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Entropy-optimized dissipative flow of Carreau–Yasuda fluid with radiative heat flux and chemical reaction

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Abstract

The main propose of this research communication is to explore the collective influence of Ohmic heating, radiative heat flux, and viscous dissipation on the entropy-optimized reactive flow of non-Newtonian fluid toward a stretched surface. The fluid flow is electrically conducted in the presence of applied magnetic field and generated by stretching phenomenon. The effects of heat generation/absorption, radiative heat flux, dissipation, and Ohmic heating are utilized in the mathematical modeling of energy expression. Furthermore, the chemical reaction is considered. The total entropy rate of the Carreau–Yasuda fluid is discussed versus four irreversibilities, i.e., heat transfer irreversibility, fluid friction irreversibility, magnetic or Ohmic heating irreversibility, and chemical reaction irreversibility and is calculated through implementation of the second law of thermodynamics. Series solutions are calculated for the desired flow expressions via homotopy analysis method. Behaviors of sundry flow parameters on the velocity, temperature, concentration, entropy rate, and Bejan number are physically discussed and the results are plotted graphically. The skin friction coefficient (drag force) and Nusselt number (heat transfer rate) are calculated numerically and discussed with the help of magnetic parameter, Weissenberg number, Prandtl number, radiation parameter and Eckert number. The obtained results reveal that entropy enhances for higher values of radiation parameter and Brinkman number.

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Abbreviations

\( \tau \) :

Extra stress tensor

\( D^{*} \) :

Deformation rate tensor

\( \mu \) :

Dynamic viscosity

\( \varGamma \) :

Time constant

\( d \) :

Model parameter or fluid parameter

\( x,y \) :

Cartesian coordinates

\( \sigma \) :

Electrical conductivity

\( \rho \) :

Density

\( k \) :

Thermal conductivity

\( T_{\infty } \) :

Ambient temperature

\( D \) :

Mass diffusivity

\( \sigma^{*} \) :

Stefan Boltzmann constant

\( k^{*} \) :

Mean absorption coefficient

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

Wall temperature

\( C_{\infty } \) :

Ambient concentration

\( M \) :

Magnetic parameter

\( R \) :

Radiation parameter

\( {\text{Ec}} \) :

Eckert number

\( {\text{Le}} \) :

Lewis number

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

Characteristics entropy generation rate

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

Gas constant

\( L \) :

Diffusion parameter

\( N_{\text{G}} \) :

Entropy number

\( \hbar_{f} ,\hbar_{\theta } ,\hbar_{\phi } \) :

Auxiliary parameters for velocity, temperature and concentration

\( f_{0} \left( \eta \right),\theta_{0} \left( \eta \right),\phi_{0} \left( \eta \right) \) :

Initial guesses

\( \dot{\gamma } \) :

Shear rate

\( \mu_{0} \) :

Zero shear rate viscosity

\( \mu_{\infty } \) :

Infinite shear rate viscosity

\( n \) :

Power law index

\( u,v \) :

Velocity components

\( \nu \) :

Kinematic viscosity

\( B_{0} \) :

Strength of magnetic field

\( T \) :

Temperature

\( Q_{0} \) :

Coefficient of heat generation/absorption

\( C \) :

Concentration

\( c_{\text{p}} \) :

Specific heat capacity

\( k_{0} \) :

Reaction rate

\( a \) :

Positive constant or stretching rate

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

Wall concentration

\( {\text{We}} \) :

Weissenberg number

\( { \Pr } \) :

Prandtl number

\( \delta \) :

Temperature ratio parameter

\( \gamma \) :

Chemical reaction parameter

\( \delta_{1} \) :

Heat generation/absorption parameter

\( \varPhi \) :

Viscous dissipation

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

Brinkman number

\( \alpha_{2} \) :

Concentration ratio parameter

\( \hbar \) :

Auxiliary parameter

\( c_{i} \) :

Arbitrary constant

\( L_{f} \left( f \right),L_{\theta } \left( \theta \right),L_{\phi } \left( \phi \right) \) :

