Multiscale and Multidisciplinary Modeling, Experiments and Design (2025) 8:383 https://doi.org/10.1007/s41939-025-00972-3 ORIGINAL PAPER Multiscale modeling of Jeffrey-Casson immiscible fluid dynamics under electrokinetic and magnetohydrodynamic effects M. Bhaskar 1 · K. Ramesh Babu 2 · S. U. Khan 3 · R. K. Lodhi 4 · F. Mebarek-Oudina 5,6 · Muhammad Sohail 7,8 · K. Ramesh 9,10 Received: 1 May 2025 / Accepted: 7 July 2025 © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025 Abstract This study presents a theoretical investigation of two immiscible non-Newtonian fluids such as Jeffrey and Casson types flowing in a vertical microchannel under the combined effects of electroosmosis, magnetic field, Hall current, buoyancy- driven convection, thermal radiation, and internal heat generation. Distinct governing equations are formulated for each fluid based on their rheological properties and solved analytically with appropriate interfacial and boundary conditions. The model introduces key non-dimensional parameters to capture the influence of electrokinetic and magnetohydrodynamic forces on fluid motion and heat transfer. The novelty of this work lies in its integration of multiple physical effects into an exact analytical framework for immiscible non-Newtonian fluid dynamics in microchannels. The results reveal that electroosmosis enhances flow velocity. Internal heat generation and radiation elevate the temperature profile, whereas higher Prandtl numbers suppress it. These findings offer valuable insights for optimizing complex fluid systems in confined geometries. Applications of this study also include the design of microfluidic devices, thermal management systems, and biomedical transport technologies. Keywords Immiscible non-Newtonian fluids · Microchannel heat transfer · Thermal radiation · Electromagnetohydrody- namics · Buoyancy forces B K. Ramesh ramesh.katta1@gmail.com 1 Department of Mathematics, Osmania University, Hyderabad, Telangana 500007, India 2 Department of Mathematics, University College of Engineering, Osmania University, Hyderabad, Telangana 500007, India 3 Department of Mathematics, Namal University, Mianwali 42250, Pakistan 4 Department of Applied Sciences, Symbiosis International (Deemed University), Symbiosis Institute of Technology, Pune 412115, India 5 Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu 602105, India 6 Department of Physics, Faculty of Sciences, University of 20 Août 1955-Skikda, B.P. 26 Road El-Hadaeik, 21000 Skikda, Algeria 7 Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Pakistan List of symbols C p Specific heat (J/kg K) T i Temperature of the fluid (K) u i Velocity of the fluid (m/s) e Electric charge (C) μ 1 Viscosity of fluid in Region-I (kg/ms) μ 2 Viscosity of fluid in Region-II (kg/ms) B Uniform magnetic field (T) J Electric current density (A/m 2 ) ρ e Charge density (A/m 2 ) σ 1 Electrical conductivity in Region-I (S/m) 8 Composite Materials Scientific Research Center of Azerbaijan State University of Economics (UNEC), 194 Murtuza Mukhtarov Street, AZ1065 Baku, Azerbaijan 9 Department of Pure and Applied Mathematics, School of Mathematical Sciences, Sunway University, Bandar Sunway, 47500 Petaling Jaya, Selangor Darul Ehsan, Malaysia 10 Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Jalandhar, Punjab 144411, India 0123456789().: V,-vol 123 Content courtesy of Springer Nature, terms of use apply. Rights reserved.