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Impacts of Stefan Blowing on Reiner–Rivlin Fluid Flow Over Moving Rotating Disk with Chemical Reaction

  • Research Article-Mechanical Engineering
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Abstract

The rotating disk system is of great importance in the context of its many practical scientific applications associated with mechanical and industrial engineering. The purpose of this study is to examine the impacts of Stefan blowing on the 3-D Reiner–Rivlin (R–R) fluid flow over a rotating disk moving in the vertical direction. Chemical reaction is accommodated in the energy equation, and partial slip effects are ignored at the disk surface. Cattaneo–Christov (CC) energy diffusion model is incubated to study heat and mass transmission. The boundary value problem (BVP) Midrich scheme is employed in Maple software to numerically solve the formulated system. The significant impacts of incorporated parameters versus involved fields are demonstrated graphically. The outcomes show that Reiner–Rivlin parameters cause a decline in tangential and radial velocity profiles along with temperature and concentration fields, both with the vertical movement of the disk or no movement with a marked difference in numerical values. Also, the heat and mass transfer rate increases with Stefan blowing parameter while a reverse trend is observed for local skin friction coefficients described in the tabular way. The vertical movement of the disk has a mixed effect on involved fields, namely velocity, temperature and concentration. The current model is calibrated by comparing the reduced form of the study to an already published literature, and a close congruence is found.

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References

  1. Northrop, A.; Owen, J.: Heat transfer measurements in rotating-disc systems part 1: the free disc. Int. J. Heat Fluid Flow 9(1), 19–26 (1988)

    Google Scholar 

  2. Northrop, A.; Owen, J.: Heat transfer measurements in rotating-disc systems Part 2: the rotating cavity with a radial outflow of cooling air. Int. J. Heat Fluid Flow 9(1), 27–36 (1988)

    Google Scholar 

  3. Childs, P.R.: Rotating Flow. Elsevier, Amsterdam (2010)

    Google Scholar 

  4. Rashed, M.K.; Abdulbari, H.A.; Salled, M.; Ismail, M.: Rotating disc apparatus: types, developments and future applications. Mod. Appl. Sci. 10(8), 198–229 (2016)

    Google Scholar 

  5. Kármán, V.: Uber laminare und turbulente Reibung. Z. Angew. Math. Mech. 1, 233–252 (1921)

    MATH  Google Scholar 

  6. Cochran, W.: The flow due to a rotating disc. Math. Proc. Camb. Philos. Soc. 30, 365–375 (1934)

    MATH  Google Scholar 

  7. Benton, E.R.: On the flow due to a rotating disk. J. Fluid Mech. 24(4), 781–800 (1966)

    MATH  Google Scholar 

  8. Stuart, J.: On the effects of uniform suction on the steady flow due to a rotating disk. Q. J. Mech. Appl. Math. 7(4), 446–457 (1954)

    MathSciNet  Google Scholar 

  9. Wagner, C.: Heat transfer from a rotating disk to ambient air. J. Appl. Phys. 19(9), 837–839 (1948)

    Google Scholar 

  10. Millsaps, K.; Pohlhausen, K.: Heat transfer by laminar flow from a rotating plate. J. Aeronaut. Sci. 19(2), 120–126 (1952)

    MathSciNet  MATH  Google Scholar 

  11. Cobb, E.; Saunders, O.: Heat transfer from a rotating disk. Proc. R. Soc. Lond. A 236(1206), 343–351 (1956)

    Google Scholar 

  12. Sparrow, E.; Gregg, J.: Heat transfer from a rotating disk to fluids of any Prandtl number. J. Heat Transf. 81(3), 249–251 (1959)

    Google Scholar 

  13. Sparrow, E.; Gregg, J.: Mass transfer, flow, and heat transfer about a rotating disk. J. Heat Transf. 82, 294–302 (1960)

    Google Scholar 

  14. Sharma, K.; Vijay, N.; Makinde, O.D.; Bhardwaj, S.B.; Singh, R.M.; Mabood, F.: Boundary layer flow with forced convective heat transfer and viscous dissipation past a porous rotating disk. Chaos Solitons Fractals 148, 111055 (2021)

    MathSciNet  Google Scholar 

  15. Sharma, K.; Vijay, N.; Kumar, S.; Makinde, O.D.: Hydromagnetic boundary layer flow with heat transfer past a rotating disc embedded in a porous medium. Heat Transf. Asian Res. 50(5), 4342–4353 (2021)

    Google Scholar 

  16. Sharma, K.: Rheological effects on boundary layer flow of ferrofluid with forced convective heat transfer over an infinite rotating disk. Pramana 95(3), 1–9 (2021)

    MathSciNet  Google Scholar 

  17. Nellis, G.; Hughes, C.; Pfotenhauer, J.: Heat transfer coefficient measurements for mixed gas working fluids at cryogenic temperatures. Cryogenics 45(8), 546–556 (2005)

