management. Appl Therm Eng. 2017;111:1202–10.

    Article  Google Scholar 

  26. Patil PM, Kulkarniand M, Hiremath PS. Effects of surface roughness on mixed convective nanofluid flow past an exponentially stretching permeable surface. Chin J Phys. 2020;64:203–18.

    Article  CAS  Google Scholar 

  27. Patil PM, Doddagoudar SH, Hiremath PS. Impacts of surface roughness on mixed convection nanofluid flow with liquid hydrogen/nitrogen diffusion. Int J Num Methods Heat Fluid Flow. 2019;29:2146–74.

    Article  Google Scholar 

  28. Gray DD, Giorgini A. The validity of Boussinesq approximation for liquids and gases. Int J Heat Mass Transf. 1976;19:545–51.

    Article  CAS  Google Scholar 

  29. Schlichting H, Gersten K. Boundary layer theory. New York: Springer; 2000.

    Book  Google Scholar 

  30. Radbill RJ, McCue AG. Quasilinearization and non-linear problems in fluid and orbital mechanics. Elsevier Publishing Co.;1970.

  31. Bellman RE, Kalaba RE. Quasilinearization and non-linear boundary value problems. New York: American Elsevier Publishing Co., Inc; 1965.

    Google Scholar 

  32. Inouye K, Tate A. Finite difference version of Quasilinearization applied to boundary layer equations. AIAA J. 1974;12:558–60.

    Article  Google Scholar 

  33. Patil PM, Shankar HF, Sheremet M. Mixed convection of Silica-Molybdenum disulphide/water hybrid nanoliquid over a rough sphere. Symmetry. 2021;13(236):1–19.

    Google Scholar 

  34. Varga RS. Matrix iterative analysis. USA: Prentice-Hall; 2000. p. 219–23.

    Book  Google Scholar 

  35. Hamilton RL, Crosser OK. Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Fundam. 1962;1:182–91.

    Article  Google Scholar 

  36. Maxwell JC. A Treatise on Electricity and Magnetism Vol I-II. Oxford: Clarendon Press; 1873.

    Google Scholar 

  37. Timofeeva EV, Routbort JL, Singh D. Particle shape effects on thermophysical properties of alumina nanofluids. J Appl Phys. 2009;106:0143041–110.

    Article  Google Scholar 

  38. Jarray A, Mehrez Z, Cafsi AE. Mixed convection Ag-MgO/water hybrid nanofluid flow in a porous horizontal channel. Eur Phys J Special Topics. 2019;228:2677–93.

    Article  CAS  Google Scholar 

  39. Himasekhar K, Sarma PK, Janardhan K. Laminar mixed convection from a vertical rotating cone. Int Comm Heat Mass Transf. 1989;16:99–106.

    Article  CAS  Google Scholar 

  40. Chamkha AJ, Al-Mudhaf A. Unsteady heat and mass transfer from a rotating vertical cone with a magnetic field and heat generation or absorption effects. Int J Therm Sci. 2005;44:267–76.

    Article  Google Scholar 

Download references

Acknowledgements

The second author is thankful for the financial support to the Department of Science and Technology-Innovation in Science Pursuit for Inspired Research (DST-INSPIRE).

Author information

Authors and Affiliations

  1. Department of Mathematics, Karnatak University, Pavate Nagar, Dharwad, 580003, India

    P. M. Patil & Bharath Goudar

  2. Wrangler Dr. D. C. Pavate Institute of Mathematical Sciences, Department of Mathematics, Karnatak University, Dharwad, 580003, India

    P. M. Patil

Authors
  1. P. M. Patil
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bharath Goudar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. M. Patil.

Ethics declarations

Conflict of interest

The author declares that they have no Conflict of interest

Additional information

Publisher's Note

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

Appendix

Appendix

The Table

Table 2 Properties of nanofluid and hybrid nanofluid
Full size table

2 presents the formulae of different properties of nanofluids and hybrid nanofluids, while the Table

Table 3 The thermo physical attributes of regular liquid and nanofluid [38]
Full size table

3 represents the thermophysical properties of water and nano additives.

Comparison with earlier results in the literature

In order to confirm the authentication of the accuracy of the results of the present analysis, the present results of gradients are compared with the previous research findings of Himasekhar et al. [39] and Chamkha and Al-Mudhaf [40] in the Table

Table 4 Comparison of the present results of Re1/2Cf and Re-1/2Nu with earlier published results when \(\varphi_{1} = \varphi_{2} = Ec = \tau = \xi = \varepsilon = 0\)
Full size table

4, which shows that the current findings are in good agreement with the results obtained in [39] and [40].

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Patil, P.M., Goudar, B. Time-dependent mixed convection flow of Ag–MgO/water hybrid nanofluid over a moving vertical cone with rough surface. J Therm Anal Calorim 147, 10693–10705 (2022). https://doi.org/10.1007/s10973-022-11246-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-022-11246-2

Keywords

Search

Navigation