Entropy generation within an arterial stenosis of Sisko nanofluid with motile gyrotactic microorganisms
Galal M. Moatimid
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Search for more papers by this authorCorresponding Author
Mona A. A. Mohamed
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Correspondence
Mona A. A. Mohamed, Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt.
Email: [email protected]
Search for more papers by this authorKhaled Elagamy
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Search for more papers by this authorAhmed A. Gaber
Department of Mathematics, College of Science and Humanities at Howtat Sudair, Majmaah University, Majmaah, Saudi Arabia
Search for more papers by this authorGalal M. Moatimid
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Search for more papers by this authorCorresponding Author
Mona A. A. Mohamed
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Correspondence
Mona A. A. Mohamed, Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt.
Email: [email protected]
Search for more papers by this authorKhaled Elagamy
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Search for more papers by this authorAhmed A. Gaber
Department of Mathematics, College of Science and Humanities at Howtat Sudair, Majmaah University, Majmaah, Saudi Arabia
Search for more papers by this authorAbstract
The investigation of entropy generation in artery stenosis utilizing Sisko nanofluid and motile gyrotactic bacteria is driven by the necessity to enhance biomedical fluid dynamics for superior drug delivery and disease diagnostics. The innovation examines the synergistic impacts of non-Newtonian fluid behavior, nanoparticle dynamics, and microbe motility on entropy formation, yielding an enhanced understanding of energy dissipation and transport events in biological flows. Therefore, an activated energy chemical reaction is examined in conjunction with the Boussinesq estimation (buoyancy-driven stream), in which the intensity is introduced as a linear expression of temperature and concentration. Furthermore, the involvement of entropy generation through the current flow may enable one to design more effective systems to control the thermal properties and the flow of nanoliquids. The foremost formulations are mathematically explained and illustrated using a fourth-order Runge–Kutta procedure. Consequently, a fundamentally meaningful graphical conception of the information is recognized to investigate the influences of the generated nondimensional physical influences. Since viral contagions are known to produce thinner blood infections, it is determined that the presence of microorganisms, which are expressed in buoyant terms, improves flow and increases their velocity. Therefore, by regulating these characteristics, the flow rate may be managed. When diagnosing narrowing channel treatment, most of the heat-related characteristics discussed here are seen to increase aspects of heat flux.
CONFLICT OF INTEREST STATEMENT
There are no conflicts of interest declared by the authors.
REFERENCES
- 1Whitmore, R.L.: Rheology of Circulation. Pergamon Press, Oxford (1968)
- 2Chakravarty, S., Mandal, P.K.: Two-dimensional blood flow through tapered arteries under stenotic conditions. Int. J. Non Linear Mech. 35, 779–793 (2000)
- 3Ismail, Z., Abdullah, I., Mustapha, N., Amin, N.: A power-law model of blood flow through a tapered overlapping stenosis artery. Appl. Math. Comput. 195, 669–680 (2008)
- 4Mekheimer, Kh.S., El Kot, M.A.: Mathematical modelling of unsteady flow of a Sisko fluid through an anisotropically tapered elastic arteries with time-variant overlapping stenosis. Appl. Math. Modell. 36, 5393–5407 (2012)
