{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T10:07:01Z","timestamp":1767866821150,"version":"3.49.0"},"reference-count":44,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,8]],"date-time":"2021-12-08T00:00:00Z","timestamp":1638921600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, a novel model of entropy generation effects measured in the Cu-blood flow of a nanofluid under the effect of ciliary-oriented motion is proposed. The effects of viscous dissipation are also taken into account. The physical model was composed with the incorporation of a low Reynolds number and long-wavelength phenomena. The exact solutions for the axial velocity, temperature and pressure gradient distribution were achieved successfully. Key findings are presented through a strategy of plotting the significant factors affecting the physical quantities of the stream. It was found that the heat absorption parameter and Brownian motion accounted for the large thermal transfer rate, while the effect of entropy was minimal compared to these factors in the center of the flow but increased on the walls in the case of Cu-blood flow. It can also be added that a more intense flow gave rise to the entropy effects. This study may be helpful in medical science as cilia play vital roles, which include cell migration and external fluid transport, in human tissues and some key organs. Moreover, the considered annulus-shaped geometry gives vital readings that are used in medical equipment such as endoscopes.<\/jats:p>","DOI":"10.3390\/sym13122358","type":"journal-article","created":{"date-parts":[[2021,12,8]],"date-time":"2021-12-08T23:30:00Z","timestamp":1639006200000},"page":"2358","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["Entropy Analysis for Cilia-Generated Motion of Cu-Blood Flow of Nanofluid in an Annulus"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0704-2230","authenticated-orcid":false,"given":"Arshad","family":"Riaz","sequence":"first","affiliation":[{"name":"Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0945-9067","authenticated-orcid":false,"given":"Elena","family":"Bobescu","sequence":"additional","affiliation":[{"name":"Department of Medical and Surgical Specialties, Faculty of Medicine, Transilvania University of Brasov, 500019 Brasov, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3329-508X","authenticated-orcid":false,"given":"Katta","family":"Ramesh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Symbiosis Institute of Technology, Symbiosis International University, Pune 412115, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7805-8259","authenticated-orcid":false,"given":"Rahmat","family":"Ellahi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan"},{"name":"Fulbright Fellow, Department of Mechanical Engineering, University of California Riverside, Riverside, CA 92521, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,8]]},"reference":[{"key":"ref_1","unstructured":"Maxwell, J.C. (1873). A Treatise on Electricity and Magnetism, Clarendon Press. [2nd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ganji, D.D., and Malvandi, A. (2016). Heat Transfer Enhancement using Nanofluid Flow in Microchannels: Simulation of Heat and Mass Transfer, William Andrew.","DOI":"10.1016\/B978-0-323-43139-2.00001-0"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"9296","DOI":"10.1038\/s41598-020-66126-2","article-title":"Hybrid nanofluid flow towards a stagnation point on a stretching\/shrinking cylinder","volume":"10","author":"Waini","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_4","first-page":"1536","article-title":"Nanofluid flow and shear layers between two parallel plates: A simulation approach","volume":"14","author":"Mahdavi","year":"2020","journal-title":"Eng. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Gul, T., Gul, R.S., Noman, W., Saeed, A., Mukhtar, S., Alghamdi, W., and Alrabaiah, H. (2020). CNTs-nanofluid flow in a rotating system between the gap of a disk and cone. Phys. Scr., 95.","DOI":"10.1088\/1402-4896\/abbf1e"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Tassaddiq, A., Khan, S., Bilal, M., Gul, T., Mukhtar, S., Shah, Z., and Bonyah, E. (2020). Heat and mass transfer together with hybrid nanofluid flow over a rotating disk. AIP Adv., 10.","DOI":"10.1063\/5.0010181"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ramzan, M., Chung, J.D., Kadry, S., Chu, Y.M., and Akhtar, M. (2020). Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary. Sci. Rep., 10.","DOI":"10.1038\/s41598-020-74855-7"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Eid, M.R., Mabood, F., and Mahny, K.L. (2020). On 3D Prandtl nanofluid flow with higher-order chemical reaction. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., 235.","DOI":"10.1177\/0954406220975429"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1515\/jnet-2019-0073","article-title":"Effects of NP shapes on non-Newtonian bio-nanofluid flow in suction\/blowing process with convective condition: Sisko model","volume":"45","author":"Eid","year":"2020","journal-title":"J. Non-Equil. Thermodyn."