Entropy optimization and Sisko material flow with nonlinear radiative heat flux and heat source/sink

  • T. Hayat
  • M. Waleed Ahmed Khan
  • M. Ijaz KhanEmail author
  • A. Alsaedi
Technical Paper


The present article illustrates the salient features of entropy optimization for flow of Sisko fluid. Fluid motion in this problem is due to rotating stretchable disk. The fluid properties are discussed in the presence of nonlinear mixed convection, Brownian motion and viscous dissipation. Entropy generation is calculated and analyzed graphically. Heat transfer is analyzed for nonlinear thermal radiation, thermophoresis parameter and heat source/sink. These governing equations are tackled for convergent series solutions. Results are shown graphically. Comparison has been made with the existing literature in the limiting cases.


Sisko fluid Rotating stretchable disk Nonlinear thermal radiation and heat source/sink Nonlinear mixed convection Brownian motion and thermophoresis forces Entropy generation 


  1. 1.
    Karman TV (1921) Uber laminare und turbulente Reibung. ZAMM-J Appl Math Mech/Z für Angew Math und Mech 1(4):233–252CrossRefzbMATHGoogle Scholar
  2. 2.
    Turkyilmazoglu M (2012) MHD fluid flow and heat transfer due to a stretching rotating disk. Int J Therm Sci 51:195–201CrossRefGoogle Scholar
  3. 3.
    Turkyilmazoglu M (2015) Bödewadt flow and heat transfer over a stretching stationary disk. Int J Mech Sci 90:246–250CrossRefGoogle Scholar
  4. 4.
    Hayat T, Qayyum S, Imtiaz M, Alsaedi A (2017) Flow between two stretchable rotating disks with Cattaneo–Christov heat flux model. Results Phys 7:126–133CrossRefGoogle Scholar
  5. 5.
    Li X, Faghri A (2011) Local entropy generation analysis on passive high-concentration DMFCs (direct methanol fuel cell) with different cell structures. Energy 36:403–414CrossRefGoogle Scholar
  6. 6.
    Oztop HF, Salem KA (2012) A review on entropy generation in natural and mixed convection heat transfer for energy systems. Renew Sustain Energy Rev 16:911–920CrossRefGoogle Scholar
  7. 7.
    Bejan A (1979) A study of entropy generation in fundamental convective heat transfer. J Heat Transf 101(4):718–725CrossRefGoogle Scholar
  8. 8.
    Bejan A (1996) Entropy Generation minimization: the method of thermodynamic optimization of finite-size systems and finite-time processes. CRC Press, Boca RatonzbMATHGoogle Scholar
  9. 9.
    Aïboud S, Saouli S (2010) Second law analysis of viscoelastic fluid over a stretching sheet subject to a transverse magnetic field with heat and mass transfer. Entropy 12(8):1867–1884CrossRefGoogle Scholar
  10. 10.
    Hayat T, Khan MI, Qayyum S, Alsaedi A (2018) Entropy generation in flow with silver and copper nanoparticles. Colloids Surf A 539:335–346CrossRefGoogle Scholar
  11. 11.
    Aïboud S, Saouli S (2010) Entropy analysis for viscoelastic magnetohydrodynamic flow over a stretching surface. Int J Non Linear Mech 45:482–489CrossRefGoogle Scholar
  12. 12.
    Butt AS, Munawar S, Ali A, Mehmood A (2012) Entropy generation in the Blasius flow under thermal radiation. Phys Scr 85:035008CrossRefzbMATHGoogle Scholar
  13. 13.
    San JY, Worek WM, Lavan Z (1987) Entropy generation in combined heat and mass transfer. Int J Heat Mass Transf 30:1359–1369CrossRefGoogle Scholar
  14. 14.
    Mahanthesh B, Gireesha BJ, Shehzad SA, Rauf A, Sampath Kumar PB (2018) Nonlinear radiated MHD flow of nanoliquids due to a rotating disk with irregular heat source and heat flux condition. Phys B 537:98–104CrossRefGoogle Scholar
  15. 15.
    Hayat T, Khan MI, Farooq M, Alsaedi A, Yasmeen T (2017) Impact of Marangoni convection in the flow of carbon–water nanofluid with thermal radiation. Int J Heat Mass Transf 106:810–815CrossRefGoogle Scholar
  16. 16.
    Khan MI, Khan MI, Waqas M, Hayat T, Alsaedi A (2017) Chemically reactive flow of Maxwell liquid due to variable thicked surface. Int Commun Heat Mass Transf 86:231–238CrossRefGoogle Scholar
  17. 17.
    Khan MWA, Waqas M, Khan MI, Alsaedi A, Hayat T (2017) MHD stagnation point flow accounting variable thickness and slip conditions. Colloid Polym Sci 295:1201–1209CrossRefGoogle Scholar
  18. 18.
    Hayat T, Khan MI, Waqas M, Alsaedi A, Khan MI (2017) Radiative flow of micropolar nanofluid accounting thermophoresis and Brownian moment. Int J Hydrogen Energy 42:16821–16833CrossRefGoogle Scholar
