Skip to main content
SpringerLink
Log in

Entropy generation and temperature-dependent viscosity in the study of SWCNT–MWCNT hybrid nanofluid

  • Original Article
  • Published:
Applied Nanoscience Aims and scope Submit manuscript

Abstract

Nanofluids are of excellent significance to scientists, because, due to their elevated heat transfer rates, they have important industrial uses. A new class of nanofluid, “hybrid nanofluid,” has recently been used to further improve the rate of heat transfer. The current phenomenon particularly concerns the analysis of the flow and heat transfer of SWCNT–MWCNT/water hybrid nanofluid with activation energy through a moving wedge. The Darcy–Forchheimer relationship specifies the nature of the flow in the porous medium. Further the impact of variable viscosity, velocity and thermal slip, thermal radiation and heat generation are also discussed in detail. The second law of thermodynamics is utilized to measure the irreversibility factor. The numerical technique bvp4c is integrated to solve the highly nonlinear differential equation. For axial velocity, temperature profile, and entropy generation, a comparison was made between nanofluid and hybrid nanofluid. The variable viscosity parameter enhances the axial velocity and diminishes the temperature distribution for both nanofluid and hybrid nanofluid. Furthermore, the solid volume fraction diminishes the velocity and concentration profile while enhancing the temperature distribution.

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
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

Abbreviations

\( \hat{u} \) :

Along x-axis velocity component

\( \hat{v} \) :

Along y-axis velocity component

\( Q(x) \) :

Volumetric rate of heat source

\( K^{**} \) :

Permeability of porous medium

\( k^{*} \) :

Coefficient of mean absorption

\( F^{**} \) :

Nonuniform inertia coefficient

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

Reaction rate constant

\( u_{\infty } (x) \) :

Free stream velocity of the fluid

\( E_{\text{a}} \) :

Activation energy

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

Mass diffusivity

\( \Pr \) :

Prandtl number

\( k( 8. 6 1\times 1 0^{ - 5} \,{\text{eV/K}}) \) :

Boltzmann constant

\( N_{1} (x) \) :

Variable slip factor

\( D_{1} (x) \) :

Variable thermal factor

\( S_{\text{c}} \) :

Schmidt number

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

Surface drag force

\( {\text{Nu}}_{x} \) :

Nusselt number

\( {\text{Br}} \) :

Brinkman number

\( F_{\text{r}} \) :

Inertia coefficient

\( E_{\text{c}} \) :

Eckert number

\( R_{\text{d}} \) :

Radiation parameter

\( R_{\text{c}} \) :

Dimensionless reaction rate

\( A,B \) :

Velocity and thermal slip parameter, respectively

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

Hybrid nanofluid density

\( \sigma^{*} \) :

Stefan–Boltzmann constant

\( \mu_{\text{hnf}} (\hat{T}) \) :

Hybrid nanofluid viscosity

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

Shear stress

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

Hybrid nanofluid thermal diffusivity

\( \lambda \) :

Moving wedge parameter

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

Heat capacity of hybrid nanofluid

\( \alpha_{1} \) :

Temperature difference

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

Viscosity of fluid

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

Density of fluid

\( (\rho C_{\text{p}} )_{\text{f}} \) :

Heat capacity of fluid

\( \gamma \) :

Dimensionless heat generation parameter

f :

Dimensionless stream function

\( \alpha_{2} \) :

Concentration difference

\( \theta_{\text{r}} \) :

Variable viscosity parameter

References

  • Ahmad S, Nadeem S, Muhammad N (2019) Boundary layer flow over a curved surface imbedded in porous medium. Commun Theor Phys 71(3):344

    Article  CAS  Google Scholar 

  • Ahmad S, Nadeem S, Muhammad N, Issakhov A (2020) Radiative SWCNT and MWCNT nanofluid flow of Falkner–Skan problem with double stratification. Phys A Stat Mech Appl. https://doi.org/10.1016/j.physa.2019.124054

    Article  Google Scholar 

  • Ahmed Z, Nadeem S, Saleem S, Ellahi R (2019) Numerical study of unsteady flow and heat transfer CNT-based MHD nanofluid with variable viscosity over a permeable shrinking surface. Int J Numer Methods Heat Fluid Flow 29(12):4607–4623

    Article  Google Scholar 

  • Alamri SZ, Ellahi R, Shehzad N, Zeeshan A (2019) Convective radiative plane Poiseuille flow of nanofluid through porous medium with slip: an application of Stefan blowing. J Mol Liq 273:292–304

    CAS  Google Scholar 

  • Alarifi IM, Alkouh AB, Ali V, Nguyen HM, Asadi A (2019) On the rheological properties of MWCNT-TiO2/oil hybrid nanofluid: an experimental investigation on the effects of shear rate, temperature, and solid concentration of nanoparticles. Powder Technol 355:157–162

    Article  CAS  Google Scholar 

  • Amini F, Miry SZ, Karimi A, Ashjaee M (2019) Experimental investigation of thermal conductivity and viscosity of SiO2/multiwalled carbon nanotube hybrid nanofluids. J Nanosci Nanotechnol 19(6):3398–3407

