<p>The current study explores Eyring–Powell nanofluid (EPF) across a curved stretching surface (CSS) in the presence of micro-organisms, thermal radiation and Lorentz force. It has implications in advanced engineering and biomedical applications. Understanding non-Newtonian fluid behaviour is crucial for optimising heat and mass transfer (HMT), thermal management and targeted drug delivery. We employed Lorentz’s force, chemical reaction and thermal radiation on the fluid flow. As is well known, HMT over the CSS is relevant in biomedical engineering for applications like drug delivery systems and medical implants. The fundamental nonlinear partial differential equations (PDEs) are converted to ordinary differential equations (ODEs) by applying suitable similarity transform and numerically solved by using the Chebyshev spectral method (CSM). Numerical results are concluded by employing tables in attractive representations, which are discussed for different values of non-dimensional curvature radius, permeability coefficient, Eyring–Powell liquid factors, radiation factor, Brownian coefficient, thermophoresis factor, heat generation (absorption) factor, chemical reaction factor, Schmidt factor, Dufour numeral, Soret numeral, magnetic factor, Eckert numeral, bio-convection, Lewis numeral, Peclet numeral and bio-convection factor on the velocity, temperature, concentration and spreading of micro-organisms. The results indicate that the velocity and concentration increase with the rise of curvature radius and permeability coefficient, whereas the distributions of temperature and micro-organisms decrease as these parameters increase. Moreover, all the temperature, concentration and micro-organisms’ distributions increase as the Brownian coefficient increases. Finally, the temperature distribution increases with the assessment of the thermophoresis factor. Conversely, the concentration and propagation of micro-organisms decrease.</p>