Deep Galerkin method computation for high machinery cooling with microbial swimmers in viscoelastic nanofluids with non-Fourier and non-Fick fluxes

Purpose Efficient thermal management remains a critical challenge for modern spacecraft due to increasing power densities and extreme operating conditions. This study aims to investigate the flow, heat and mass transfer characteristics of third-grade nanofluid containing microbial swimmers over a horizontal cylinder under the influence of an inclined magnetic field, incorporating non-Fourier heat flux and non-Fick mass flux models. Design/methodology/approach The highly nonlinear coupled system of ordinary differential equations is solved numerically using the deep Galerkin method (DGM), a robust physics-informed deep learning approach. Findings The effects of key parameters such as thermal relaxation parameter (λ1), concentration relaxation parameter (λt), curvature parameter (γ) and third-grade viscoelastic fluid parameter on velocity, temperature, concentration and motile density profiles are thoroughly analyzed. Quantitative results show that an increase in the thermal relaxation parameter reduces the skin-friction coefficient by approximately 13% (from 3.417 to 2.968) while decreasing the local Nusselt number and increasing the local Sherwood and density numbers. A similar trend is observed with the concentration relaxation parameter. Microbial swimmers significantly enhance micro-convection and the inclined magnetic field together with the relaxation parameters provide effective control over thermal and mass boundary layers. Overall, the third-grade viscoelastic nanofluid with microbial swimmers demonstrates superior and tunable thermal performance compared with conventional fluids. Originality/value The present analysis demonstrates that third grade viscoelastic nanofluids with microbial swimmers offer superior thermal performance compared to conventional fluids, making them promising candidates for advanced bio-inspired spacecraft cooling systems. This work provides valuable insights for the development of next-generation passive and active thermal management technologies for satellites and deep-space missions.