197700c8-c12d-42d8-a061-98680fcc19c120240229043526593wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON FLUID MECHANICS2224-347X1790-508710.37394/232013http://wseas.org/wseas/cms.action?id=4036123202412320241910.37394/232013.2024.19https://wseas.com/journals/fluids/2024.phpAmineEl HarfoufMultidisciplinary Laboratory of Research and Innovation (LaMRI), Energy, Materials, Atomic and Information Fusion (EMAFI) Team, Polydisciplinary Faculty of Khouribga, Sultan Moulay Slimane University, MOROCCORachidHerbaziIntelligent Systems and Applications Laboratory (LSIA), EMSI, Tangier, MOROCCOSanaa HayaniMounirMultidisciplinary Laboratory of Research and Innovation (LaMRI), Energy, Materials, Atomic and Information Fusion (EMAFI) Team, Polydisciplinary Faculty of Khouribga, Sultan Moulay Slimane University, MOROCCOHassaneMes-AdiLaboratory of Process Engineering, Computer Science and Mathematics, National School of Applied Sciences of the Khouribga University of Sultan Moulay Slimane, MOROCCOAbderrahimWakifFaculty of Sciences Aïn Chock, Laboratory of Mechanics, Hassan II University, Casablanca, MOROCCOA numerical investigation is conducted into a two-dimensional mathematical model of magnetized unsteady incompressible Williamson fluid flow over a sensor surface with fixed thermal conductivity and external squeezing accompanied by viscous dissipation effect. Based on the flow geometry under consideration, the current flow model was created. The momentum equation takes into consideration the magnetic field when describing the impact of Lorentz forces on flow behavior. The energy equation takes varying thermal conductivity into account while calculating heat transmission. The extremely complex nonlinear, unstable governing flow equations for the now under investigation are coupled in nature. Due to the inability of analytical or direct methods, the Runge-Kutta scheme (RK-4) via similarity transformations approach is used to tackle the physical problem under consideration. The physical behavior of various control factors on the flow phenomena is described using graphs and tables. For increasing values of the Weissenberg parameter and the permeable velocity parameter, the temperature boundary layer thickens. As the permeable velocity parameter and squeezed flow index increased, the velocity profile shrank. 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