    Article  CAS  Google Scholar 

  • Bejan Adrian (1979) A study of entropy generation in fundamental convective heat transfer. J Heat Transf 101(4):718–725

    Article  Google Scholar 

  • Bejan A, Kestin J (1983) Entropy generation through heat and fluid flow. J Appl Mech 50:475

    Article  Google Scholar 

  • Bhatti MM, Sheikholeslami M, Shahid A, Hassan M, Abbas T (2019) Entropy generation on the interaction of nanoparticles over a stretched surface with thermal radiation. Colloids Surf A 570:368–376

    Article  CAS  Google Scholar 

  • Buongiorno J (2006) Convective transport in nanofluids. J Heat Transf 128(3):240–250

    Article  Google Scholar 

  • Choi SUS, Eastman JA (1995) Enhancing thermal conductivity of fluids with nanoparticles. No. ANL/MSD/CP-84938; CONF-951135-29. Argonne National Lab, Lemont

  • Dzulkifli NF, Bachok N, Pop I, Yacob NA, Arifin NM, Rosali H (2019) Soret and Dufour effects on unsteady boundary layer flow and heat transfer in copper-water nanofluid over a shrinking sheet with partial slip and stability analysis. J Nanofluids 8(7):1601–1608

    Article  Google Scholar 

  • Ellahi R, Hassan M, Zeeshan A, Khan AA (2016) The shape effects of nanoparticles suspended in HFE-7100 over wedge with entropy generation and mixed convection. Appl Nanosci 6(5):641–651

    Article  CAS  Google Scholar 

  • Ellahi R, Alamri SZ, Basit A, Majeed A (2018) Effects of MHD and slip on heat transfer boundary layer flow over a moving plate based on specific entropy generation. J Taibah Univ Sci 12(4):476–482

    Article  Google Scholar 

  • Ellahi R, Hussain F, Ishtiaq F, Hussain A (2019a) Peristaltic transport of Jeffrey fluid in a rectangular duct through a porous medium under the effect of partial slip: an application to upgrade industrial sieves/filters. Pramana 93(3):34

    Article  Google Scholar 

  • Ellahi R, Sait SM, Shehzad N, Mobin N (2019b) Numerical simulation and mathematical modeling of electroosmotic Couette-Poiseuille flow of MHD power-law nanofluid with entropy generation. Symmetry 11(8):1038

    Article  CAS  Google Scholar 

  • Esfe MH, Alirezaie A, Rejvani M (2017) An applicable study on the thermal conductivity of SWCNT-MgO hybrid nanofluid and price-performance analysis for energy management. Appl Therm Eng 111:1202–1210

    Article  Google Scholar 

  • Esfe MH, Emami MRS, Amiri MK (2019) Experimental investigation of effective parameters on MWCNT–TiO2/SAE50 hybrid nanofluid viscosity. J Therm Anal Calorim 137(3):743–757

    Article  Google Scholar 

  • Feroz N, Shah Z, Islam S, Alzahrani EO, Khan W (2019) Entropy generation of carbon nanotubes flow in a rotating channel with hall and ion-slip effect using effective thermal conductivity model. Entropy 21:52

    Article  CAS  Google Scholar 

  • Goodarzi M, Toghraie D, Reiszadeh M, Afrand M (2019) Experimental evaluation of dynamic viscosity of ZnO–MWCNTs/engine oil hybrid nanolubricant based on changes in temperature and concentration. J Therm Anal Calorim 136(2):513–525

    Article  CAS  Google Scholar 

  • Hussien AA, Abdullah MZ, Yusop NM, Al-Kouz W, Mahmoudi E, Mehrali M (2019) Heat transfer and entropy generation abilities of MWCNTs/GNPs hybrid nanofluids in microtubes. Entropy 21(5):480

    Article  CAS  Google Scholar 

  • Javed MF, Waqas M, Khan NB, Muhammad R, Rehman MU, Khan MI, Khan SW, Hassan MT (2019) On entropy generation effectiveness in flow of power law fluid with cubic autocatalytic chemical reaction. Appl Nanosci 9(5):1205–1214

    Article  CAS  Google Scholar 

  • Khan NS, Zuhra S, Shah Q (2019) Entropy generation in two phase model for simulating flow and heat transfer of carbon nanotubes between rotating stretchable disks with cubic autocatalysis chemical reaction. Appl Nanosci 9(8):1797–1822

    Article  CAS  Google Scholar 

  • Lu D, Ramzan M, Ahmad S, Shafee A, Suleman M (2018) Impact of nonlinear thermal radiation and entropy optimization coatings with hybrid nanoliquid flow past a curved stretched surface. Coatings 8(12):430

    Article  Google Scholar 

  • Nadeem S, Ahmed Z, Saleem S (2016) The effect of variable viscosities on micropolar flow of two nanofluids. Zeitschrift für Naturforschung A 71(12):1121–1129

