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Computational Investigation of Stefan Blowing Effect on Flow of Second-Grade Fluid Over a Curved Stretching Sheet

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Abstract

Non-Newtonian fluids have extensive range of applications in the field of industries like plastics processing, manufacturing of electronic devices, lubrication flows, medicine and medical equipment. Stimulated from these applications, a theoretical analysis is carried out to scrutinize the flow of a second-grade liquid over a curved stretching sheet with the impact of Stefan blowing condition, thermophoresis and Brownian motion. The modelled governing equations for momentum, thermal and concentration are deduced to a system of ordinary differential equations by introducing suitable similarity transformations. These reduced equations are solved using Runge–Kutta–Fehlberg fourth fifth order method (RKF-45) by adopting shooting technique. The solutions for the flow, heat and mass transference features are found numerically and presented with the help of graphical illustrations. Results reveal that, curvature and Stefan blowing parameters have propensity to rise the heat transfer. Further, second grade fluid shows high rate of mass and heat transfer features when related to Newtonian fluid for upsurge in values of Brownian motion parameter.

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Abbreviations

u, v :

Velocity components

C f :

Skin friction coefficient

a :

Stretching constant

r, s :

Coordinates

C :

Concentration

θ :

Dimensionless temperature

χ :

Non-dimensional concentration

D B :

Brownian diffusion coefficient

\(\alpha_{1}^{*}\) :

Second grade fluid parameter

ν f :

Kinematic viscosity

τ :

Ratio of the effective heat capacity

ω :

Stefan blowing parameter

R :

Distance

P :

Dimensionless pressure

C ∞ :

Ambient concentration

D T :

Thermophoresis diffusion co-efficient

Nu :

Nusselt number

\(f^{\prime }\) :

Dimensionless velocity

μ f :

Dynamic viscosity

τ rs :

Wall shear stress

P :

Pressure

κ :

Curvature parameter

T w :

Surface temperature

Sc :

Schmidt number

Pr:

Prandtl number

ρ f :

Density of liquid

T :

Temperature

N t :

Thermophoresis parameter

N b :

Brownian motion parameter

T ∞ :

Ambient temperature

Re:

Local Reynolds number

Sh :

Local Sherwood number

C w :

Surface concentration

q w :

Wall mass flux

\(\left( {\rho C_{p} } \right)_{f}\) :

Specific heat capacity

k f :

Thermal conductivity

References

  1. Hayat, T., Ahmad, S., Khan, M.I., Alsaedi, A.: Non-Darcy Forchheimer flow of ferromagnetic second grade fluid. Results Phys. 7, 3419–3424 (2017). https://doi.org/10.1016/j.rinp.2017.08.041

    Article  Google Scholar 

  2. Jamshed, W., Nisar, K.S., Gowda, R.J.P., Kumar, R.N., Prasannakumara, B.C.: Radiative heat transfer of second grade nanofluid flow past a porous flat surface: a single-phase mathematical model. Phys. Scr. 96(6), 064006 (2021). https://doi.org/10.1088/1402-4896/abf57d

    Article  Google Scholar 

  3. Sharma, B., Kumar, S., Cattani, C., Baleanu, D.: Nonlinear dynamics of Cattaneo–Christov heat flux model for third-grade power-law fluid. J. Comput. Nonlinear Dyn. (2019). https://doi.org/10.1115/1.4045406

    Article  Google Scholar 

  4. Riaz, M.B., Saeed, S.T., Baleanu, D.: Role of magnetic field on the dynamical analysis of second grade fluid: an optimal solution subject to non-integer differentiable operators. J. Appl. Comput. Mech. 7(1), 54–68 (2021). https://doi.org/10.22055/jacm.2020.34862.2489

    Article  Google Scholar 

  5. Punith Gowda, R.J., Naveen Kumar, R., Jyothi, A.M., Prasannakumara, B.C., Sarris, I.E.: Impact of binary chemical reaction and activation energy on heat and mass transfer of marangoni driven boundary layer flow of a non-Newtonian nanofluid. Processes 9(4), 702 (2021). https://doi.org/10.3390/pr9040702