Linear operators

References

  1. C.Y. Wang, Fluid flow due to a stretching cylinder. Phys. Fluids 31, 466 (1988)

    Article  ADS  Google Scholar 

  2. T. Hayat, M.I. Khan, M. Farooq, A. Alsaedi, M. Waqas, T. Yasmeen, Impact of Cattaneo–Christov heat flux model in flow of variable thermal conductivity fluid over a variable thicked surface. Int. J. Heat Mass Transf. 99, 702–710 (2016)

    Article  Google Scholar 

  3. A. Ishak, R. Nazar, I. Pop, Uniform suction/blowing effect on flow and heat transfer due to a stretching cylinder. Appl. Math. Model. 32, 2059–2066 (2008)

    Article  Google Scholar 

  4. M.I. Khan, M. Waqas, T. Hayat, A. Alsaedi, A comparative study of Casson fluid with homogeneous-heterogeneous reactions. J. Colloid Interface Sci. 498, 85–90 (2017)

    Article  ADS  Google Scholar 

  5. M.A.A. Mahmoud, Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Math. Comput. Model. 54, 1228–1237 (2011)

    Article  MathSciNet  Google Scholar 

  6. P.J. Carreau, Rheological equations from molecular network theories. Trans. Soc. Rheol. 16, 99–127 (1972)

    Article  Google Scholar 

  7. K. Yasuda, Investigation of the analogies between viscometric and linear viscoelastic properties of polystyrene fluids, PhD Thesis. Massachusetts Institute Technology, Department of Chemical Engineering, 1979

  8. G.R. Kefayati, H. Tang, Three-dimensional Lattice Boltzmann simulation on thermosolutal convection and entropy generation of Carreau–Yasuda fluids. Int. J. Heat Mass Transf. 131, 346–364 (2019)

    Article  Google Scholar 

  9. T. Hayat, F.M. Abbasi, A. Alsaedi, F. Alsaadi, Hall and Ohmic heating effects on the peristaltic transport of a Carreau–Yasuda fluid in an asymmetric channel. Zeitschrift für Naturforschung A 69, 43–51 (2014)

    Article  ADS  Google Scholar 

  10. J.M. Peralta, B.E. Meza, S.E. Zorrilla, Analytical solutions for the free-draining flow of a Carreau–Yasuda fluid on a vertical plate. Chem. Eng. Sci. 68, 391–402 (2017)

    Article  Google Scholar 

  11. H.C. Lee, A nonlinear weighted least-squares finite elementmethod for the Carreau–Yasuda non-Newtonian model. J. Math. Anal. Appl. 432, 844–861 (2015)

    Article  MathSciNet  Google Scholar 

  12. M. Kiyasatfar, Convective heat transfer and entropy generation analysis of non-Newtonian power-law fluid flows in parallel-plate and circular microchannels under slip boundary conditions. Int. J. Therm. Sci. 128, 15–27 (2018)

    Article  Google Scholar 

  13. G.R. Kefayati, H. Tang, MHD thermosolutal natural convection and entropy generation of Carreau fluid in a heated enclosure with two inner circular cold cylinders, using LBM. Int. J. Heat Mass Transf. 126, 508–530 (2018)

    Article  Google Scholar 

  14. T. Hayat, A. Tanveer, A. Alsaedi, Mixed convective peristaltic flow of Carreau–Yasuda fluid with thermal deposition and chemical reaction. J. Heat Mass Transf. 96, 474–481 (2016)

    Article  Google Scholar 

  15. M.I. Khan, S. Afzal, T. Hayat, M. Waqas, A. Alsaedi, Activation energy for the Carreau–Yasuda nanomaterial flow: analysis of the entropy generation over a porous medium. J. Mol. Liq. 297, 111905 (2020)

    Article  Google Scholar 

  16. A. Bejan, Second-law analysis in heat transfer and thermal design. Adv. Heat Transf. 15, 1–58 (1982)

    Article  Google Scholar 

  17. R. Muhammad, M.I. Khan, N.B. Khan, M. Jameel, Magnetohydrodynamics (MHD) radiated nanomaterial viscous material flow by a curved surface with second order slip and entropy generation. Comput. Methods Programs Biomed. 189, 105294 (2020)