    Article  CAS  Google Scholar 

  • Nadeem S, Ahmad S, Muhammad N (2018) Computational study of Falkner-Skan problem for a static and moving wedge. Sens Actuators B Chem 263:69–76

    Article  CAS  Google Scholar 

  • Nadeem S, Hayat T, Khan AU (2019a) Numerical study of 3D rotating hybrid SWCNT–MWCNT flow over a convectively heated stretching surface with heat generation/absorption. Phys Scr 94(7):075202

    Article  CAS  Google Scholar 

  • Nadeem S, Khan MN, Khan MN, Muhammad N, Ahmad S (2019) Erratum to: mathematical analysis of bio-convective micropolar nanofluid erratum to: journal of computational design and engineering. J Comput Des Eng. https://doi.org/10.1016/j.jcde.2019.04.001

    Article  Google Scholar 

  • Noreen S, Rashidi MM, Qasim M (2017) Blood flow analysis with considering nanofluid effects in vertical channel. Appl Nanosci 7(5):193–199

    Article  CAS  Google Scholar 

  • Riaz A, Bhatti MM, Ellahi R, Zeeshan A, Sait SM (2020) Mathematical analysis on an asymmetrical wavy motion of blood under the influence entropy generation with convective boundary conditions. Symmetry 12(1):102

    Article  Google Scholar 

  • Sarafraz MM, Pourmehran O, Yang B, Arjomandi M, Ellahi R (2020) Pool boiling heat transfer characteristics of iron oxide nano-suspension under constant magnetic field. Int J Therm Sci 147:106131

    Article  CAS  Google Scholar 

  • Shahsavar A, Sardari PT, Toghraie D (2019) Free convection heat transfer and entropy generation analysis of water-Fe3O4/CNT hybrid nanofluid in a concentric annulus. Int J Numer Methods Heat Fluid Flow 29(3):915–934

    Article  Google Scholar 

  • Sheikholeslami M, Ellahi R, Shafee A, Li Z (2019) Numerical investigation for second law analysis of ferrofluid inside a porous semi annulus. Int J Numer Methods Heat Fluid Flow 29(3):1079–1102

    Article  Google Scholar 

  • Suleman M, Ramzan M, Ahmad S, Lu D, Muhammad T, Chung JD (2019) A numerical simulation of silver–water nanofluid flow with impacts of newtonian heating and homogeneous–heterogeneous reactions past a nonlinear stretched cylinder. Symmetry 11(2):295

    Article  CAS  Google Scholar 

  • White FM (2015) Introduction to fluid mechanics. McGraw-Hill Education, New York

    Google Scholar 

  • Yih KA (1999) MHD forced convection flow adjacent to a non-isothermal wedge. Int Commun Heat Mass Transf 26(6):819–827

    Article  CAS  Google Scholar 

  • Zadkhast M, Toghraie D, Karimipour A (2017) Developing a new correlation to estimate the thermal conductivity of MWCNT-CuO/water hybrid nanofluid via an experimental investigation. J Therm Anal Calorim 129(2):859–867

    Article  CAS  Google Scholar 

  • Zaib A, Haq RU (2019) Magnetohydrodynamics mixed convective flow driven through a static wedge including TiO2 nanomaterial with micropolar liquid: Similarity dual solutions via finite difference method. Proc Inst Mech Eng Part C: J Mech Eng Sci 233(16):5813–5825

    Article  CAS  Google Scholar 

  • Zaib A, Haq RU, Chamkha AJ, Rashidi MM (2019) Impact of partial slip on mixed convective flow towards a Riga plate comprising micropolar TiO2-kerosene/water nanoparticles. Int J Numer Methods Heat Fluid Flow 29(5):164. https://doi.org/10.1108/HFF-06-2018-0258

    Article  Google Scholar 

  • Zeeshan A, Shehzad N, Abbas T, Ellahi R (2019a) Effects of radiative electro-magnetohydrodynamics diminishing internal energy of pressure-driven flow of titanium dioxide-water nanofluid due to entropy generation. Entropy 21(3):236

    Article  CAS  Google Scholar 

  • Zeeshan A, Ellahi R, Mabood F, Hussain F (2019) Numerical study on bi-phase coupled stress fluid in the presence of Hafnium and metallic nanoparticles over an inclined plane. Int J Numer Methods Heat Fluid Flow. https://doi.org/10.1108/hff-11-2018-0677

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan

    Shafiq Ahmad & Naeem Ullah

  2. Mathematics and Its Applications in Life Sciences Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Sohail Nadeem

  3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Sohail Nadeem

Authors
  1. Shafiq Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sohail Nadeem
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Naeem Ullah
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sohail Nadeem.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ahmad, S., Nadeem, S. & Ullah, N. Entropy generation and temperature-dependent viscosity in the study of SWCNT–MWCNT hybrid nanofluid. Appl Nanosci 10, 5107–5119 (2020). https://doi.org/10.1007/s13204-020-01306-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13204-020-01306-0

Keywords

Search

Navigation