    Article  Google Scholar 

  6. Alsaedi, A., Hayat, T., Qayyum, S., Yaqoob, R.: Eyring–Powell nanofluid flow with nonlinear mixed convection: entropy generation minimization. Comput. Methods Programs Biomed. 186, 105183 (2020). https://doi.org/10.1016/j.cmpb.2019.105183

    Article  Google Scholar 

  7. 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). https://doi.org/10.1002/num.22680

    Article  Google Scholar 

  8. IjazKhan, M., Qayyum, S., Nigar, M., Chu, Y., Kadry, S.: Dynamics of Arrhenius activation energy in flow of Carreau fluid subject to Brownian motion diffusion. Numer. Methods Partial Differ. Equ. (2020). https://doi.org/10.1002/num.22615

    Article  Google Scholar 

  9. Irfan, M., Khan, M., Khan, W.A.: Heat sink/source and chemical reaction in stagnation point flow of Maxwell nanofluid. Appl. Phys. A 126(11), 892 (2020). https://doi.org/10.1007/s00339-020-04051-x

    Article  Google Scholar 

  10. Khan, M., Salahuddin, T., Malik, M.Y., Alqarni, M.S., Alqahtani, A.M.: Numerical modeling and analysis of bioconvection on MHD flow due to an upper paraboloid surface of revolution. Phys. Stat. Mech. Appl. 553, 124231 (2020). https://doi.org/10.1016/j.physa.2020.124231

    Article  MathSciNet  Google Scholar 

  11. Basir, Md.FMd., Uddin, M.J., Bég, O.A., Ismail, A.IMd.: Influence of Stefan blowing on nanofluid flow submerged in microorganisms with leading edge accretion or ablation. J. Braz. Soc. Mech. Sci. Eng. 39(11), 4519–4532 (2017). https://doi.org/10.1007/s40430-017-0877-7

    Article  Google Scholar 

  12. Alamri, S.Z., Ellahi, R., Shehzad, N., Zeeshan, A.: Convective radiative plane Poiseuille flow of nanofluid through porous medium with slip: an application of Stefan blowing. J. Mol. Liq. 273, 292–304 (2019). https://doi.org/10.1016/j.molliq.2018.10.038

    Article  Google Scholar 

  13. Amirsom, N.A., Uddin, M.J., Ismail, A.IMd..: MHD boundary layer bionano convective non-Newtonian flow past a needle with Stefan blowing: Amirsom et al. Heat Transf. Asian Res. 48(2), 727–743 (2019). https://doi.org/10.1002/htj.21403

    Article  Google Scholar 

  14. Ali, B., Hussain, S., Abdal, S., Mehdi, M.M.: Impact of Stefan blowing on thermal radiation and Cattaneo–Christov characteristics for nanofluid flow containing microorganisms with ablation/accretion of leading edge: FEM approach. Eur. Phys. J. Plus 135(10), 821 (2020). https://doi.org/10.1140/epjp/s13360-020-00711-2

    Article  Google Scholar 

  15. Lund, L.A., Omar, Z., Raza, J., Khan, I., Sherif, E.-S.M.: Effects of Stefan blowing and slip conditions on unsteady MHD Casson nanofluid flow over an unsteady shrinking sheet: dual solutions. Symmetry 12(3), 487 (2020)

    Article  Google Scholar 

  16. Sakiadis, B.C.: Boundary-layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface. AIChE J. 7(2), 221–225 (1961). https://doi.org/10.1002/aic.690070211

    Article  Google Scholar 

  17. Crane, L.J.: Flow past a stretching plate. Z. Angew. Math. Phys. 21(4), 645–647 (1970). https://doi.org/10.1007/BF01587695

    Article  Google Scholar 

  18. Qayyum, S., Hayat, T., Alsaedi, A.: Optimization of entropy generation in motion of magnetite–Fe3O4 nanoparticles due to curved stretching sheet of variable thickness. Int. J. Numer. Methods Heat Fluid Flow 29(9), 3347–3365 (2019). https://doi.org/10.1108/HFF-12-2018-0782

    Article  Google Scholar 

  19. Hayat, T., Qayyum, S., Alsaedi, A., Ahmad, B.: Entropy generation minimization: Darcy–Forchheimer nanofluid flow due to curved stretching sheet with partial slip. Int. Commun. Heat Mass Transf. 111, 104445 (2020). https://doi.org/10.1016/j.icheatmasstransfer.2019.104445

