Due to its extensive applicability and employment in different systems, the study of thermal transport is a significant area of research. The main goal of this investigation is to analyse the impact of thermal radiation as well as the Navier-Stokes condition upon the two-dimensional flow of second-grade as well as Walter's B ternary nanoliquids through a permeable shrinking flat surface. The phrase “ternary nanofluid” refers to a suspension of three different types of nanoparticles, notably silver (Ag), SWCNTs, and graphene particles, in water as the base fluid. The inverse Darcy phenomenon has an effect on the momentum equation as well. The energy equation also accounted for nonlinear thermal radiations as well as heat source and sink components. The phenomenon is portrayed as a nonlinear system of partial differential equations. The model equations are transformed into a non-dimensional series of ordinary differential equations by replacing similarity. Afterwards, the transformed ODEs were tackled analytically in order to establish an analytical solution of the energy equation in terms of a confluent hyper-geometric function by utilizing similarity conversion. This research reveals that the velocity field is reduced significantly by the slip parameter. The benefits of a few emerging factors, such as the viscoelastic parameter, inverse Darcy number, slip parameter, solid volume fraction, radiation, Prandtl number, and skin friction coefficient effects on solution, have been displayed through plots and discussed. Additionally, it has been concluded from this analysis that ternary nanofluids have a higher thermal flow rate than hybrid or standard nanofluids.