{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T15:15:19Z","timestamp":1769094919129,"version":"3.49.0"},"reference-count":37,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2016,3,11]],"date-time":"2016-03-11T00:00:00Z","timestamp":1457654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Entropy generation during peristaltic flow of nanofluids in a non-uniform two dimensional channel with compliant walls has been studied. The mathematical modelling of the governing flow problem is obtained under the approximation of long wavelength and zero Reynolds number (creeping flow regime). The resulting non-linear partial differential equations are solved with the help of a perturbation method. The analytic and numerical results of different parameters are demonstrated mathematically and graphically. The present analysis provides a theoretical model to estimate the characteristics of several Newtonian and non-Newtonian fluid flows, such as peristaltic transport of blood.<\/jats:p>","DOI":"10.3390\/e18030090","type":"journal-article","created":{"date-parts":[[2016,3,14]],"date-time":"2016-03-14T11:03:45Z","timestamp":1457953425000},"page":"90","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":80,"title":["Analysis of Entropy Generation in the Flow of Peristaltic Nanofluids in Channels With Compliant Walls"],"prefix":"10.3390","volume":"18","author":[{"given":"Munawwar","family":"Abbas","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanqin","family":"Bai","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6309-8688","authenticated-orcid":false,"given":"Mohammad","family":"Rashidi","sequence":"additional","affiliation":[{"name":"Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, Shanghai 201804, China"},{"name":"ENN-Tongji Clean Energy Institute of Advanced Studies, Shanghai 200072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Bhatti","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,3,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.jnnfm.2014.05.003","article-title":"Simulation of an elastic particle in Newtonian and Viscoelastic fluids subjected to confined shear flow","volume":"210","author":"Villone","year":"2014","journal-title":"J. Non-Newton. Fluid Mech."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.jmaa.2014.06.072","article-title":"Regularity criterion for generalized Newtonian fluids in bounded domains","volume":"421","author":"Bae","year":"2015","journal-title":"J. Math. Anal. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/j.powtec.2013.12.015","article-title":"Transient vertically motion of a soluble particle in a Newtonian fluid media","volume":"253","author":"Hatami","year":"2014","journal-title":"Powder Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1080\/00986445.2011.586756","article-title":"A study of non-Newtonian flow and heat transfer over a non-isothermal wedge using the homotopy analysis method","volume":"199","author":"Rashidi","year":"2012","journal-title":"Chem. Eng. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7108","DOI":"10.1016\/j.amc.2011.01.026","article-title":"Power law fluid model for blood flow through a tapered artery with a stenosis","volume":"217","author":"Nadeem","year":"2011","journal-title":"Appl. Math. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1016\/j.jfranklin.2013.04.027","article-title":"Investigation of the heat transfer of a non-Newtonian fluid flow in an axisymmetric channel with porous wall using Parameterized Perturbation Method (PPM)","volume":"351","author":"Ashorynejad","year":"2014","journal-title":"J. Frankl. Inst."},{"key":"ref_7","unstructured":"Choi, S.U.S. (1995, January 12\u201317). Enhancing thermal conductivity of fluids with nanoparticles. Proceedings of ASME International Mechanical Engineering Congress & Exposition, San Francisco, CA, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"911","DOI":"10.18869\/acadpub.jafm.67.223.23941","article-title":"Dual Solutions for MHD Jeffery\u2013Hamel Nano-fluid Flow in Non-parallel Walls using Predictor Homotopy Analysis Dual Solutions Method","volume":"8","author":"Freidoonimehr","year":"2015","journal-title":"J. Appl. Fluid Mech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1007\/s00521-012-1316-4","article-title":"MHD natural convection in a nanofluid filled inclined enclosure with sinusoidal wall using CVFEM","volume":"24","author":"Sheikholeslami","year":"2014","journal-title":"Neural Comput. Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.ijthermalsci.2014.08.009","article-title":"Unsteady MHD free convective flow past a permeable stretching vertical surface in a nano-fluid","volume":"87","author":"Freidoonimehr","year":"2015","journal-title":"Int. J. Therm. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.ijthermalsci.2014.06.009","article-title":"Nano fluid flow in tapering stenosed arteries with permeable walls","volume":"85","author":"Akbar","year":"2014","journal-title":"Int. J. Therm. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Freidoonimehr, N., Rostami, B., Rashidi, M.M., and Momoniat, E. (2014). Analytical Modelling of Three-Dimensional Squeezing Nanofluid Flow in a Rotating Channel on a Lower Stretching Porous Wall. Math. Probl. Eng.","DOI":"10.1155\/2014\/692728"},{"key":"ref_13","unstructured":"Abbas, M.A., Bai, Y., Bhatti, M.M., and Rashidi, M.M. (2015). Three dimensional peristaltic flow of hyperbolic tangent fluid in non-uniform channel having flexible walls. Alex. Eng. J., in press."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2403","DOI":"10.1016\/j.physa.2007.12.017","article-title":"Peristaltic flow of a couple stress fluid in an annulus: Application of an endoscope","volume":"387","author":"Mekheimer","year":"2008","journal-title":"Physica A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.joems.2014.10.007","article-title":"Rheological properties of Reiner-Rivlin fluid model for blood flow through tapered artery with stenosis","volume":"24","author":"Akbar","year":"2016","journal-title":"J. Egypt. Math. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1016\/j.aej.2015.03.030","article-title":"Peristaltic transport of MHD flow and heat transfer in an asymmetric channel: Effects of variable viscosity, velocity-slip and temperature jump","volume":"54","author":"Sinha","year":"2015","journal-title":"Alex. Eng. J."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Abbas, M.A., Bai, Y., Rashidi, M.M., and Bhatti, M.M. (2015). Application of drug delivery in megnetohydrodynamics peristaltic blood flow of nano fluid in a nan-uniform channel. J. Mech. Med. Biol.","DOI":"10.1142\/S0219519416500524"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1016\/S0096-3003(03)00672-6","article-title":"Peristaltic flow of blood under effect of a magnetic field in a non-uniform channels","volume":"153","author":"Mekheimer","year":"2004","journal-title":"Appl. Math. Comput."},{"key":"ref_19","first-page":"1","article-title":"Multi-Step dtm simulation of magneto-peristaltic flow of a conducting Williamson viscoelastic fluid","volume":"9","author":"Keimanesh","year":"2013","journal-title":"Int. J. Appl. Math. Mech."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"720","DOI":"10.1016\/0360-5442(80)90091-2","article-title":"Second law analysis in heat transfer","volume":"5","author":"Bejan","year":"1980","journal-title":"Energy"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Bejan, A. (1996). Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-Time Systems and Finite-Time Processes, CRC Press.","DOI":"10.1063\/1.362674"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1016\/j.energy.2009.03.014","article-title":"Local entropy generation for saturated two-phase flow","volume":"34","author":"Revellin","year":"2009","journal-title":"Energy"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Salas, H., Cuevas, S., and de Haro, M.L. (1999). Entropy generation analysis of magnetohydrodynamic induction devices. J. Phys. D Appl. Phys., 32.","DOI":"10.1088\/0022-3727\/32\/20\/304"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1411","DOI":"10.3390\/e17031411","article-title":"Entropy Generation Analysis for a CNT Suspension Nanofluid in Plumb Ducts with Peristalsis","volume":"17","author":"Akbar","year":"2015","journal-title":"Entropy"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.energy.2014.12.034","article-title":"Entropy generation and energy conversion rate for the peristaltic flow in a tube with magnetic field","volume":"82","author":"Akbar","year":"2015","journal-title":"Energy"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/j.ijheatmasstransfer.2013.03.004","article-title":"Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid","volume":"62","author":"Rashidi","year":"2013","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_27","unstructured":"Rashidi, M.M., Bagheri, S., Momoniat, E., and Freidoonimehr, N. (2015). Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet. Ain Shams Eng. J., in press."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5891","DOI":"10.3390\/e16115891","article-title":"Heat Transfer Characteristics of a Speaker Using Nano-Sized Ferrofluid","volume":"16","author":"Lee","year":"2014","journal-title":"Entropy"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"5777","DOI":"10.3390\/e16115777","article-title":"Multiscale Compression Entropy of Microvascular Blood Flow Signals: Comparison of Results from Laser Speckle Contrastand Laser Doppler Flowmetry Data in Healthy Subjects","volume":"16","author":"Baumert","year":"2014","journal-title":"Entropy"},{"key":"ref_30","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_31","doi-asserted-by":"crossref","first-page":"144","DOI":"10.3390\/e15010144","article-title":"Numerical study of entropy generation in a flowing nanofluid used in micro-and minichannels","volume":"15","author":"Hassan","year":"2013","journal-title":"Entropy"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/j.physa.2014.09.053","article-title":"Entropy generation of nanofluid in presence of magnetic field using Lattice Boltzmann Method","volume":"417","author":"Sheikholeslami","year":"2015","journal-title":"Physica A"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Baag, S., Mishra, S.R., Dash, G.C., and Acharya, M.R. (2016). Entropy generation analysis for viscoelastic MHD flow over a stretching sheet embedded in a porous medium. Ain Shams Eng. J., in press.","DOI":"10.1016\/j.asej.2015.10.017"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1016\/j.ijheatmasstransfer.2013.06.010","article-title":"A review of entropy generation in nanofluid flow","volume":"65","author":"Mahian","year":"2013","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1017\/S0022112069000899","article-title":"Peristaltic pumping with long wavelength at low Reynolds number","volume":"37","author":"Shapiro","year":"1969","journal-title":"J. Fluid Mech."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1007\/BF01332164","article-title":"Peristaltic transport of a power-law fluid: Application to the ductus efferentes of the reproductive tract","volume":"27","author":"Srivastava","year":"1988","journal-title":"Rheol. Acta."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/0021-9290(76)90130-5","article-title":"Peristaltic pumping in non-uniform tubes","volume":"9","author":"Gupta","year":"1976","journal-title":"J. Biomech."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/3\/90\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:20:37Z","timestamp":1760210437000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/3\/90"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,11]]},"references-count":37,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,3]]}},"alternative-id":["e18030090"],"URL":"https:\/\/doi.org\/10.3390\/e18030090","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,11]]}}}