- 5Mekheimer, Kh.S., El Kot, M.A.: Suspension model for blood flow through catheterized curved artery with time-variant overlapping stenosis. Eng. Sci. Technol. Int. J. 18, 452–462 (2015)
- 6El-dabe, N.T.M., Moatimid, G.M., Hassan, M.A., Mostapha, D.R.: Analytical solution of the peristaltic flow of a Jeffrey nanofluid in a tapered artery with mild stenosis and slip condition. Int. J. Innov. Appl. Stud. 12(1), 1–32 (2015)
- 7El-dabe, N.T.M., Moatimid, G.M., Hassan, M.A., Mostapha, D.R.: Electrohydrodynamic peristaltic flow of a viscoelastic Oldroyed fluid with a mild stenosis Application of an endscope. J. Appl. Mech. Tech. Phys. 57(1), 38–54 (2016)
- 8El-dabe, N.T.M., Moatimid, G.M., Hassan, M.A., Mostapha, D.R.: Effect of partial slip on peristaltic flow of a Sisko fluid with mild stenosis through a porous medium. Appl. Math. Inf. Sci. 10(2), 673–687 (2016)
10.18576/amis/100227 Google Scholar
- 9Manchi, R., Ponalagusamy, R.: Modeling of pulsatile EMHD flow of Au-blood in an inclined porous tapered atherosclerotic vessel under periodic body acceleration. Arch. Appl. Mech. 91, 3421–3447 (2021)
- 10Li, D., Li, K.: Time periodic pulse electroosmotic flow of Jeffrey fluids in a circular microchannel under the depletion effect. J. Mech. Sci. Technol. 36 (4), 1–10 (2022)
- 11Moatimid, G.M., Mohamed, M.A.A., Elagamy, Kh., Gaber, AA.: Effect of motile gyrotactic microorganisms on arterial stenosis Sisko nanofluid flow through porous medium: A Numerical Study. Spec. Top. Rev. Porous Media 15(5), 41–62 (2024)
- 12Zohra, F.T., Uddin, M.J., Ismail, A.I.M.: Magnetohydrodynamic bio-nano convective Naiver slip flow of micropolar fluid in a stretchable horizontal channel. Heat Trans. 48, 3636–3656 (2019)
10.1002/htj.21560 Google Scholar
- 13Zohra, F.T., Uddin, M.J., Basir, M.F., Ismail, A.I.: Magnetohydrodynamic bio nano-convective slip flow with Stefan blowing effects over a rotating disc. J. Nanomater., Nanoeng. Nanosyst. 234(3-4), 83–97 (2020)
- 14Amirsom, N.A., Uddin, M.J., Basir, M.F., Ismail, A.I., Bėg, O.A., Kadir, A.: Three-dimensional bio convection nanofluid flow from a bi-axial stretching sheet with anisotropic slip. Sains Malays. 48(5), 1137–1149 (2019)
- 15Uddin, M.J., Amirsom, N.A., Bėg, O.A., Ismail, A.I.: Computation of bio-nano-convection power law slip flow from a needle with blowing effects in a porous medium. Waves Random Complex Media 35(2), 2991-3011 (2025)
- 16Uddin, M.J., Bėg, O.A., Ismail, A.I.: Radiative convective nanofluid flow past a stretching/shrinking sheet with slip effects. J. Thermophys. Heat Transfer 29 (3), 513–523 (2015)
- 17Bėg, O.A., Bėg, T., Khan, W.A., Uddin, M.J.: Multiple slip effects on nanofluid dissipativeflow in a converging/diverging channel: A numerical study. Heat Trans. 51, 1040–1061 (2022)
- 18Moatimid, G.M., Mohamed, M.A.A., Elagamy, Kh.: Peristaltic transport of Rabinowitsch nanofluid with moving microorganisms. Sci. Rep. 13, 1863 (2023)
- 19Moatimid, G.M., Mohamed, M.A.A., Elagamy, Kh.: A pulsatile Williamson nanofluid flow with motile microorganisms between two permeable walls: Effect of modified Darcy's law. J. Porous Media 26(12), 57–86 (2023)
- 20He, J.-H., Moatimid, G.M., Mohamed, M.A.A., Elagamy, Kh.: A stretching cylindrical Carreau nanofluid border layer movement with motile microorganisms and variable thermal characteristics. Int. J. Mod. Phys. B 38(17), 2450223 (2023)
- 21Moatimid, G.M., Mohamed, M.A.A., Elagamy, Kh.: Sutterby nanofluid flow with microorganisms around a curved expanding surface through a porous medium: Thermal diffusion and diffusion thermo impacts. J. Porous Media 27, 19–48 (2024)
- 22Moatimid, G.M., Mohamed, M.A.A., Elagamy, Kh., Sankar, M.: A pulsatile movement of an annular Ree–Eyring nanofluid with gyrotactic motile microorganisms and time-varying conditions. Numer. Heat Transf.; A: Appl. 2024, 1–28 (2024).
