The transport of heat and momentum in non Newtonian and viscoelastic fluids has become one of the most intellectually rich and technologically relevant areas in modern fluid mechanics. This is largely because a vast range of industrial, geophysical, and biomedical processes involve fluids whose rheological behavior deviates significantly from the Newtonian assumption. Polymer melts, biological fluids, lubricants, slurries, and suspensions exhibit elastic memory, shear dependent viscosity, and stress relaxation effects that profoundly modify their flow and heat transfer characteristics. When such fluids interact with porous structures, oscillating boundaries, stretching sheets, magnetic fields, radiation, or temperature dependent material properties, the resulting transport processes become strongly coupled, nonlinear, and sensitive to multiple physical mechanisms. The present article develops a unified theoretical and interpretive framework for understanding these interactions by synthesizing and critically extending the body of knowledge represented in the provided references.

The central objective of this work is to examine how viscoelasticity, micropolarity, second grade and Maxwell type constitutive behaviors interact with porous media, radiative heat transfer, thermal conductivity variations, magnetic forces, and moving or stretching boundaries. Drawing strictly from the cited literature, the article reconstructs the intellectual evolution of these models from early studies on Stokes oscillatory flow and plane wall motion to modern investigations of magnetohydrodynamic and radiative flows over stretching sheets and through porous substrates. The methodological emphasis is placed on analytical and semi analytical solution strategies, including exact solutions, similarity transformations, perturbation approaches, and approximate analytical schemes such as homotopy based methods. Rather than reproducing equations, the study provides detailed conceptual explanations of how these techniques operate and what their physical implications are.

The results discussed reveal that non Newtonian rheology fundamentally alters velocity distributions, thermal boundary layer thickness, wall shear stresses, and heat transfer rates. Elastic memory tends to delay momentum diffusion, while second grade effects can either enhance or suppress flow depending on the competition between normal stress differences and viscous dissipation. Variable thermal conductivity introduces strong nonlinear coupling between temperature and velocity fields, while thermal radiation acts as an effective heat source that thickens thermal boundary layers. Magnetic fields generate Lorentz forces that dampen motion and convert kinetic energy into thermal energy, thus modifying both flow resistance and temperature profiles. Porous media impose additional drag and alter buoyancy driven convection, particularly when combined with non Newtonian stress responses.