<p>Theoretical study on heat and mass transport in tangent hyperbolic fluid using mathematical modeling and numerical simulations has been the cheapest means for exploring the phenomenon. Physical laws and boundary conditions under some realistic assumptions are solved numerically. Convergence and grid-independent analysis are performed under a specified computational tolerance. Several numerical experiments are done to explore the behaviors and trends of field variables against related parameters<b>.</b> Bar graphs are a quick review of the trend in quantities related to the data size. Therefore, the trend of the Nusselt number and wall shear stresses is identified through bar graphs. The comparison between the wall heat transfer rates for nano, di-nano, and tri-nano-fluids is provided. The thermal relaxation parameter has shown a decreasing effect on the temperature of the fluid. This decreasing behavior is noted in all three types of fluid considered in the study. The highest wall heat flux is noticed in the case of tri-nanofluid. Thus, in non-Fourier heat transfer, the Nusselt number has the highest value compared to that in Fourier heat transfer. Thus, in a thermal system, the efficiency of a fluid subjected to non-Fourier heat transfer is much better than that of a fluid subjected to Fourier heat transfer. The presence of a porous medium in the fluid results in a decrease in wall heat flux (the Nusselt number). The Ohmic dissipation and viscous dissipation both provide heat to the fluid. This results in increasing its overall energy and, consequently, its temperature increases. Thus, the thermal performance of the fluid is reduced. It means that the heat dissipation due to viscous dissipation and Joule heating (Ohmic dissipation) undermined the thermal efficiency of the fluid.</p>