},{"key":"ref_10","first-page":"251","article-title":"Computational analysis of bioconvective flow of nanofluid containing gyrotactic microorganisms over a nonlinear stretching sheet with variable viscosity using HAM","volume":"7","author":"Mondal","year":"2020","journal-title":"J. Comput. Des. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Warke, A.S., Ramesh, K., Mebarek-Oudina, F., and Abidi, A. (2021). Numerical investigation of the stagnation point flow of radiative magnetomicropolar liquid past a heated porous stretching sheet. J. Therm. Anal. Calorim., 1\u201312.","DOI":"10.1007\/s10973-021-10976-z"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1166\/jon.2021.1782","article-title":"Buoyant convective flow and heat dissipation of cu\u2013h2o nanoliquids in an annulus through a thin baffle","volume":"10","author":"Pushpa","year":"2021","journal-title":"J. Nanofluids"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Marzougui, S., Mebarek-Oudina, F., Magherbi, M., and Mchirgui, A. (2021). Entropy generation and heat transport of Cu\u2013water nanoliquid in porous lid-driven cavity through magnetic field. Int. J. Numer. Methods Heat Fluid Flow.","DOI":"10.1108\/HFF-04-2021-0288"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Mebarek-Oudina, F., Fares, R., Aissa, A., Lewis, R.W., and Abu-Hamdeh, N.H. (2021). Entropy and convection effect on magnetized hybrid nano-liquid flow inside a trapezoidal cavity with zigzagged wall. Int. Commun. Heat Mass Transf., 125.","DOI":"10.1016\/j.icheatmasstransfer.2021.105279"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1140\/epjp\/s13360-021-01394-z","article-title":"A study of dual stratification on stagnation point Walters\u2019 B nanofluid flow via radiative Riga plate: A statistical approach","volume":"136","author":"Shafiq","year":"2021","journal-title":"Eur. Phys. J. Plus."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Arain, M.B., Bhatti, M.M., Zeeshan, A., and Alzahrani, F.S. (2021). Bioconvection reiner-rivlin nanofluid flow between rotating circular plates with induced magnetic effects, activation energy and squeezing phenomena. Mathematics, 9.","DOI":"10.3390\/math9172139"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.powtec.2020.08.083","article-title":"Boiling flow of graphene nanoplatelets nano-suspension on a small copper disk","volume":"377","author":"Goodarzi","year":"2021","journal-title":"Powder Technol."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Goggolidou, P. (2018). Cilia: Development and Disease, CRC Press.","DOI":"10.1201\/9781315119380"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.cmpb.2016.04.008","article-title":"Influences of slip and Cu-blood nanofluid in a physiological study of cilia","volume":"131","author":"Sadaf","year":"2016","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1007\/s00397-020-01222-8","article-title":"Micro rheology of Jeffrey nanofluid through cilia beating subject to the surrounding temperature","volume":"59","author":"Shaheen","year":"2020","journal-title":"Rheol. Acta"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Imran, A., Akhtar, R., Zhiyu, Z., Shoaib, M., and Raja, M.A.Z. (2020). Heat transfer analysis of biological nanofluid flow through ductus efferentes. AIP Adv., 10.","DOI":"10.1063\/1.5135298"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Nadeem, S., and Sadaf, H. (2015). Trapping study of nanofluids in an annulus with cilia. AIP Adv., 5.","DOI":"10.1063\/1.4937474"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1140\/epjp\/i2016-16065-y","article-title":"Ciliary motion phenomenon of viscous nanofluid in a curved channel with wall properties","volume":"131","author":"Nadeem","year":"2016","journal-title":"Eur. Phys. J. Plus."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1109\/TNB.2015.2401972","article-title":"Theoretical analysis of Cu-blood nanofluid for metachronal wave of cilia motion in a curved channel","volume":"14","author":"Nadeem","year":"2015","journal-title":"IEEE Trans. Nanobiosci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1140\/epjp\/s13360-019-00029-8","article-title":"A numerical simulation of the creeping flow of TiO2-SiO2\/C2H6O2 hybrid-nano-fluid through a curved configuration due to metachronal waves propulsion of beating cilia","volume":"135","author":"Javid","year":"2020","journal-title":"Eur. Phys. J. Plus."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Awais, M., Shah, Z., Perveen, N., Ali, A., Kumam, P., and Thounthong, P. (2020). MHD effects on ciliary-induced peristaltic flow coatings with rheological hybrid nanofluid. Coatings, 10.","DOI":"10.3390\/coatings10020186"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2927","DOI":"10.3934\/mbe.2019144","article-title":"Effect of nano-particles on MHD flow of tangent hyperbolic fluid in a ciliated tube: An application to fallopian tube","volume":"16","author":"Maqbool","year":"2019","journal-title":"Math. Biosci. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1016\/j.cjph.2017.03.005","article-title":"Mathematical model for ciliary-induced transport in MHD flow of Cu-H2O nanofluids with magnetic induction","volume":"55","author":"Akbar","year":"2017","journal-title":"Chin. J. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1680","DOI":"10.1016\/j.net.2017.09.007","article-title":"Entropy analysis in a cilia transport of nanofluid under the influence of magnetic field","volume":"49","author":"Abrar","year":"2017","journal-title":"Nucl. Eng. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"68","DOI":"10.3389\/fphy.2021.631903","article-title":"Numerical treatment for dynamics of second law analysis and magnetic induction effects on ciliary induced peristaltic transport of hybrid nanomaterial","volume":"9","author":"Awan","year":"2021","journal-title":"Front. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Abrar, M.N., Sagheer, M., and Hussain, S. (2020). Entropy generation during peristaltically flowing nanofluid in an axisymmetric channel with flexible walls. Phys Scr., 95.","DOI":"10.1088\/1402-4896\/ab4aab"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Bhatti, M.M., Elelamy, A.F., Sait, S.M., and Ellahi, R. (2020). Hydrodynamics Interactions of Metachronal Waves on Particulate-Liquid Motion through a Ciliated Annulus: Application of Bio-Engineering in Blood Clotting and Endoscopy. Symmetry, 12.","DOI":"10.3390\/sym12040532"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Ahmad Farooq, A., Shah, Z., and Alzahrani, E.O. (2019). Heat Transfer Analysis of a Magneto-Bio-Fluid Transport with Variable Thermal Viscosity Through a Vertical Ciliated Channel. Symmetry, 11.","DOI":"10.3390\/sym11101240"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Munawar, S., and Saleem, N. (2020). Second Law Analysis of Ciliary Pumping Transport in an Inclined Channel Coated with Carreau Fluid under a Magnetic Field. Coatings, 10.","DOI":"10.3390\/coatings10030240"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1115\/1.3451063","article-title":"A study of entropy generation in fundamental convective heat transfer","volume":"101","author":"Bejan","year":"1979","journal-title":"J. Heat Transfer."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/BF02703797","article-title":"Entropy generation in a pipe due to non-Newtonian fluid flow: Constant viscosity case","volume":"31","author":"Pakdemirli","year":"2006","journal-title":"Sadhana"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1016\/j.ijnonlinmec.2010.01.007","article-title":"Entropy analysis for viscoelastic magnetohydrodynamic flow over a stretching surface","volume":"45","author":"Saouli","year":"2010","journal-title":"Int. J. Non Linear Mech."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1108\/HFF-10-2018-0606","article-title":"Numerical investigation for second law analysis of ferrofluid inside a porous semi annulus: An application of entropy generation and exergy loss","volume":"29","author":"Sheikholeslami","year":"2019","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1647","DOI":"10.1007\/s00231-012-1009-7","article-title":"Entropy generation in non-Newtonian fluids due to heat and mass transfer in the entrance region of ducts","volume":"48","author":"Galanis","year":"2012","journal-title":"Heat Mass Transf."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1155\/2014\/413213","article-title":"Parametric analysis of entropy generation in magneto-hemodynamic flow in a semi-porous channel with OHAM and DTM","volume":"11","author":"Rashidi","year":"2014","journal-title":"Appl. Bionics Biomech."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"834","DOI":"10.1108\/HFF-06-2019-0506","article-title":"A hybrid investigation on numerical and analytical solutions of electro-magnetohydrodynamics flow of nanofluid through porous media with entropy generation","volume":"30","author":"Ellahi","year":"2019","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Bhatti, M.M., Abbas, T., Rashidi, M.M., and Ali, M.E.S. (2016). Numerical simulation of entropy generation with thermal radiation on MHD Carreaunanofluid towards a shrinking sheet. Entropy, 18.","DOI":"10.3390\/e18060200"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"AbdollahzadehJamalabadi, M.Y., Hooshmand, P., Hesabi, A., Kwak, M.K., Pirzadeh, I.I., Keikha, A.J., and Negahdari, M. (2016). Numerical investigation of thermal radiation and viscous effects on entropy generation in forced convection blood flow over an axisymmetric stretching sheet. Entropy, 18.","DOI":"10.3390\/e18060203"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1615\/JPorMedia.2021036038","article-title":"Assessment of entropy generation and heat transfer in three-dimensional hybrid nanofluids flow due to convective surface and base fluids","volume":"24","author":"Upreti","year":"2021","journal-title":"J. Porous Media"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2358\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:42:53Z","timestamp":1760168573000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2358"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,8]]},"references-count":44,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["sym13122358"],"URL":"https:\/\/doi.org\/10.3390\/sym13122358","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,8]]}}}