    Article  Google Scholar 

  20. Punith Gowda, R.J., Al-Mubaddel, F.S., Kumar, R.N., Prasannakumara, B.C., Issakhov, A., Gorji, M.R., Al-Turki, Y.A.: Computational modelling of nanofluid flow over a curved stretching sheet using Koo–Kleinstreuer and Li (KKL) correlation and modified Fourier heat flux model. Chaos Solitons Fractals 145, 110774 (2021)

    Article  MathSciNet  Google Scholar 

  21. Ganga, B., Charles, S., Hakeem, A.K.A., Nadeem, S.: Three dimensional MHD Casson fluid flow over a stretching surface with variable thermal conductivity. J. Appl. Math. Comput. Mech. 20(1), 25–36 (2021). https://doi.org/10.17512/jamcm.2021.1.03

    Article  MathSciNet  Google Scholar 

  22. Iftikhar, N., Baleanu, D., Riaz, M.B., Husnine, S.M.: Heat and mass transfer of natural convective flow with slanted magnetic field via fractional operators. J. Appl. Comput. Mech. 7(1), 189–212 (2021). https://doi.org/10.22055/jacm.2020.34930.2514

    Article  Google Scholar 

  23. Qureshi, S., Ramos, H.: L-stable explicit nonlinear method with constant and variable step-size formulation for solving initial value problems. Int. J. Nonlinear Sci. Numer. Simul. 19(7–8), 741–751 (2018)

    Article  MathSciNet  Google Scholar 

  24. Aliya, T., Shaikh, A.A., Qureshi, S.: Development of a nonlinear hybrid numerical method. Adv. Differ. Equ. Control Process. 19(3), 275–285 (2018)

    Article  Google Scholar 

  25. Qureshi, S.: Fox H-functions as exact solutions for Caputo type mass spring damper system under Sumudu transform. J. Appl. Math. Comput. Mech. 20(1), 83–89 (2021). https://doi.org/10.17512/jamcm.2021.1.08

    Article  MathSciNet  Google Scholar 

  26. Qureshi, S., Yusuf, A.: A new third order convergent numerical solver for continuous dynamical systems. J. King Saud Univ. Sci. 32(2), 1409–1416 (2020)

    Article  Google Scholar 

  27. Baleanu, D., Sajjadi, S.S., Jajarmi, A., Defterli, O., Asad, J.H., Tulkarm, P.: The fractional dynamics of a linear triatomic molecule. Rom. Rep. Phys. 73(1), 105 (2021)

    Google Scholar 

  28. Jajarmi, A., Baleanu, D.: A new iterative method for the numerical solution of high-order non-linear fractional boundary value problems. Front. Phys. (2020). https://doi.org/10.3389/fphy.2020.00220

    Article  Google Scholar 

  29. Gao, W., Ghanbari, B., Baskonus, H.M.: New numerical simulations for some real world problems with Atangana–Baleanu fractional derivative. Chaos Solitons Fractals 128, 34–43 (2019). https://doi.org/10.1016/j.chaos.2019.07.037

    Article  MathSciNet  Google Scholar 

  30. Salari, A., Ghanbari, B.: Existence and multiplicity for some boundary value problems involving Caputo and Atangana–Baleanu fractional derivatives: a variational approach. Chaos Solitons Fractals 127, 312–317 (2019). https://doi.org/10.1016/j.chaos.2019.07.022

    Article  MathSciNet  MATH  Google Scholar 

  31. Imtiaz, M., Mabood, F., Hayat, T., Alsaedi, A.: Homogeneous–heterogeneous reactions in MHD radiative flow of second grade fluid due to a curved stretching surface. Int. J. Heat Mass Transf. 145, 118781 (2019)

    Article  Google Scholar 

  32. Amjad, M., Zehra, I., Nadeem, S., Abbas, N.: Thermal analysis of Casson micropolar nanofluid flow over a permeable curved stretching surface under the stagnation region. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973-020-10127-w

