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Arrhenius activated energy impacts on irreversibility optimization due to unsteady stagnation point flow of radiative Casson nanofluids

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Abstract

This paper aims to examine the influences of a binary chemical reaction and Arrhenius activated energy on the unsteady external flow with a stagnation point over a vertical stretched surface. The worked suspension is Casson non-Newtonian nanofluids, and two-phase nanofluid formulation is considered. Here, the nanoparticles near the surface are passively controlled, and the viscous dissipation and Joule heating impacts are assumed. Non-similar solutions are introduced and solved using Blottner technique based on finite difference method. It is focused on the system entropy, thickness of the thermal and mass boundary layers. The major findings show that the radiation parameter enhances the irreversibility owing to the heat transfer, and hence, the Bejan coefficient is rising. Also, the velocity ratio rising causes a diminishing in the skin friction coefficient.

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References

  1. R. Saidur, K.Y. Leong, H. Mohammad, A review on applications and challenges of nanofluids. Renew. Sustain. Energy Rev. 15, 1646–1668 (2011)

    Article  Google Scholar 

  2. B. Xiao, X. Zhang, W. Wang, G. Long, H. Chen, H. Kang, W. Ren, A fractal model for water flow through unsaturated porous rocks. Fractals 26, 1840015 (2018)

    Article  ADS  MATH  Google Scholar 

  3. G. Long, G. Xu, The effects of perforation erosion on practical hydraulic-fracturing applications. SPE J. 22, 645–659 (2017)

    Article  Google Scholar 

  4. K.V. Wong, O. De Leon, Applications of nanofluids: Current and future. Adv. Mech. Eng. 2, 519659 (2010)

    Article  Google Scholar 

  5. S.U.S. Choi, J.A. Estman, Enhancing thermal conductivity of fluids with nanoparticles. ASME-Publ. Fed 231, 99–106 (1995)

    Google Scholar 

  6. J. Buongiorno, Convective transport in nanofluids. J. Heat Transf. 128, 240–250 (2006)

    Article  Google Scholar 

  7. W.A. Khan, I. Pop, Boundary-layer flow of a nanofluid past a stretching sheet. Int. J. Heat Mass Transf. 53, 2477–2483 (2010)

    Article  MATH  Google Scholar 

  8. O.D. Makinde, A. Aziz, Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. Int. J. Therm. Sci. 50, 1326–1332 (2011)

    Article  Google Scholar 

  9. M. Sheikholeslami, A. Shafee, M. Ramzan, Z. Li, Investigation of Lorentz forces and radiation impacts on nanofluid treatment in a porous semi annulus via Darcy law. J. Mol. Liquids 272, 8–14 (2018)

    Article  Google Scholar 

  10. Z. Li, M. Sheikholeslami, A. Shafee, M. Ramzan, R. Kandasamy, Q.M. Al-Mdallal, Influence of adding nanoparticles on solidification in a heat storage system considering radiation effect. J. Mol. Liquids 273, 589–605 (2018)

    Article  Google Scholar 

  11. T. Muhammad, D.-C. Lu, B. Mahanthesh, M.R. Eid, M. Ramzan, A. Dar, Significance of Darcy-Forchheimer porous medium in nanofluid through carbon nanotubes. Commun. Theor. Phys. 70, 361 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  12. A.A.M. Arafa, Z.Z. Rashed, S.E. Ahmed, Radiative MHD bioconvective nanofluid flow due to gyrotactic microorganisms using Atangana-Baleanu Caputo fractional derivative. Phys. Scr. 96(5), 055211 (2021)

    Article  ADS  Google Scholar 

  13. M. Ramzan, N. Ullah, J.D. Chung, D. Lu, U. Farooq, Buoyancy effects on the radiative magneto Micropolar nanofluid flow with double stratification, activation energy and binary chemical reaction. Sci. Rep. 7, 12901 (2017)

    Article  ADS  Google Scholar 

  14. A.A.M. Arafa, Z.Z. Rashed, S.E. Ahmed, Radiative flow of non Newtonian nanofluids within inclined porous enclosures with time fractional derivative. Sci. Rep. 11(1), 1–18 (2021)

