The tangent hyperbolic fluid model is interesting models in all the non-Newtonian fluid model, which is developed for particular applications in chemical engineering systems such as polymer solution, ceramic processing, fluid beds and oil recovery. Hence the intent of the present study is to explore the flow and thermal behavior of tangent hyperbolic fluid flowing through an upright microchannel. In the analysis, water and ethylene glycol are the base fluid with titanium and copper nanoparticles considered. The combined impact of nonlinear thermal radiation, no slip, buoyancy force, and Newton boundary condition on the thermal performance are studied, and further the skin friction and Nusselt number are examined. The thermal dependent heat source effect was also taken into account. The governing equations were solved numerically by employing Runge-Kutta Fehlberg’s fourth-fifth order. The impact of the pertinent constraint on the Nusselt number, thermal field, flow field, skin friction, Bejan number, and entropy generation are depicted graphically and examined. Entropy generation rises by 15% when ethylene glycol is a base fluid and 12% when the water a base fluid, with an enhancement of the Brinkman number by 200%. The outturn entrenched that the heat transfer rate in water-based hybrid nanofluid is more remarkable when compared with the heat transfer rate of EG-based hybrid nanofluid. It is noted that the significant increment in Nusselt number has been attained through a rise in the Weissenberg number and power law index.