    Article  Google Scholar 

  33. Sajid, M., Ali, N., Javed, T., Abbas, Z.: Stretching a curved surface in a viscous fluid. Chin. Phys. Lett. 27(2), 024703 (2010). https://doi.org/10.1088/0256-307X/27/2/024703

    Article  Google Scholar 

  34. Abbas, Z., Naveed, M., Sajid, M.: Heat transfer analysis for stretching flow over a curved surface with magnetic field. J. Eng. Thermo Phys. 22(4), 337–345 (2013). https://doi.org/10.1134/s1810232813040061

    Article  Google Scholar 

  35. Bulut, H., Sulaiman, T.A., Baskonus, H.M., Akturk, T.: Complex acoustic gravity wave behaviors to some mathematical models arising in fluid dynamics and nonlinear dispersive media. Opt. Quantum Electron. 50(1), 19 (2018)

    Article  Google Scholar 

  36. Shafiq, A., Hammouch, Z., Turab, A.: Impact of radiation in a stagnation point flow of Walters’ B fluid towards a Riga plate. Therm. Sci. Eng. Prog. 6, 27–33 (2018)

    Article  Google Scholar 

  37. Cattani, C.: Harmonic wavelet solutions of the Schrodinger equation. Int. J. Fluid Mech. Res. 30(5), 463–472 (2003)

    Article  MathSciNet  Google Scholar 

  38. Shafiq, A., Hammouch, Z., Sindhu, T.N.: Bioconvective MHD flow of tangent hyperbolic nanofluid with Newtonian heating. Int. J. Mech. Sci. 133, 759–766 (2017)

    Article  Google Scholar 

  39. Shafiq, A., Rashidi, M.M., Hammouch, Z., Khan, I.: Analytical investigation of stagnation point flow of Williamson liquid with melting phenomenon. Phys. Scr. 94(3), 035204 (2019)

    Article  Google Scholar 

  40. Mohyud-Din, S.T., Khan, S.I., Khan, U., Ahmed, N., Yang, X.J.: Squeezing flow of MHD fluid between parallel disks. Int. J. Comput. Methods Eng. Sci. Mech. 49(1), 42–47 (2018)

    Article  MathSciNet  Google Scholar 

  41. Sharma, B., Kumar, S., Cattani, C., Baleanu, D.: Nonlinear dynamics of Cattaneo–Christov heat flux model for third-grade power-law fluid. J. Comput. Nonlinear Dyn. 15(1), 011009 (2020)

    Article  Google Scholar 

  42. Arslan, D.: The comparison study of hybrid method with RDTM for solving Rosenau–Hyman equation. Appl. Math. Nonlinear Sci. 5(1), 267–274 (2020)

    Article  MathSciNet  Google Scholar 

  43. Cheemaa, N., Seadawy, A.R., Chen, S.: More general families of exact solitary wave solutions of the nonlinear Schrodinger equation with their applications in nonlinear optics. Eur. Phys. J. Plus 133, 547 (2018)

    Article  Google Scholar 

  44. Asif, N.A., Hammouch, Z., Riaz, M.B., Bulut, H.: Analytical solution of a Maxwell fluid with slip effects in view of the Caputo–Fabrizio derivative. Eur. Phys. J. Plus 133(7), 1–13 (2018)

    Article  Google Scholar 

  45. Yavuz, M., Bonyah, E.: New approaches to the fractional dynamics of schistosomiasis disease model. Phys. A 525, 373–393 (2019)

    Article  MathSciNet  Google Scholar 

  46. Eskitascioglu, E.I., Aktas, M.B., Baskonus, H.M.: New complex and hyperbolic forms for Ablowitz–Kaup–Newell–Segur wave equation with fourth order. Appl. Math. Nonlinear Sci. 4(1), 105–112 (2019)

    MathSciNet  Google Scholar 

  47. Yang, X.J.: The vector power-law calculus with applications in power-law fluid flow. Therm. Sci. 24, 4289–4302 (2020)

    Article  Google Scholar 

  48. Seadawy, A., Kumar, D., Hosseini, K., Samadani, F.: The system of equations for the ion sound and Langmuir waves and its new exact solutions. Results Phys. 9, 1631–1634 (2018)