    Article  Google Scholar 

  15. Z. Li, M. Ramzan, A. Shafee, S. Saleem, Q.M. Al-Mdallal, A.J. Chamkha, Numerical approach for nanofluid transportation due to electric force in a porous enclosure. Microsyst. Technol. 25, 1–14 (2018)

    Google Scholar 

  16. A.A.M. Arafa, S.E. Ahmed, M.M. Allan, Peristaltic flow of non-homogeneous nanofluids through variable porosity and heat generating porous media with viscous dissipation: entropy analyses. Case Stud. Thermal Eng. 32, 101882 (2022)

    Article  Google Scholar 

  17. D. Zhang, Y. Shen, Z. Zhou, J. Qu, L. Zhou, J. Wang, F. Zhang, Convection heat transfer performance of fractal tube bank under cross flow. Fractals (2018). https://doi.org/10.1142/S0218348X18500731

    Article  Google Scholar 

  18. S.E. Ahmed, A.A.M. Arafa, S.A. Hussein, MHD Ellis nanofluids flow around rotating cone in the presence of motile oxytactic microorganisms. Int. Commun. Heat Mass Transf. 134, 106056 (2022)

    Article  Google Scholar 

  19. A. Bejan, Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-size Systems and Finite-time Processes (CRC Press, 2013)

    Book  MATH  Google Scholar 

  20. H. Sithole, H. Mondal, P. Sibanda, Entropy generation in a second grade magnetohydrodynamic nanofluid flow over a convectively heated stretching sheet with nonlinear thermal radiation and viscous dissipation. Results Phys. 9, 1077–1085 (2018)

    Article  ADS  Google Scholar 

  21. N. Dalir, M. Dehsara, S.S. Nourazar, Entropy analysis for magnetohydrodynamic flow and heat transfer of a jeffrey nanofluid over a stretching sheet. Energy 79, 351–362 (2015)

    Article  Google Scholar 

  22. M.M. Rashidi, M. Ali, N. Freidoonimehr, F. Nazari, Parametric analysis and optimization of entropy generation in unsteady mhd flow over a stretching rotating disk using artificial neural network and particle swarm optimization algorithm. Energy 55, 497–510 (2013)

    Article  Google Scholar 

  23. G. Ibánez, S. Cuevas, Entropy generation minimization of a mhd (magnetohydrodynamic) flow in a microchannel. Energy 35(10), 4149–4155 (2010)

    Article  Google Scholar 

  24. F. Mabood, R.G. Abdel-Rahman, G. Lorenzini, Effect of melting heat transfer and thermal radiation on Casson fluid flow in porous medium over moving surface with magnetohydrodynamic. J. Eng. Thermophys. 28(6), 1925–1932 (2016)

    Google Scholar 

  25. K.G. Kumar, Exploration of flow and heat transfer of non-Newtonian nanofluid over a stretching sheet by considering slip factor. Int. J. Num. Methods Heat Fluid Flow. 30(4), 1991–2001 (2019)

    Article  Google Scholar 

  26. F. Mabood, M. Imtiaz, T. Hayat, A. Alsaedi, Unsteady convective boundary layer flow of Maxwell fluid with nonlinear thermal radiation: a numerical study. Int. J. Nonlinear Sci. Num. Simul. 17(5), 221–229 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  27. R. Naz, F. Mabood, M. Sohail, I. Tlili, Thermal and species transportation of Eyring-Powell material over a rotating disk with swimming microorganisms: applications to metallurgy. J. Mater. Res. Technol. 9(3), 5577–5590 (2020)

    Article  Google Scholar 

  28. M. Archana, M.M. Praveena, K.G. Kumar, S.A. Shehzad, M. Ahmad, unsteady squeezed Casson nanofluid flow by considering the slip condition and time-dependent magnetic field. Heat Transf. 49(8), 4907–4922 (2020)

    Article  Google Scholar 

  29. T.A. Yusuf, F. Mabood, Slip effects and entropy generation on inclined MHD flow of Williamson fluid through a permeable wall with chemical reaction via DTM. Math. Model. Eng. Prob. 7(1), 1–9 (2020)