- 23Moatimid, G.M., Mohamed, M.A.A., Elagamy, Kh.: A motion of Jeffrey nanofluid in porous medium with motile microorganisms between two revolving stretching discs: Effect of Hall currents. J. Porous Media 25(10), 83–101 (2022)
10.1615/JPorMedia.2022043529 Google Scholar
- 24Hayat, T., Khan, M.: On the MHD flow of fractional generalized Burgers’ fluid with modified. Acta Mech. Sin. 23, 257–261 (2007)
- 25Gisinger, S., Dörnbrack, A., Schröttle, J.: A modified Darcy's law. Theor. Comput. Fluid Dyn. 29, 343–347 (2015)
- 26Hayat, T., Bibi, F., Farooq, S., Khan, A.A.: Nonlinear radiative peristaltic flow of Jefrey nanofluid with activation energy and modified Darcy's law. J. Braz. Soc. Mech. Sci. Eng. 41, 296 (2019)
10.1007/s40430-019-1771-2 Google Scholar
- 27Alabi, O.O., Popoola, O.I., Adegoke, J.A.: Modification of Darcy's law for extremely fine-grained soils. Electron. J. Geotech. Eng. 17, 1305–1321 (2012)
- 28Imomnazarov, Kh.: Modified Darcy laws for conducting porous media. Math. Comput. Modell. 40, 5–10 (2004)
10.1016/j.mcm.2004.01.001 Google Scholar
- 29Alabi, O.O., Popoola, O.I., Adegoke, J.A.: Modification of fluid flow equation in saturated porous media. Global J. Pure Appl. Sci. 15(3-4), 395–400 (2009)
- 30Ehlers, W.: Darcy, Forchheimer, Brinkman and Richards: Classical hydromechanical equations and their significance in the light of the TPM. Arch. Appl. Mech. 92, 619–639 (2022)
- 31Bhatti, M.M., Marin, M., Zeeshan, A., Ellahi, R., Abdelsalam, S.I.: Swimming of motile gyrotactic microorganisms and nanoparticles in blood flow through anisotropically tapered arteries. Front. Phys. 8(95), 9 pages (2020)
- 32https://my.clevelandclinic.org/health/diseases/22031-subglottic-stenosis
- 33Wang, Y., Hayat, T., Ali, N., Oberlack, M.: Magnetohydrodynamic peristaltic motion of a Sisko fluid in a symmetric or asymmetric channel. Physica A Stat. Mech. Appl. 387, 347–362 (2008)
- 34Hayat, T., Ayub, S., Tanveer, A., Alsaedi, A.: Numerical simulation for MHD Williamson fluid utilizing modified Darcy's law. Results Phys. 10, 751–759 (2018)
- 35Mittal, A.S., Patel, H.R.: Influence of thermophoresis and Brownian motion on mixed convection two dimensional MHD Casson fluid flow with non-linear radiation and heat generation. Physica A Stat. Mech. Appl. 537, 122710 (2020)
- 36Khan, M., Hafeez, A., Ahmed, J.: Impacts of non-linear radiation and activation energy on the axisymmetric rotating flow of Oldroyd-B fluid. Physica A 580, 124085 (2021)
- 37Khan, S.A., Hayat, T., Alsaedi, A.: Bioconvection entropy optimized flow of Reiner–Rivlin nanoliquid with motile microorganisms. Alex. Eng. J. 79, 81–92 (2023)
- 38Hussaina, S., Haq, F., Ghazwani, H.A., Saleem, M., Hussain, A.: Entropy optimization in bio-convective chemically reactive flow of micropolar nanomaterial with activation energy and gyrotactic microorganisms. Case Stud. Therm. Eng. 55, 104131 (2024)
10.1016/j.csite.2024.104131 Google Scholar
- 39https://extras.csc.fi/math/nag/mark21/pdf/D02/d02agf.pdf .
