Impact of variable viscosity effects on Eyring–Powell nanofluid stream over a thin needle with applications in microbial fuel cells

Abstract The work investigates the effect of varying viscosity on non-Newtonian Eyring–Powell nanoliquid across thin-needle geometry. The work aims to boost transport efficiency and thermal regulation in microbial fuel cells by integrating rheological complexity with nanoparticle-augmented heat and mass transfer. It emphasizes the importance of adjusting fluid properties to achieve enhanced electrochemical performance and greater energy output. The investigation analyses the continuous, two-dimensional stream of an Eyring–Powell nanoliquid with varying viscosity over a moving slender needle, particularly emphasizing its relevance to microbial fuel cells. The flow is analyzed in a permeable zone influenced by dual heat sources, activation energy, and bioconvection driven by motile microorganisms. The variable viscosity of the fluid reflects changes in temperature, concentration, and microorganisms, which substantially influence momentum, heat, and mass transport. By employing the right similarity alterations, the governing partial differential equations are transformed into ordinary differential equations and analytically resolved via the Homotopy perturbation method. The present study provides a substantially more comprehensive physical description by coupling variable viscosity, magnetohydrodynamics, porous media, nonlinear heat generation, activation energy, chemical reaction, nanoparticle transport, and bioconvection of motile microorganisms within a unified framework. This combination of mechanisms has not previously been investigated using the Homotopy perturbation method. The most important discovery was that the transport behavior is controlled by the strong coupling between temperature-dependent viscosity, nanoparticle migration, microorganism bioconvection, and magnetic damping. This showed that these mechanisms can be used to simultaneously control mass transport, flow, and heat transfer. The findings enable more precise prediction and optimization of non-Newtonian bioconvective nanofluid systems by offering a deeper physical understanding of the controlling transport processes. For the design and optimization of microbial fuel cells, bioelectrochemical reactors, biosensors, microfluidic devices, and advanced thermal management systems, where effective control of heat transfer, nanoparticle dispersion, and microorganism distribution was crucial, the results provided helpful guidelines. The findings provide significant theoretical insights for the design of sophisticated energy systems that integrate non-Newtonian nanofluids with biological transport mechanisms.