Novel heat exploration investigation for bioconvected Oldroyd-B nanofluid with variable thermal conductivity and Arrhenius energy induced by nailed boundary

Oldroyd-B nanofluids have potential applications in enhanced heat transfer systems, drug delivery, and advanced material processing due to their unique rheological properties. Bioconvection finds applications in biomedical research, environmental monitoring, and optimizing fluid dynamics in biotechnological and pharmaceutical processes. Due to these applications current study investigates bioconvection in the flow of Oldroyd-B nanofluid subjected to Joule heating with convected boundaries. For uniqueness of problem the effects of variable thermal connectivity and activation energy are taken into account. In addation the influence of heat source and thermal radiation are part of current model. The governing PDEs of mathematical model incorporates the Oldroyd-B rheological framework to capture the viscoelastic nature of the fluid are transformed into ODEs via similarity solution. Matlab platform via shooting algorithm is involved to solve transformed system. Through numerical simulations the stimulus of involving parameters on velocity f '(eta) temperature theta(eta), concentration phi(eta), and microbes profile X(eta) are displayed in graphical and tabulated form. For strength of problem the streamlines and graphs of physical quantities are also designed. It is noted that velocity curve decreased for increasing value of magnetics parameter and opposite trend is noted in velocity distribution for increasing value of mixed convection parameter lambda. Moreover, thermal layer theta is diminished for growing value of Pr, a reverse relation is noted in concentration profile for value of activation energy.