- 40Soliman, M.S., Mohamed, R.A., Aly, A.M., Ahmed, S.E.: Magnetohydrodynamic Maxwell nanofluids flow over a stretching surface through a porous medium: effects of non-linear thermal radiation, convective boundary conditions and heat generation/absorption. Int. J. Aerosp. Mech. Eng. 13(6), 436–443 (2019)
- 41Ibrahim, W.: Magnetohydrodynamics (MHD) flow of a tangent hyperbolic fluid with nanoparticles past a stretching sheet with second order slip and convective boundary condition. Results in Phys. 7, 3723–3731 (2017)
- 42Pal, D., Mandal, G.: Double diffusive magnetohydrodynamic heat and mass transfer of nanofluids over a nonlinear stretching/shrinking sheet with viscous-Ohmic dissipation and thermal radiation. Propuls. Power Res. 6(1), 58–69 (2017)
- 43Kotnurkar, A.S., Katagi, D.C.: Bioconvective peristaltic flow of a third-grade nanofluid embodying gyrotactic microorganisms in the presence of Cu-blood nanoparticles with permeable walls. Multidiscip. Model. Mater. Struct. 17(2), 293–316 (2021)
- 44Awais, M., Hayat, T., Ali, A., Irum, S.: Velocity, thermal and concentration slip effects on a magneto-hydrodynamic nanofluid flow. Alex. Eng. J. 55, 2107–2114 (2016)
- 45Gbadeyan, J.A., Olanrewaju, M.A., Olanrewaju, P.O.: Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition in the presence of magnetic field and thermal radiation. Aust. J. Basic Appl. Sci. 5(9), 1323–1334 (2011)
- 46Nadeem, S., Ul Haq, R., Akbar, N.S., Lee, C., Khan, Z.H.: Numerical study of boundary layer flow and heat transfer of Oldroyd-B nanofluid towards a stretching sheet. PLoS One 8, e69811 (2013)
- 47Alebraheem, J., Ramzan, M.: Flow of nanofluid with Cattaneo–Christov heat flux model. Appl. Nanosci. 10, 2989–2999 (2020)
- 48Abou-zeid, M.Y., El-zahrani, S.S., Mansour, H.M.: Mathematical modeling for pulsatile flow of a non-Newtonian fluid with heat and mass transfer in a porous medium between two permeable parallel plates. J. Nucl. Part. Phys. 4(3), 100–115 (2014)
- 49Abou-zeid, M.Y.: Effects of thermal-diffusion and viscous dissipation on peristaltic flow of micropolar non-Newtonian nanofluid: Application of homotopy perturbation method. Results Phys. 6, 481–495 (2016)
- 50Abdelmalek, Z., Hussainc, A., Bilal, S., Sherif, E.M., Thounthong, P.: Brownian motion and thermophoretic diffusion influence on thermophysical aspects of electrically conducting viscoinelastic nanofluid flow over a stretched surface. J. Mater. Res. Technol. 9(5), 11948–11957 (2020)
- 51Elbashbeshy, E.M.A., Asker, H.G., Nagy, B.: The effects of heat generation absorption on boundary layer flow of a nanofluid containing gyrotactic microorganisms over an inclined stretching cylinder. Ain Shams Eng. J. 13, 101690 (2022)
- 52Sabu, A.S., Mackolil, J., Mahanthesh, B., Mathew, A.: Reiner–Rivlin nanomaterial heat transfer over a rotating disk with distinct heat source and multiple slip effects. Appl. Math. Mech. (English Ed.) 42(10), 1495–1510 (2021)
10.1007/s10483-021-2772-7 Google Scholar
- 53Mabood, F., Mackolil, J., Mahanthesh, B., Rauf, A., Shehzad, S.A.: Dynamics of Sutterby fluid flow due to a spinning stretching disk with non-Fourier/Fick heat and mass flux models. Appl. Math. Mech. (English Ed.) 42(9), 1247–1258 (2021)
10.1007/s10483-021-2770-9 Google Scholar
- 54Khan, N.M., Abidi, A., Khan, I., Alotaibi, F., Alghtani, A.H., Aljohani, M.A., Galal, A.M.: Dynamics of radiative Eyring–Powell MHD nanofluid containing gyrotactic microorganisms exposed to surface suction and viscosity variation. Case Stud. Therm. Eng. 28(4), 101659 (2021)
10.1016/j.csite.2021.101659 Google Scholar