Dynamics of Surface Corrugation on Transient Radiative Heat Transfer and Flow Analysis in Microchannels

A novel aspect of the present study is to analyze shear stress (SS) and rate of heat through a non‐Newtonian fluid at the corrugated walls of a rough circular microchannel, an area largely unexplored in existing literature. The interplay among slip length, thermal radiation, and internal heat generation is rigorously captured by closed‐form perturbation solutions, offering new insights into heat and momentum transport in viscoelastic fluids under confined oscillatory conditions. The nonlinear equations for momentum and energy transport are defined and solved using the perturbation approach, yielding closed‐form functions for velocity and heat transfer. A complete theoretical and graphical analysis is performed to investigate the consequences of major fundamental parameters affecting flow and thermal behavior. The effects of slip length and thermal radiation on velocity and temperature distributions are thoroughly investigated, respectively. The results are also validated through a comparative analysis with the given literature. The findings show that radiative heat transfer and heat source have a significant impact on the distribution of thermal energy. The temperature field becomes more intense as the radiative and source parameters increase, but decreases as the Reynolds number, time, corrugation parameter, and Prandtl number increase. Moreover, as the relaxation time increases, SS decreases, indicating that Jaffery's fluid's elastic resistance reduces wall stress. Given the relevance of oscillatory non‐Newtonian flows in confined geometries, the present findings offer guidance for biomedical and microfluidic applications, concentrated‐solar receivers, and gas‐turbine cooling passages.