Purpose This study explores the coupled effects of magnetic fields, internal heat generation and thermal radiation and Brownian motion on the flow and heat transfer behavior of a Casson fluid over parabolic surfaces. These geometries are commonly found in aerospace, optical, and solar energy applications, where precise thermal prediction is essential. The primary objective is to evaluate the thermal performance of water-based Fe3O4/TiO hybrid nanofluids exhibiting shear-dependent characteristics. Design/methodology/approach The governing partial differential equations describing fluid motion, heat transfer, nanoparticle transport and microorganism distribution are transformed into dimensionless forms and solved numerically via the MATLAB BVP4C boundary value solver. Parametric analyses assess the influence of transverse magnetization, radiative energy transfer and volumetric heat generation. Findings This study reveals that radiation substantially enhances mass transfer, with a measured increase in the Nusselt number of up to 5.3%. Furthermore, internal heat generation bolsters microbial motility, leading to an increase in the concentration of motile microorganisms of up to 4.7%. Overall thermal transport across the parabolic geometry is further improved by the incorporation of water-based Fe3O4/TiO hybrid nanoparticles. Originality/value This work provides a comprehensive multiphysics assessment of hybrid nanofluid flow over paraboloid surfaces within the Casson and Williamson fluid framework, an area with limited prior exploration. The insights gained offer practical value for the design and optimization of aerospace components, optical systems and solar concentrators operating under magnetic and radiative influences.
Abdullah et al. (Mon,) studied this question.