{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,15]],"date-time":"2026-02-15T21:19:34Z","timestamp":1771190374690,"version":"3.50.1"},"reference-count":53,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T00:00:00Z","timestamp":1666828800000},"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>Pulsatory movements appear in a variety of fascinating applications involving periodic flow propagation and control. Pulsing encourages mixing and, as a result, mass and heat exchange with the boundaries. Pulsing also helps to decrease surface fouling by allowing solid particles to migrate. An exact solution of the Navier\u2013Stokes equations for the transport of an incompressible viscous fluid in a channel with arbitrary pressure distribution is described in this study. The flow is defined by two primary parameters: the pulsation parameter, which is determined by the periodic pressure gradient, and the kinetic Reynolds number, which is determined by the pulsation frequency. The purpose of employing hybrid nanofluid (HNF) is to increase the base fluid\u2019s thermal conductivity. We regard Ag and Au as nanoparticles (NPs) and blood as a base fluid for this phenomenon. Broadening this reveals that the consideration of nanoparticles has impressively extended the warm movement at the parcels of both turbulent and laminar frameworks. Attention is paid to the slope of speed, temperature, and voltage. The geometric model is therefore described using a symmetry technique. We developed the governing equation for this problem\u2019s analytical solutions. The velocity and temperature fields solution is given in the form of the Bessel and modified Bessel functions. Graph results show the mathematical benefits of the current limits: for instance, Hartmann number M, solid volume part of nanoparticles \u03d5, Reynolds number Re\u03b2, Prandtl number Pr, intermittent slob limit, etc. The strain angles introduced in the stress contrast, frictional force, velocity profile, and temperature profile were obtained, and the characteristics of the vortex were investigated. Resources at various boundaries of the perceptual flow are examined. As with the final essence, the smoothest results are analyzed and recorded. It has also been discovered that the velocity may be regulated by the external magnetic field, which affects the temperature profiles and hence the heat transfer, which can be enhanced or lowered by mastering the magnetic field.<\/jats:p>","DOI":"10.3390\/sym14112254","type":"journal-article","created":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T22:36:17Z","timestamp":1666910177000},"page":"2254","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["MHD Pulsatile Flow of Blood-Based Silver and Gold Nanoparticles between Two Concentric Cylinders"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0188-5133","authenticated-orcid":false,"given":"Faisal","family":"Shahzad","sequence":"first","affiliation":[{"name":"Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9438-6132","authenticated-orcid":false,"given":"Wasim","family":"Jamshed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4380-2401","authenticated-orcid":false,"given":"Farheen","family":"Aslam","sequence":"additional","affiliation":[{"name":"Department of Biotechnology, Lahore College for Women University, Lahore 54000, Pakistan"}]},{"given":"Rasheeda","family":"Bashir","sequence":"additional","affiliation":[{"name":"Department of Biotechnology, Lahore College for Women University, Lahore 54000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3151-9967","authenticated-orcid":false,"given":"El Sayed M.","family":"Tag El Din","sequence":"additional","affiliation":[{"name":"Electrical Engineering, Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt"}]},{"given":"Hamiden Abd El-Wahed","family":"Khalifa","sequence":"additional","affiliation":[{"name":"Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt"},{"name":"Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia"}]},{"given":"Agaeb Mahal","family":"Alanzi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.rinp.2016.11.057","article-title":"MHD pulsatile flow of engine oil based carbon nanotubes between two concentric cylinders","volume":"7","author":"Haq","year":"2017","journal-title":"Results Phys."},{"key":"ref_2","first-page":"491","article-title":"Effect of magnetic field on blood flow","volume":"18","author":"Vardanyan","year":"1973","journal-title":"Biofizika"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1088\/0959-5309\/40\/1\/328","article-title":"The amplitude of sound waves in resonators","volume":"40","author":"Richardson","year":"1928","journal-title":"Proc. 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