    Article  Google Scholar 

  18. R. Muhammad, M.I. Khan, M. Jameel, N.B. Khan, Fully developed Darcy-Forchheimer mixed convective flow over a curved surface with activation energy and entropy generation. Comput. Methods Programs Biomed. 188, 105298 (2020)

    Article  Google Scholar 

  19. M.I. Khan, A. Kumar, T. Hayat, M. Waqas, R. Singh, Entropy generation in flow of Carreau nanofluid. J. Mol. Liq. 278, 677–687 (2019)

    Article  Google Scholar 

  20. Z. Zhang, Z. Li, C. Lou, Numerical analysis of radiative entropy generation in a parallel plate system with non-uniform temperature distribution participation medium. J. Quant. Spectrosc. Radiat. Transfer 225, 319–326 (2019)

    Article  ADS  Google Scholar 

  21. M. Rashid, M.I. Khan, T. Hayat, M.I. Khan, A. Alsaedi, Entropy generation in flow of ferromagnetic liquid with nonlinear radiation and slip condition. J. Mol. Liq. 276, 441–452 (2019)

    Article  Google Scholar 

  22. Y. Liu, Y. Jian, W. Yan, Entropy generation of electromagnetohydrodynamic (EMHD) flow in a curved rectangular microchannel. Int. J. Heat Mass Transf. 127, 901–913 (2018)

    Article  Google Scholar 

  23. S.Z. Abbas, M.I. Khan, S. Kadry, W.A. Khan, M. Israr-Ur-Rehman, M. Waqas, Fully developed entropy optimized second order velocity slip MHD nanofluid flow with activation energy. Comput. Methods Programs Biomed. 190, 105362 (2020)

    Article  Google Scholar 

  24. S.Z. Abbas, W.A. Khan, S. Kadry, M.I. Khan, M. Waqas, M.I. Khan, Entropy optimized Darcy-Forchheimer nanofluid (silicon dioxide, molybdenum disulfide) subject to temperature dependent viscosity. Comput. Methods Programs Biomed. 190, 105363 (2020)

    Article  Google Scholar 

  25. M.K. Nayak, A.K.A. Hakeem, B. Ganga, M.I. Khan, M. Waqas, O.D. Makinde, Entropy optimized MHD 3D nanomaterial of non-Newtonian fluid: a combined approach to good absorber of solar energy and intensification of heat transport. Comput. Methods Programs Biomed. 186, 105131 (2020)

    Article  Google Scholar 

  26. S.J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University, 1992

  27. S. Qayyum, M.I. Khan, T. Hayat, A. Alsaedi, M. Tamoor, Entropy generation in dissipative flow of Williamson fluid between two rotating disks. Int. J. Heat Mass Transf. 127, 933–942 (2018)

    Article  Google Scholar 

  28. T. Hayat, M.I. Khan, A. Alsaedi, M.I. Khan, Joule heating and viscous dissipation in flow of nanomaterial by a rotating disk. Int. Commun. Heat Mass Transfer 89, 190–197 (2017)

    Article  Google Scholar 

  29. T. Hayat, M.I. Khan, M. Farooq, N. Gull, A. Alsaedi, Unsteady three-dimensional mixed convection flow with variable viscosity and thermal conductivity. J. Mol. Liq. 223, 1297–1310 (2016)

    Article  Google Scholar 

  30. S.J. Liao, Homotopy analysis method in non-linear differential equations (Springer, Berlin, 2012)

    Book  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Riphah International University, Faisalabad Campus, Faisalabad, 38000, Pakistan

    M. Ijaz Khan

  2. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Faris Alzahrani

Authors
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Correspondence to M. Ijaz Khan.

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Khan, M.I., Alzahrani, F. Entropy-optimized dissipative flow of Carreau–Yasuda fluid with radiative heat flux and chemical reaction. Eur. Phys. J. Plus 135, 516 (2020). https://doi.org/10.1140/epjp/s13360-020-00532-3

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