    Google Scholar 

  18. Lienhard, I.; John, H.: A Heat Transfer Textbook. Phlogiston Press (2005)

  19. Fang, T.: Flow and mass transfer for an unsteady stagnation-point flow over a moving wall considering blowing effects. J. Fluids Eng. 136(7), 071103 (2014)

    Google Scholar 

  20. Fang, T.; Jing, W.: Flow, heat, and species transfer over a stretching plate considering coupled Stefan blowing effects from species transfer. Commun. Nonlinear Sci. Numer. Simul. 19(9), 3086–3097 (2014)

    MathSciNet  MATH  Google Scholar 

  21. Latiff, N.; Uddin, M.; Ismail, A.M.: Stefan blowing effect on bioconvective flow of nanofluid over a solid rotating stretchable disk. Propuls. Power Res. 5(4), 267–278 (2016)

    Google Scholar 

  22. Uddin, M.J.; Kabir, M.; Bég, O.A.: Computational investigation of Stefan blowing and multiple-slip effects on buoyancy-driven bioconvection nanofluid flow with microorganisms. Int. J. Heat Mass Transf. 95, 116–130 (2016)

    Google Scholar 

  23. Zohra, F.; Uddin, M.; Ismail, A.; Bég, O.A.; Kadir, A.: Anisotropic slip magneto-bioconvection flow from a rotating cone to a nanofluid with Stefan blowing effects. Chin. J. Phys. 56(1), 432–448 (2018)

    Google Scholar 

  24. Tuz Zohra, F.; Uddin, M.J.; Basir, M.F.; Ismail, A.I.M.: Magnetohydrodynamic bio-nano-convective slip flow with Stefan blowing effects over a rotating disc. Proc. Inst. Mech. Eng. Part N J. Nanomater. Nanoeng. Nanosyst. 234(3–4), 83–97 (2020)

    Google Scholar 

  25. Hoseinzadeh, S.; Sohani, A.; Shahverdian, M.H.; Shirkhani, A.; Heyns, S.: Acquiring an analytical solution and performing a comparative sensitivity analysis for flowing Maxwell upper-convected fluid on a horizontal surface. Therm. Sci. Eng. Prog. 23, 100901 (2021)

    Google Scholar 

  26. Mabood, F.; Rauf, A.; Prasannakumara, B.; Izadi, M.; Shehzad, S.: Impacts of Stefan blowing and mass convention on flow of Maxwell nanofluid of variable thermal conductivity about a rotating disk. Chin. J. Phys. 71, 260–272 (2021)

    MathSciNet  Google Scholar 

  27. Bég, O.A.; Kabir, M.N.; Uddin, M.J.; Izani Md Ismail, A.; Alginahi, Y.M.: Numerical investigation of Von Karman swirling bioconvective nanofluid transport from a rotating disk in a porous medium with Stefan blowing and anisotropic slip effects. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 235(19), 3933–3951 (2021)

    Google Scholar 

  28. Hoseinzadeh, S.; Sohani, A.; Ashrafi, T.G.: An artificial intelligence-based prediction way to describe flowing a Newtonian liquid/gas on a permeable flat surface. J. Therm. Anal. Calorim. 147(6), 4403–4409 (2022)

    Google Scholar 

  29. Kandasamy, R.; Hashim, I.; et al.: Effect of chemical reaction, heat and mass transfer on nonlinear boundary layer past a porous shrinking sheet in the presence of suction. Nucl. Eng. Des. 240(5), 933–939 (2010)

    Google Scholar 

  30. Krishnamurthy, M.; Prasannakumara, B.; Gireesha, B.; Gorla, R.S.R.: Effect of chemical reaction on MHD boundary layer flow and melting heat transfer of Williamson nanofluid in porous medium. Eng. Sci. Technol. Int. J. 19(1), 53–61 (2016)

    Google Scholar 

  31. Hayat, T.; Muhammad, T.; Shehzad, S.A.; Alsaedi, A.; Al-Solamy, F.: Radiative three-dimensional flow with chemical reaction. Int. J. Chem. Reactor Eng. 14(1), 79–91 (2016)

    Google Scholar 

  32. Cattaneo, C.: Sulla conduzione del calore. Atti Sem. Mat. Fis. Univ. Modena 3, 83–101 (1948)

    MathSciNet  MATH  Google Scholar 

  33. Christov, C.: On frame indifferent formulation of the Maxwell–Cattaneo model of finite-speed heat conduction. Mech. Res. Commun. 36(4), 481–486 (2009)

    MathSciNet  MATH  Google Scholar 

  34. Ciarletta, M.; Straughan, B.: Uniqueness and structural stability for the Cattaneo–Christov equations. Mech. Res. Commun. 37(5), 445–447 (2010)

