Analysis of non-Newtonian fluid with phase flow model

Abbas, N.; Nadeem, S.; Saleem, A.; Issakhov, A.; Abdel-Sattar, M. A.; Aly, Sh.

doi:10.24200/sci.2021.53475.3258

Analysis of non-Newtonian fluid with phase flow model

Document Type : Review Article

Authors

¹ Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan

² - Mathematics and Its Applications in Life Sciences Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam. - Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam.

³ Al-Farabi Kazakh National University, Faculty of Mechanics and Mathematics, av. al-Farabi 71, Almaty, Kazakhstan

⁴ Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia

⁵ Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt

10.24200/sci.2021.53475.3258

Abstract

We considered a stagnation point of Non-Newtonian Fluid with Phase Flow Model over a stretching surface with slip conditions. Two types of the nanoparticle used, namely Cu and 〖Al〗_2 O_3 with base fluid H_2 O. Acceptable to theoretical study, the mathematical model has been constructed through flow assumptions. Partial differential equations are made by applying the boundary layer approximations on the momentum and energy equations. The suitable similarity transformations are applied to the partial equations which are converted into ordinary differential equations. These equations are solved by numerical scheme, namely BVP4C method. The involving physical parameters effect is shown by graphs and tables. Our work shows a good agreement with the decay literature. The expressions F''(0) and -θ'(0) achieve fewer values by hybrid nanofluid than that of nanofluid. Moreover F''(0) and -θ'(0) increase for large values of the dimensionless parameter (N) where as F'(ξ) and θ(ξ).increase for large values of Φ_2.

Keywords

20.1001.1.10263098.2021.28.6.52.5

References

References:

