{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T23:28:23Z","timestamp":1768692503656,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,7]],"date-time":"2022-05-07T00:00:00Z","timestamp":1651881600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shanghai Major Science Popularization","award":["20DZ2306500"],"award-info":[{"award-number":["20DZ2306500"]}]},{"name":"Shanghai Major Science Popularization","award":["19DZ2290400"],"award-info":[{"award-number":["19DZ2290400"]}]},{"name":"Special Project for Capacity Improvement of Shanghai Professional Technical Service Platform","award":["20DZ2306500"],"award-info":[{"award-number":["20DZ2306500"]}]},{"name":"Special Project for Capacity Improvement of Shanghai Professional Technical Service Platform","award":["19DZ2290400"],"award-info":[{"award-number":["19DZ2290400"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper deals with the MHD peristaltic flow of Williamson fluids through a porous medium between two joint cylinders. The fluid flow was considered to be that of a non-Newtonian fluid, i.e., a Williamson fluid. The inner tube was uniform, while the flexible outer tube had a Sine wave moving down its wall. The analytical solutions for velocity and temperature were obtained as functions (Bessell functions of the first and second types). The solution for velocity profile, temperature, and concentration distribution were obtained as functions of the physical parameters of the problem (Darcy number, magnetic parameter, Grasoff thermal number, Reynolds number, Prantl number, and Schmidt number) along with other physical parameters. The effect of the physical parameters was discussed graphically. A comparison with previously published graphical results was also carried out. The ambition of the present paper is to contribute to practical applications in geographical and physiological fluid dynamics, such as on sandstone, in the human lungs, on beach sand, on limestone, and in the bile duct. This study is based on theoretical research and can be helpful in the fields of fluid mechanics and mathematics.<\/jats:p>","DOI":"10.3390\/sym14050953","type":"journal-article","created":{"date-parts":[[2022,5,8]],"date-time":"2022-05-08T23:27:25Z","timestamp":1652052445000},"page":"953","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Analytical Solution for the MHD Flow of Non-Newtonian Fluids between Two Coaxial Cylinders"],"prefix":"10.3390","volume":"14","author":[{"given":"Li","family":"Chen","sequence":"first","affiliation":[{"name":"Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Shanghai 201804, China"},{"name":"School of Automotive Studies, Tongji University, Shanghai 201804, China"}]},{"given":"Munawwar Ali","family":"Abbas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Baltistan Skardu, Skardu 16200, Pakistan"}]},{"given":"Wissam Sadiq","family":"Khudair","sequence":"additional","affiliation":[{"name":"Directorate of Education Babylon, Ministry of Education, Babylon 51014, Iraq"}]},{"given":"Bo","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Tongji University, Shanghai 201804, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1615\/HeatTransRes.2018016105","article-title":"Entropy generation in blood flow with heat and mass transfer for the Ellis fluid model","volume":"49","author":"Bhatti","year":"2018","journal-title":"Heat Transf. 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