The transport of momentum and heat in non-Newtonian fluids over stretching surfaces has become one of the most central themes in modern theoretical and applied fluid mechanics due to its relevance in polymer extrusion, metallurgical processing, coating technologies, biomedical transport, and thermal management systems. Among the many classes of non-Newtonian models, second grade and viscoelastic fluids represent a particularly important family because they simultaneously capture elasticity, normal stress effects, and memory while remaining mathematically tractable for boundary layer analysis. In realistic industrial and biomedical environments, however, fluid properties such as viscosity and thermal conductivity are rarely constant. Instead, they vary strongly with temperature, shear rate, and even concentration of suspended particles. Furthermore, thermal radiation, heat sources and sinks, magnetic fields, and electromagnetic forcing often coexist, especially in high temperature polymer processing, liquid metal transport, microfluidics, and magneto-biofluid applications.

This study develops a comprehensive, theoretically consistent and physically interpretable framework for the coupled flow and heat transfer of second grade and viscoelastic fluids over stretching sheets and plates when viscosity and thermal conductivity vary with temperature and when electromagnetic and radiative effects are present. Building exclusively on the body of literature provided, the work synthesizes results from stretching sheet theory, viscoelastic boundary layer dynamics, magnetohydrodynamics, variable property transport, and biofluidic microtransport into a unified descriptive methodology. The formulation is grounded in the similarity transformation philosophy introduced for stretching surfaces and extended by later authors to non-Newtonian and magnetized flows. The roles of heat generation and absorption, radiation, viscous dissipation, porous substrates, and electromagnetic body forces are all incorporated conceptually.

Rather than presenting equations, this article provides a detailed, narrative-based explanation of how the governing physics, boundary layer structure, and thermodynamic coupling evolve under these complex conditions. Results reported in the literature are reinterpreted to reveal deep physical mechanisms. It is shown that variable viscosity introduces a strong asymmetry between momentum and thermal diffusion layers, while variable thermal conductivity fundamentally alters how heat propagates away from the surface, especially in radiative environments. Second grade elasticity is found to either stabilize or destabilize the flow depending on whether elastic memory reinforces or resists surface stretching. Magnetic fields suppress velocity while enhancing thermal energy retention, a trend that becomes even more pronounced in viscoelastic fluids due to the additional elastic stresses.