  19. 19.
    Sheikholeslami M (2017) Magnetic field influence on CuO–H2O nanofluid convective flow in a permeable cavity considering various shapes for nanoparticles. Int J Hydrogen Energy 42:19611–19621CrossRefGoogle Scholar
  20. 20.
    Khan MI, Waqas M, Hayat T, Alsaedi A, Khan MI (2017) Significance of nonlinear radiation in mixed convection flow of magneto Walter-B nanoliquid. Int J Hydrogen Energy 42:26408–26416CrossRefGoogle Scholar
  21. 21.
    Hayat T, Khan MI, Farooq M, Alsaedi A, Waqas M, Yasmeen T (2016) Impact of Cattaneo–Christov heat flux model in flow of variable thermal conductivity fluid over a variable thicked surface. Int J Heat Mass Transf 99:702–710CrossRefGoogle Scholar
  22. 22.
    Javed MF, Khan MI, Khan NB, Muhammad R, Rehmand MU, Khan SW, Khan TA (2018) Axisymmetric flow of Casson fluid by a swirling cylinder. Results Phys 9:1250–1255CrossRefGoogle Scholar
  23. 23.
    Hayat T, Khan MI, Farooq M, Yasmeen T, Alsaedi A (2016) Stagnation point flow with Cattaneo–Christov heat flux and homogeneous-heterogeneous reactions. J Mol Liq 220:49–55CrossRefGoogle Scholar
  24. 24.
    Khan NB, Ibrahim Z, Nguyen LTT, Javed MF, Jameel M (2017) Numerical investigation of the vortex-induced vibration of an elastically mounted circular cylinder at high Reynolds number (Re = 104) and low mass ratio using the RANS code. PLoS ONE 12:e0185832CrossRefGoogle Scholar
  25. 25.
    Khan MI, Waqas M, Hayat T, Alsaedi A (2017) A comparative study of Casson fluid with homogeneous-heterogeneous reactions. J Colloid Interface Sci 498:85–90CrossRefGoogle Scholar
  26. 26.
    Khan NB, Ibrahim Z, Khan MI, Hayat T, Javed MF (2018) VIV study of an elastically mounted cylinder having low mass-damping ratio using RANS model. Int J Heat Mass Transf 121:309–314CrossRefGoogle Scholar
  27. 27.
    Khan MI, Waqas M, Hayat T, Khan MI, Alsaedi A (2017) Behavior of stratification phenomenon in flow of Maxwell nanomaterial with motile gyrotactic microorganisms in the presence of magnetic field. Int J Mech Sci 132:426–434CrossRefGoogle Scholar
  28. 28.
    Khan NB, Ibrahim Z, Badry ABBM, Jameel M, Javed MF (2018) Numerical investigation of flow around cylinder at Reynolds number = 3900 with large eddy simulation technique: effect of spanwise length and mesh resolution. Proc Inst Mech Eng Part M J Eng Marit Environ. Google Scholar
  29. 29.
    Khan MI, Hayat T, Khan MI, Alsaedi A (2016) Activation energy impact in nonlinear radiative stagnation point flow of cross nanofluid. Int Commun Heat Mass Transf 91:216–224CrossRefGoogle Scholar
  30. 30.
    Khan NB, Ibrahim Z (2018) Numerical investigation of vortex-induced vibration of an elastically mounted circular cylinder with One-degree of freedom at high Reynolds number using different turbulent models. Proc Inst Mech Eng Part M J Eng Marit Environ. Google Scholar
  31. 31.
    Hayat T, Tamoor M, Khan MI, Alsaedi A (2016) Numerical simulation for nonlinear radiative flow by convective cylinder. Results Phys 6:1031–1035CrossRefGoogle Scholar
  32. 32.
    Hayat T, Qayyum S, Khan MI, Alsaedi A (2018) Entropy generation in magnetohydrodynamic radiative flow due to rotating disk in presence of viscous dissipation and Joule heating. Phys Fluids 30:017101CrossRefGoogle Scholar
  33. 33.
    Hayat T, Khan MWA, Alsaedi A, Khan MI (2017) Corrigendum to Squeezing flow of second grade liquid subject to non-Fourier heat flux and heat generation/absorption. Colloid Polym Sci 295:2439Google Scholar
  34. 34.
    Waqas M, Khan MI, Hayat T, Alsaedi A, Khan MI (2017) On Cattaneo–Christov double diffusion impact for temperature-dependent conductivity of Powell-Eyring liquid. Chin J Phys 55:729–737CrossRefGoogle Scholar
  35. 35.
    Hayat T, Waqas M, Khan MI, Alsaedi A, Shehzad SA (2017) Magnetohydrodynamic flow of Burgers fluid with heat source and power law heat flux. Chin J Phys 55:318–330CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • T. Hayat
    • 1
    • 2
  • M. Waleed Ahmed Khan
    • 1
  • M. Ijaz Khan
    • 1
    Email author
  • A. Alsaedi
    • 2
  1. 1.Department of MathematicsQuaid-I-Azam UniversityIslamabadPakistan
  2. 2.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

Personalised recommendations