    Article  Google Scholar 

  49. Yavuz, M.: Characterizations of two different fractional operators without singular kernel. Math. Model. Nat. Phenom. 14(3), 302 (2019)

    Article  MathSciNet  Google Scholar 

  50. Baskonus, H.M., Kayan, M.: Regarding new wave distributions of the nonlinear integro-partial ITO differential and fifth-order integrable equations. Appl. Math. Nonlinear Sci. (2021). https://doi.org/10.2478/amns.2021.1.00006

    Article  Google Scholar 

  51. Dusunceli, F.: New exact solutions for generalized (3+1) shallow water-like (SWL) equation. Appl. Math. Nonlinear Sci. 4(2), 365–370 (2019)

    Article  MathSciNet  Google Scholar 

  52. Farah, N., Seadawy, A.R., Ahmad, S., Rizvi, S.T.R., Younis, M.: Interaction properties of soliton molecules and Painleve analysis for nano bioelectronics transmission model. Opt. Quantum Electron. 52, 1–15 (2020)

    Article  Google Scholar 

  53. Baskonus, H.M., Bulut, H., Sulaiman, T.A.: New complex hyperbolic structures to the Lonngren–Wave equation by using sine-Gordon expansion method. Appl. Math. Nonlinear Sci. 4(1), 141–150 (2019)

    MathSciNet  Google Scholar 

  54. Yel, G., Cattani, C., Baskonus, H.M., Gao, W.: On the complex simulations with dark–bright to the Hirota–Maccari system. J. Comput. Nonlinear Dyn. 16(6), 061005 (2021)

    Article  Google Scholar 

  55. Soomro, F.A., Hammouch, Z.: Heat transfer analysis of CuO–water enclosed in a partially heated rhombus with heated square obstacle. Int. J. Heat Mass Transf. 118, 773–784 (2018)

    Article  Google Scholar 

  56. Ali, A., Seadawy, A.R., Dianchen, Lu.: Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz–Kaup–Newell–Segur water wave dynamical equation via two methods and its applications. Open Phys. 16, 219–226 (2018)

    Article  Google Scholar 

  57. Ghalib, M.M., Zafar, A.A., Riaz, M.B., Hammouch, Z., Shabbir, K.: Analytical approach for the steady MHD conjugate viscous fluid flow in a porous medium with nonsingular fractional derivative. Phys. A Stat. Mech. Appl. 554, 123941 (2020)

    Article  MathSciNet  Google Scholar 

  58. Tan, W., Masuoka, T.: Stokes’ first problem for a second-grade fluid in a porous half-space with heated boundary. Int. J. Non-Linear Mech. 40(4), 515–522 (2005). https://doi.org/10.1016/j.ijnonlinmec.2004.07.016

    Article  MATH  Google Scholar 

  59. Fetecǎu, C., Fetecǎu, C., Zierep, J.: Decay of a potential vortex and propagation of a heat wave in a second-grade fluid. Int. J. Non-Linear Mech. 37(6), 1051–1056 (2002). https://doi.org/10.1016/S0020-7462(01)00028-2

    Article  MATH  Google Scholar 

  60. Fetecau, C., Fetecau, C.: Starting solutions for some unsteady unidirectional flows of a second-grade fluid. Int. J. Eng. Sci. 43(10), 781–789 (2005). https://doi.org/10.1016/j.ijengsci.2004.12.009

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This projected work was partially (not financial) supported by Harran University with the project HUBAP ID:21132.

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Authors and Affiliations

  1. Department of Studies and Research in Mathematics, Davangere University, Davangere, Karnataka, India

    R. J. Punith Gowda, R. Naveen Kumar, B. C. Prasannakumara & D. G. Prakasha

  2. Department of Mathematics and Science Education, Faculty of Education, University of Harran, 63200, Sanliurfa, Turkey

    Haci Mehmet Baskonus

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Punith Gowda, R.J., Baskonus, H.M., Naveen Kumar, R. et al. Computational Investigation of Stefan Blowing Effect on Flow of Second-Grade Fluid Over a Curved Stretching Sheet. Int. J. Appl. Comput. Math 7, 109 (2021). https://doi.org/10.1007/s40819-021-01041-2

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