    Google Scholar 

  30. L.J. Crane, Flow past a stretching plate, Zeitsch. Angew. Math. Phys. ZAMP 21(4), 645–647 (1970)

    ADS  Google Scholar 

  31. P.S. Gupta, A.S. Gupta, Heat and mass transfer on a stretching sheet with suction or blowing. Can. J. Chem. Eng. 55(6), 744–746 (1977)

    Article  Google Scholar 

  32. E. Magyari, B. Keller, Heat, and mass transfer in the boundary layers on an exponentially stretching continuous surface. J. Phys. D. Appl. Phys. 32(5), 577 (1999)

    Article  ADS  Google Scholar 

  33. E.M.A. Elbashbeshy, Heat transfer over an exponentially stretching continuous surface with suction. Arch. Mech. 53(6), 643–651 (2001)

    MATH  Google Scholar 

  34. A. Zeeshan, M.M. Maskeen, O.U. Mehmood, Hydromagnetic nanofluid flow past a stretching cylinder embedded in non-Darcian Forchheimer porous media. Neural Comput. Applic. 30(11), 3479–3489 (2018)

    Article  Google Scholar 

  35. A. Ahmad, S. Asghar, Flow and heat transfer over hyperbolic stretching sheets. Appl. Math. Mech. 33(4), 445–454 (2012)

    Article  MathSciNet  Google Scholar 

  36. F.U. Rehman, S. Nadeem, R.U. Haq, Heat transfer analysis for three-dimensional stagnation-point flow over an exponentially stretching surface. Chin. J. Phys. 55(4), 1552–1560 (2017)

    Article  Google Scholar 

  37. K.R. Rajagopal, A.S. Gupta, An exact solution for the flow of a non-Newtonian fluid past an infinite porous plate. Meccanica 19(2), 158–160 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  38. H.I. Andersson, V. Kumaran, On sheet-driven motion of power-law fluids. Int. J. Non-Linear Mech. 41(10), 1228–1234 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. M. Jalil, S. Asghar, M. Mushtaq, Analytical solutions of the boundary layer flow of power-law fluid over a power-law stretching surface. Commun. Nonlinear Sci. Numer. Simul. 18(5), 1143–1150 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. A. Hussain, M.Y. Malik, M. Awais, T. Salahuddin, S. Bilal, Computational and physical aspects of MHD Prandtl-Eyring fluid flow analysis over a stretching sheet. Neural Comput. Applic. 31(1), 425–433 (2019)

    Article  Google Scholar 

  41. A.R. Bestman, Natural convection boundary layer with suction and mass transfer in a porous medium. Int. J. Energy Res. 14(4), 389–396 (1990)

    Article  Google Scholar 

  42. A. Zeeshan, N. Shehzad, R. Ellahi, Analysis of activation energy in Couette- Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions. Results Phys. 8, 502–512 (2018)

    Article  ADS  Google Scholar 

  43. M.D. Shamshuddin, F. Mabood, A numerical model for analysis of binary chemical reaction and activation energy of thermo solutal micropolar nanofluid flow through permeable stretching sheet: nanoparticle study. Phys. Scr. 96(7), 075206 (2021)

    Article  Google Scholar 

  44. M. Mustafaa, T. Hayat, S. Obaidat, Boundary layer flow of a nanofluid over an exponentially stretching sheet with convective boundary conditions. Int. J. Num. Methods Heat Fluid Flow 23, 945–959 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  45. S.T. Mohyud-Din, U. Khan, N. Ahmed, B. Bin-Mohsin, Heat and mass transfer analysis for MHD flow of nanofluid in convergent/divergent channels with stretchable walls using Buongiorno’s model. Neural Comput. Applic. 28(12), 4079–4092 (2017)

    Article  Google Scholar 

  46. S.M. Rassoulinejad-Mousavi, H.R. Seyf, S. Abbasbandy, Heat transfer through a porous saturated channel with permeable walls using two-equation energy model. J. Porous Media 16(3), 241–254 (2013)

    Article  Google Scholar 

  47. F.G. Awad, S. Motsa, M. Khumalo, Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy. PLoS One 9(9), e107622 (2014)

    Article  ADS  Google Scholar 

  48. Z. Shafique, M. Mustafa, A. Mushtaq, Boundary layer flow of Maxwell fluid in rotating frame with binary chemical reaction and activation energy. Results Phys. 6, 627–633 (2016)

