MHD Casson fluid flow and heat transfer over a bidirectional stretching sheet with variable thermal conductivity and dissipative-radiative heat transfer

Understanding heat transfer in non-Newtonian fluids under magnetic fields is crucial for industrial, biological, and engineering applications. Studying MHD Casson fluid flow over a bidirectional stretched sheet is essential to understand intricate heat transfer behaviours in processes like metal stretching and polymer extrusion. This study examines MHD Casson fluid flow and heat transfer over a bidirectional stretching sheet, considering variable thermal conductivity, viscous dissipation, and thermal radiation. Velocity slip condition is applied which applies further complexity into problem. The governing PDEs are converted into coupled ODEs using similarity transformation and solved numerically using spectral quasilinearisation method (SQLM). It has been observed that the Eckert number has a great impact on the heat transfer coefficient, it increases by about (Formula presented.) with an enhancement of the Eckert number from (Formula presented.) to (Formula presented.) Both (Formula presented.) and (Formula presented.) directional velocity profiles decrease with Hartmann number, Casson parameter, and the slip velocity parameter (Formula presented.) and (Formula presented.) This study's findings are relevant to biomedical engineering (e.g. targeted drug delivery) and polymer manufacturing (e.g. extrusion and film stretching). The inclusion of bidirectional stretching and slip conditions also makes it applicable to microfluidic and nanofluidic applications. The results are further validated by their agreement with earlier research. © 2025 Informa UK Limited, trading as Taylor & Francis Group.