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Abstract In today's rapidly advancing world, more deliberate development and implementation of energy‐efficient thermal management systems is emergent. In industrial and engineering contexts, the regulation of heat and mass transfer phenomena is heavily swayed by factors such as heat and mass fluxes, and wall temperature, and concentration levels. In cryogenic containers, understanding heat flux and wall temperature is essential for maintaining ultra‐low temperatures over extended periods. In this context, our paper embarks on modeling the transient dynamics of a radiant Casson fluid adjacent to a steeped plate, which is featured by its emission of both heat and mass fluxes. The plate is under two thermal conditions, namely uniform wall temperature (UWT) and uniform heat flux (UHF), which are crucial in modulating both upward and downward heat transport processes. The Laplace transform (LT) technique yields close‐form solutions for the model's governing equations. The distribution of flow and salient physical quantities are graphed and elucidated in response to intricate physical parameters. A comparative graphical analysis of UWT and UHF scenarios reveals stark differences. Notably, the fluid's flow rate appears considerably amplified in the UWT scenario compared to the UHF one. Furthermore, the UHF setting profoundly influences the heat and mass transportation within the fluid's flow realm. A pronounced Casson parameter tends to thin out the velocity profile. Concurrently, a heightened radiation parameter results in a reduction in fluid temperature. The theoretical framework explored in our study is not just an academic exercise but holds tangible applicability across varied sectors. This spans from rocket chamber cooling, where fine‐tuned heat flux conditions are paramount for safeguarding operations, to industries like cosmetics and food processing, which demand meticulous thermal regulation to ensure product excellence.
Das et al. (Mon,) studied this question.