1. Rivlin, R.S., and Ericksen, J.L. "Stress-deformation relations for isotropic materials", In Collected Papers of RS Rivlin, pp. 911-1013, Springer, New York, NY (1997).
2. Labropulu, F.A "Few more exact solutions of a second grade fluid via inverse method", Mechanics Research Communications, 27(6), pp. 713-720 (2000).
3. Yurusoy, M., Pakdemirli, M., and Noyan, O.F. "Lie group analysis of creeping flow of a second grade fluid", International Journal of Non-Linear Mechanics, 36(6), pp. 955-960 (2001).
4. Shkoller, S. "Smooth global Lagrangian flow for the 2D Euler and second-grade fluid equations", Applied Mathematics Letters, 14(5), pp. 539-543 (2001).
5. Labropulu, F. "D'Alembert motions for non-Newtonian second grade fluid", International Journal of Non-linear Mechanics, 38(7), pp. 1027-1036 (2003).
6. Nadeem, S., Hussain, A., Malik, M.Y., and Hayat, T. "Series solutions for the stagnation flow of a secondgrade fluid over a shrinking sheet", Applied Mathematics and Mechanics, 30(10), p. 1255 (2009).
7. Mehmood, R., Nadeem, S., and Akbar, N.S. "Nonorthogonal stagnation point flow of a micropolar second grade fluid towards a stretching surface with heat transfer", Journal of the Taiwan Institute of Chemical Engineers, 44(4), pp. 586-595 (2013).
8. Akinbobola, T.E. and Okoya, S.S. "The flow of second grade fluid over a stretching sheet with variable thermal conductivity and viscosity in the presence of heat source/sink", Journal of the Nigerian Mathematical Society, 34(3), pp. 331-342 (2015).
9. Majeed, A., Javed, T., and Ghaffari, A. "Numerical investigation on flow of second grade fluid due to stretching cylinder with Soret and Dufour effects", Journal of Molecular Liquids, 221, pp. 878-884 (2016).
10. Khan, M., ur Rahman, M., and Manzur, M. "Axisymmetric flow and heat transfer to modified second grade fluid over a radially stretching sheet", Results in Physics, 7, pp. 878-889 (2017).
11. Ghadikolaei, S.S., Hosseinzadeh, K., Yassari, M.,Sadeghi, H., and Ganji, D.D. "Analytical and numerical solution of non-Newtonian second-grade fluid flow on a stretching sheet", Thermal Science and Engineering Progress, 5, pp. 309-316 (2018).
12. Alamri, S.Z., Khan, A.A., Azeez, M., and Ellahi, R. "Effects of mass transfer on MHD second grade fluid towards stretching cylinder: A novel perspective of Cattaneo-Christov heat flux model", Physics Letters A., 383(2-3), pp. 276-281 (2019).
13. Bilal, S., Mustafa, Z., Rehman, K.U., and Malik, M.Y. "MHD second grade nano fluid flow induced by a rotatory cone", Journal of Nano fluids, 8(4), pp. 876- 884 (2019).
14. Elkoumy, S.R., Barakat, E.I., and Abdelsalam, S.I. "Hall and transverse magnetic field effects on peristaltic flow of a Maxwell fluid through a porous medium", Global J. Pure Appl. Math., 9(2), pp. 187- 203 (2013).
15. Mekheimer, K.S., Hasona, W.M., El-Shekhipy, A.A., and Zaher, A.Z. "Electrokinetics of dielectric non- Newtonian bio fluids with heat transfer through a flexible channel", Numerical Study. Computational Methods in Science and Technology, 23(4), pp. 331-341 (2017).
16. Mekheimer, K.S., Hasona, W.M., Abo-Elkhair, R.E., and Zaher, A.Z. "Peristaltic blood flow with gold nanoparticles as a third grade nanofluid in catheter: Application of cancer therapy", Physics Letters A., 382(2-3), pp. 85-93 (2018).
17. Abdelsalam, S.I., Bhatti, M.M., Zeeshan, A., Riaz, A.,and Beg, O.A. "Metachronal propulsion of electricallyconducting viscoelastic particle-fluid suspension in a ciliated channel under transverse magnetic field: mathematical modelling", Physica Scripta, 94, pp. 115301- 115314 (2019).
18. Eldesoky, I.M., Abdelsalam, S.I., El-Askary, W.A., and Ahmed, M.M. "The integrated thermal effect in conjunction with slip conditions on peristaltically induced particle-fluid transport in a catheterized pipe", Journal of Porous Media, 23(7), pp. 695-713 (2020).
19. Crane, L.J. "Flow past a stretching plate", Zeitschrift fur Angewandte Mathematik und Physik ZAMP, 21(4),pp. 645-647 (1970).
20. Mekheimer, K.S., Salem, A.M., and Zaher, A.Z.Peristaltically induced flow due to a surface acoustic wavy moving wall", Chinese Journal of Physics, 51(5), pp. 968-982 (2013).
21. Mekheimer, K.S., Salem, A.M., and Zaher, A.Z. "Peristatcally induced MHD slip flow in a porous medium due to a surface acoustic wavy wall", Journal of the Egyptian Mathematical Society, 22(1), pp. 143-151 (2014).
22. Malvandi, A., Hedayati, F., and Ganji, D.D. "Nanofluid flow on the stagnation point of a permeable non-linearly tretching/shrinking sheet", Alexandria Engineering Journal, 57(4), pp. 2199-2208 (Dec. 2018).
23. Abdelsalam, S.I. and Mekheimer, K.S. "Couple stress fluid flow in a rotating channel with peristalsis", Journal of Hydrodynamics, 30(2), pp. 307-316 (2018).
24. Abdelsalam, S.I. and Bhatti, M.M. "The study of non-Newtonian nanofluid with hall and ion slip effects on eristaltically induced motion in a non-uniform channel", RSC advances, 8(15), pp. 7904-7915 (2018).
25. Mekheimer, K.S., Zaher, A.Z., and Hasona, W.M. "Entropy of AC electro-kinetics for blood mediated gold or copper nanoparticles as a drug agent for thermotherapy of oncology", Chinese Journal of Physics 65, pp. 123-138 (June 2020).
26. Bhatti, M.M., Marin, M., Zeeshan, A., Ellahi, R., and Abdelsalam, S.I. "Swimming of motile gyrotactic microorganisms
and nanoparticles in blood flow through anisotropically tapered arteries", Frontiers in Physics, 8, p. 95 (2020).
27. Khan, M., Salahuddin, T., Tanveer, A., Malik, M.Y., and Hussain, A. "Change in internal energy of thermal diffusion stagnation point Maxwell nanofluid flow along with solar radiation and thermal conductivity", Chinese Journal of Chemical Engineering, 27(10), pp. 2352-2358 (2019).
