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This study investigates the unsteady, incompressible, one-dimensional flow of a second grade flow over an infinitely vertical moving cylinder, emphasizing novel thermal and mass stratification effects relevant to industrial engineering and heat transfer systems. Employing the Caputo time-fractional derivative framework, the model incorporates the combined buoyant forces due to mass and heat transfer, offering a generalized perspective on transient behavior in complex fluid systems. Using the Laplace transform technique, analytical equations for temperature, velocity, and concentration profiles are generated to simplify the analysis, assuming unit values for the Schmidt and Prandtl numbers . Comparative assessments between long-term steady-state and unsteady-state solutions are conducted, highlighting dynamic transitions. The effects of significant dimensionless parameters on solutal and thermal transfer are thoroughly examined. Graphical results for Sherwood and Nusselt numbers and skin friction provide insights into boundary layer characteristics. The findings demonstrate that both thermal and mass stratifications significantly alter the flow dynamics, underlining their importance in the design, optimization, and performance analysis of industrial engineering applications involving fluid flow and heat exchange, such as chemical reactors, thermal regulation units, and energy conversion systems.
Rafique et al. (Mon,) studied this question.