In the modern era, the integration of nanotechnology with solar radiation has emerged as an innovative approach to enhance thermal transfer efficiency across various technological and industrial sectors. This study investigates the thermal transfer performance of a ternary hybrid Tangent hyperbolic nanofluid flow in a porous medium within a parabolic trough solar collector (PTSC) over a stretching surface. The working fluid consists of a dispersion of copper (Cu), iron oxide ( \(Fe_3O_4\) ), and silica ( \(SiO_2\) ) nanoparticles in ethylene glycol (EG). The analysis thermal transfer incorporates the Cattaneo-Christov thermal conduction model and quadratic solar radiation as the heat source, subject to a convective boundary condition. The effects of various parameters, including magnetic field strength, variable viscosity, viscous dissipation, buoyancy and inertia forces, are considered. Additionally, entropy generation is analyzed to assess the thermal management system. The governing conservation equations are transformed into non-linear ordinary differential equations (ODEs) using suitable non-dimensional variables and solved numerically with the Keller-box method (KBM), an implicit finite difference scheme. The impact of control parameters on fluid velocity, temperature field, drag coefficient, Nusselt number, and entropy generation is examined through graphical and tabular representations using MATLAB R2023a. The results indicates that higher magnetic field strength, viscosity parameter, inertia constant, and slip parameter reduce the flow of velocity field. However, temperature as well as entropy generation exhibit an increasing trend with viscosity and magnetic field strength. Furthermore, an increase in thermal radiation and the Biot number enhances both entropy and energy transfer in solar aircraft applications, whereas energy profiles decrease with thermal time relaxation. The rate of heat transfer was enhanced with nanoparticle volume fraction, achieving maximum values \(8.5\%\) , \(18.9\%\) , and \(31.6\%\) for \(\phi = 0.1\) , \(\phi = 0.2\) , and \(\phi =0.3\) , respectively. Generally, the ternary hybrid nanofluid shows a higher heat transfer enhancement ( \(4.01\%\) ) compared to the convectional hybrid nanofluid ( \(3.57\%\) ) at higher value.