28. Nadeem, S., Ahmed, Z., and Saleem, S. "Carbon nanotubes effects in magneto nanofluid flow over a curved stretching surface with variable viscosity", Microsystem Technologies, 25(7), pp. 2881-2888 (2020).
29. Choi, U.S. "Enhancing thermal conductivity of fluids with nanoparticles", Development and Applications of Non-Newtonian Flows Edited by Siginer, DA and Wang, HP, EFD-Vol. 231/MD-Vol. 66. ASME (1995).
30. Mahian, O., Kianifar, A., Kalogirou, S.A., Pop, I., and Wongwises, S.A. "Review of the applications of nanofluids in solar energy", International Journal of Heat and Mass Transfer, 57(2), pp. 582-594 (2013).
31. Turkyilmazoglu, M. "Nanofluid flow and heat transfer due to a rotating disk", Computers and Fluids, 94, pp. 139-146 (2014).
32. Abbas, N., Saleem, S., Nadeem, S., Alderremy, A.A.,and Khan, A.U. "On stagnation point flow of a micro polar nanofluid past a circular cylinder with velocity and thermal slip", Results in Physics, 9, pp. 1224-1232 (2018).
33. Abdelsalam, S.I. and Bhatti, M.M. "The impact of impinging TiO2 nanoparticles in Prandtl nanofluid along with endoscopic and variable magnetic field effects on peristaltic blood flow", Multidiscipline Modeling in Materials and Structures, 14(3), pp. 530-548 (2018).
34. Eldesoky, I., Abdelsalam, S., El-Askary, W., El-Refaey, A., and Ahmed, M. "Joint effect of thermal energy and magnetic field on particulate fluid suspension in a catheterized tube", Bionanoscience, 9(3), pp. 723-739 (2019).
35. Abdelsalam, S.I. and Bhatti, M.M. "New insight into AuNP applications in tumour treatment and cosmetics through wavy annuli at the nanoscale", Scientific Reports, 9(1), pp. 1-14 (2019).
36. Bhatti, M.M., Zeeshan, A., Ellahi, R., Beg, O.A., and Kadir, A. "Effects of coagulation on the two-phase peristaltic pumping of magnetized Prandtl bio fluid through an endoscopic annular geometry containing a porous medium", Chinese Journal of Physics, 58, pp. 222-234 (2019).
37. Abd Elmaboud, Y. and Abdelsalam, S.I. "DC/AC magnetohydrodynamic-micropump of a generalized Burger's fluid in an annulus", Physica Scripta, 94(11), p. 115209 (2019).
38. Abd Elmaboud, Y., Abdelsalam, S.I., Mekheimer, K.S., and Vafai, K. "Electromagnetic flow for two-layer immiscible fluids", Engineering Science and Technology, An International Journal, 22(1), pp. 237-248 (2019).
39. Sohail, M., Naz, R., and Abdelsalam, S.I. "Application of non-Fourier double diffusions theories to the boundary-layer
ow of a yield stress exhibiting fluid model", Physica A: Statistical Mechanics and its Applications, 537, p. 122753 (2020).
40. Abumandour, R.M., Eldesoky, I.M., Kamel, M.H., Ahmed, M.M., and Abdelsalam, S.I. "Peristaltic thrusting of a thermal-viscosity nanofluid through a resilient vertical pipe", Zeitschrift fur Naturforschung, A., 75(8), pp. 727-738 (2020).
41. Momin, G.G. "Experimental investigation of mixed convection with water-Al2O3 and hybrid nanofluid in inclined tube for laminar flow", Int. J. Sci. Technol. Res., 2, pp. 195-202 (2013).
42. Suresh, S., Venkitaraj, K.P., Selvakumar, P., and Chandrasekar, M. "Synthesis of Al2O3-Cu/water hybrid nanofluids using two step method and its thermo physical properties", Colloids and Surfaces A: Physicochemical and Engineering Aspects, 388(1-3), pp. 41-48 (2011).
43. Nadeem, S., Abbas, N., and Khan, AU. "Characteristics of three dimensional stagnation point flow of Hybrid nanofluid past a circular cylinder", Results in Physics, 8, pp. 829-835 (2018).
44. Nadeem, S. and Abbas, N. "On both MHD and slip effect in micropolar hybrid nanofluid past a circular cylinder under stagnation point region", Canadian Journal of Physics, (ja) (2018).
45. Eldesoky, I.M., Abdelsalam, S.I., El-Askary, W.A., and Ahmed, M.M. "Concurrent development of thermal energy with magnetic field on a particle-fluid suspension through a porous conduit", BioNano Science, 9(1), pp. 186-202 (2019).
46. Abdelsalam, S.I. and Bhatti, M.M. "Anomalous reactivity of thermo-bioconvective nano fluid towards oxytactic microorganisms", Applied Mathematics and Mechanics, 41(5), pp. 711-724 (2020).
47. Abdelsalam, S.I. and Sohail, M. "Numerical approach of variable thermophysical features of dissipated viscous nanofluid comprising gyrotactic microorganisms", Pramana, Journal of Physics, 94(1) (2020).
48. Abdelsalam, S.I., Mekheimer, K.S., and Zaher,A.Z. "Alterations in blood stream by electroosmotic forces of hybrid nanofluid through diseased artery: Aneurysmal/ stenosed segment", Chinese Journal of Physics, 67, pp. 314-329 (Oct. 2020).
49. Sadaf, H. and Abdelsalam, S.I. "Adverse effects of a hybrid nanofluid in a wavy non-uniform annulus with convective boundary conditions", RSC Advances, 10(26).
50. Sohail, M., Naz, R., and Abdelsalam, S.I. "On the onset of entropy generation for a nanofluid with thermal radiation and gyrotactic microorganisms through 3D flows", Physica Scripta, 95(4), 045206 (2020).
51. Ariel, P.D. "On extra boundary condition in the stagnation point flow of a second grade fluid", International Journal of Engineering Science, 40(2), pp. 145- 162 (2002).
52. Wang, C.Y. "Stagnation flow towards a shrinking sheet", International Journal of Non-Linear Mechanics, 43(5), pp. 377-382 (2008).
53. Bachok, N., Ishak, A., and Pop, I. "Stagnation-point flow over a stretching/shrinking sheet in a nanofluid", Nanoscale Research Letters, 6(1), p. 623 (2011).
54. Malvandi, A., Hedayati, F., and Ganji, D.D. "Nanofluid flow on the stagnation point of a permeable non-linearly stretching/shrinking sheet", Alexandria Engineering Journal 57(4), pp. 2199-2208 (2017).
55. Yacob, N.A., Ishak, A., and Pop, I. "Falkner-Skan problem for a static or moving wedge in nanofluids", International Journal of Thermal Sciences, 50(2), pp. 133-139 (2011).