Abstract
<jats:p> This study aims to examine the elastic deformation of a Diamond-SiO <jats:sub>2</jats:sub> -Co <jats:sub>3</jats:sub> O <jats:sub>4</jats:sub> /NaAlg based ternary hybrid nanofluid across a thin needle with activation energy, using modified and classical Hamilton-Crosser models. Using an appropriate similarity variable, the constitutive PDEs are transmuted into a system of connected ODEs. The efficient bvp4c method is then utilized to mathematically solve the resultant equations. The Diamond-CoO <jats:sub>4</jats:sub> -SiO <jats:sub>2</jats:sub> /NaC <jats:sub>6</jats:sub> H <jats:sub>7</jats:sub> O <jats:sub>6</jats:sub> -based THNF using the classical and modified HCM offers important insights into improving thermal performance in sophisticated heat transfer applications. By accounting for the effects of LTNE phenomena, these models aid in the prediction of the effective thermal conductivity of nanofluids, guaranteeing more precise thermal management solutions. The nuclear reactors, solar thermal collectors, electronic device thermal management, and high-performance cooling systems are just a few of the technical fields where the results can be used because effective heat dissipation is essential. For both modified and classical HCM, the liquid phase thermal distribution and liquid and solid rate of heat transfer upsurge although the solid phase thermal distributions decline as the interphase heat transfer parameter rises. </jats:p>