    MATH  Google Scholar 

  35. Hayat, T.; Qayyum, S.; Imtiaz, M.; Alsaedi, A.: Flow between two stretchable rotating disks with Cattaneo–Christov heat flux model. Results Phys. 7, 126–133 (2017)

    Google Scholar 

  36. Hafeez, A.; Khan, M.; Ahmed, J.: Flow of Oldroyd-B fluid over a rotating disk with Cattaneo–Christov theory for heat and mass fluxes. Comput. Methods Programs Biomed. 191, 105374 (2020)

    Google Scholar 

  37. Ghasemi, M.H.; Hoseinzadeh, S.; Heyns, P.S.; Wilke, D.N.: Numerical analysis of non-Fourier heat transfer in a solid cylinder with dual-phase-lag phenomenon. Comput. Model. Eng. Sci. 122, 399–414 (2020)

    Google Scholar 

  38. Waqas, H.; Khan, S.A.; Bhatti, M.; Hussain, S.: Bioconvection mechanism using third-grade nanofluid flow with Cattaneo–Christov heat flux model and Arrhenius kinetics. Int. J. Mod. Phys. B 35(17), 2150178 (2021)

    MathSciNet  MATH  Google Scholar 

  39. Ali, Z.; Zeeshan, A.; Bhatti, M.; Hobiny, A.; Saeed, T.: Insight into the dynamics of Oldroyd-B fluid over an upper horizontal surface of a paraboloid of revolution subject to chemical reaction dependent on the first-order activation energy. Arab. J. Sci. Eng. 46(6), 6039–6048 (2021)

    Google Scholar 

  40. Ghasemi, M.H.; Hoseinzadeh, S.; Memon, S.: A dual-phase-lag (DPL) transient non-Fourier heat transfer analysis of functional graded cylindrical material under axial heat flux. Int. Commun. Heat Mass Transfer 131, 105858 (2022)

    Google Scholar 

  41. Turkyilmazoglu, M.: Fluid flow and heat transfer over a rotating and vertically moving disk. Phys. Fluids 30(6), 063605 (2018)

    Google Scholar 

  42. Shehzad, S.; Abbas, Z.; Rauf, A.; Abdelmalek, Z.: Dynamics of fluid flow through Soret-Dufour impacts subject to upward and downward motion of rotating disk. Int. Commun. Heat Mass Transf. 120, 105025 (2021)

    Google Scholar 

  43. Jayadevamurthy, P.G.R.; Rangaswamy, N.K.; Prasannakumara, B.C.; Nisar, K.S.: Emphasis on unsteady dynamics of bioconvective hybrid nanofluid flow over an upward–downward moving rotating disk. Numer. Methods Partial Differ. Equ. (2020)

  44. Khan, M.; Ahmed, J.; Ali, W.; Nadeem, S.: Chemically reactive swirling flow of viscoelastic nanofluid due to rotating disk with thermal radiations. Appl. Nanosci. 10(12), 5219–5232 (2020)

    Google Scholar 

  45. Khan, M.; Ahmed, J.; Ali, W.: Thermal analysis for radiative flow of magnetized Maxwell fluid over a vertically moving rotating disk. J. Therm. Anal. Calorim. 143(6), 4081–4094 (2021)

    Google Scholar 

  46. Sharma, K.; Kumar, S.; Vijay, N.: Numerical simulation of MHD heat and mass transfer past a moving rotating disk with viscous dissipation and ohmic heating. Multidiscip. Model. Mater. Struct. 18(1), 153–165 (2021)

    Google Scholar 

  47. Kumar, S.; Sharma, K.: Entropy optimized radiative heat transfer of hybrid nanofluid over vertical moving rotating disk with partial slip. Chin. J. Phys. 77, 861–873 (2022)

    MathSciNet  Google Scholar 

  48. Reiner, M.: A mathematical theory of dilatancy. Am. J. Math. 67(3), 350–362 (1945)

    MathSciNet  MATH  Google Scholar 

  49. Rivlin, R.: Hydrodynamics of non-Newtonian fluids. Nature 160(4070), 611 (1947)

    MathSciNet  Google Scholar 

  50. Tabassum, M.; Mustafa, M.: A numerical treatment for partial slip flow and heat transfer of non-Newtonian Reiner–Rivlin fluid due to rotating disk. Int. J. Heat Mass Transf. 123, 979–987 (2018)

    Google Scholar 

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  1. Malaviya National Institute of Technology, Jaipur, 302017, India

    Sanjay Kumar & Kushal Sharma

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  1. Sanjay Kumar
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  2. Kushal Sharma
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Correspondence to Kushal Sharma.

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Kumar, S., Sharma, K. Impacts of Stefan Blowing on Reiner–Rivlin Fluid Flow Over Moving Rotating Disk with Chemical Reaction. Arab J Sci Eng 48, 2737–2746 (2023). https://doi.org/10.1007/s13369-022-07008-9

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  • DOI: https://doi.org/10.1007/s13369-022-07008-9

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