The study of viscoelastic and non Newtonian fluids has remained one of the most intellectually demanding and practically relevant areas of fluid mechanics for several decades because of the intrinsic coupling between fluid microstructure, memory effects, and macroscopic transport phenomena. Among the various constitutive models developed to describe such materials, the second grade fluid model has been especially significant due to its capacity to represent normal stress differences and elastic effects while still allowing mathematically tractable analysis. In many engineering and geophysical applications, these fluids flow through porous structures, interact with magnetic fields, and experience strong thermal gradients, making the problem even more complex and multidimensional. This research presents a comprehensive theoretical and analytical investigation of transient and steady flow behavior of second grade viscoelastic fluids under magnetohydrodynamic influence, thermal radiation, and porous medium effects in configurations such as stretching sheets, oscillating and impulsively started plates, and stagnation point flows.

Drawing strictly on established developments from prior literature, the present article integrates classical boundary layer theory, transient Stokes problems, and modern non Newtonian modeling to develop a unified framework for understanding how viscoelasticity, magnetic forces, thermal diffusion, and porous resistance jointly determine velocity, temperature, and stress fields. The analysis is deeply grounded in earlier foundational work on impulsive and oscillatory plate motions in viscous fluids, as well as later extensions to second grade fluids, thermal transport, and porous media. Particular attention is devoted to the subtle interplay between elastic memory and diffusive momentum transport, which leads to markedly different transient responses compared with Newtonian fluids. The role of thermal radiation, variable thermal conductivity, viscous dissipation, and convective boundary conditions is examined in detail to reveal how heat transfer mechanisms are altered by fluid rheology and magnetic damping.

By synthesizing a large body of prior results, this study demonstrates that second grade fluids exhibit richer and more sensitive transient and steady behavior than classical viscous fluids, especially in magnetohydrodynamic and porous environments. Velocity overshoots, delayed boundary layer development, enhanced or suppressed heat transfer, and strong coupling between flow and thermal fields emerge as robust qualitative features. The results also highlight how stretching surfaces, peristaltic motion, and natural convection geometries further amplify or modify these effects. The work provides a coherent theoretical foundation that can be used by engineers and applied scientists to predict, control, and optimize transport processes involving viscoelastic fluids in industrial, biomedical, and geophysical systems.