    Article  ADS  Google Scholar 

  49. D. Pal, H. Mondal, Influence of chemical reaction and thermal radiation on mixed convection heat and mass transfer over a stretching sheet in Darcian porous medium with Soret and Dufour effects. Energy Convers. Manag. 2, 102–108 (2012)

    Article  Google Scholar 

  50. S. Abdal, S. Hussain, I. Siddique, A. Ahmadian, M. Ferrara, On solution existence of MHD Casson nanofluid transportation across an extending cylinder through porous media and evaluation of priori bounds. Sci. Rep. 11(1), 7799 (2021)

    Article  ADS  Google Scholar 

  51. A.M. Jyothi, R.N. Kumar, R.P. Gowda, B.C. Prasannakumara, Significance of Stefan blowing effect on flow and heat transfer of Casson nanofluid over a moving thin needle. Commun. Theor. Phys. 73, 095005 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  52. C. Fetecau, R. Ellahi, S.M. Sait, Mathematical analysis of Maxwell fluid flow through a porous plate channel induced by a constantly accelerating or oscillating wall. Math. 9, 90 (2021)

    Article  Google Scholar 

  53. Z. Abbas, M. Sheikh, S.S. Motsa, Numerical solutionof binary chemical reaction on stagnation pointflow of Casson fluid over a stretching/shrinking sheetwith thermal radiation. Energy 95, 12 (2016)

    Article  Google Scholar 

  54. J.C. Williams, T.B. Rhyne, Boundary layerdevelopment on a wedge impulsively set into motion. SIAM J. Appl. Math. 38, 215 (1980)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  55. S.Z. Shuja, B.S. Yilbas, M.O. Budair, Natural convectionin a square cavity with a heat generating body:entropy consideration. Heat Mass Transf. 36, 343 (2000)

    Article  ADS  Google Scholar 

  56. H.F. Oztop, K.A. Al-Salem, Review on entropy generationin natural and mixed convection heat transferfor energy systems”. Renew. Sustain. Energy Rev. 16, 911 (2012)

    Article  Google Scholar 

  57. C.Y. Wang, Stagnation flow towards a shrinking sheet. Int. J. Non-Linear Mech. 43, 377 (2008)

    Article  ADS  Google Scholar 

  58. K. Bhattacharyya, T. Hayat, A. Alsaedi, Analyticsolution for magnetohydrodynamic boundarylayer flow of Casson fluid over a stretching/shrinkingsheet with wall mass transfer. Chin. Phys. B 22, 024702 (2013)

    Article  Google Scholar 

  59. Z. Abbas, M. Sheikh, I. Pop, Stagnation-point flow of a hydromagnetic viscous fluid over stretching/shrinking sheet with generalized slip condition in the presence of homogeneous–heterogeneous reactions. J. Taiwan Inst. Chem. Eng. 55, 69 (2015)

    Article  Google Scholar 

  60. I.S. Oyelakin, H. Sithole Mthethwa, Peri K. Kameswaran, S. Shaw, P. Sibanda. Entropy generation optimization for unsteady stagnation Casson nanofluid flow over a stretching sheet with binary chemical reaction and Arrhenius activation energy using bivariate spectral quasi- linearization method. International Journal of Ambient Energy. (2021), Online

  61. F.G. Blottner, Finite difference methods of solution of the boundary-layer equations, 8 (1970) 193–205

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Large Groups Project under grant number (R.G.P2/22/43).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Khalid University, Abha, 62529, Saudi Arabia

    Sameh E. Ahmed

  2. Department of Mathematics, Faculty of Science, South Valley University, Qena, 83523, Egypt

    Sameh E. Ahmed

  3. Department of Mathematics, College of Science and Arts, Qassim University, Al Mithnab, Saudi Arabia

    Anas A. M. Arafa

  4. Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, Egypt

    Anas A. M. Arafa

  5. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

    Sameh A. Hussein

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Ahmed, S.E., Arafa, A.A.M. & Hussein, S.A. Arrhenius activated energy impacts on irreversibility optimization due to unsteady stagnation point flow of radiative Casson nanofluids. Eur. Phys. J. Plus 137, 1222 (2022). https://doi.org/10.1140/epjp/s13360-022-03434-8

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