Existence and uniqueness solution of transient natural convection flow past a cylinder model with viscous dissipation and stratification

Stratification is the layering of a fluid due to concentration or temperature differences. The flow of fluid past a cylinder and the study of stratification in parabolic flow are of significant interest due to their role in minimizing energy losses by reducing viscous interactions between adjacent fluid layers and the pipe wall. Thermal stratification causes the temperature to vary more sharply with distance, creating stable layers that resist vertical mixing. In contrast, mass stratification leads to density gradients in the flow direction. A thorough understanding of these dynamics is crucial for developing effective strategies for managing, mitigating, and controlling flow. This study incorporates temperature-dependent diffusion and convection terms into the energy and concentration equations. Parabolic flow is particularly relevant in mass and heat transfer processes involving an infinite vertical plate, which may be subjected to various boundary conditions such as constant or variable temperature, heat flux, or concentration. These problems have attracted considerable attention due to their applications in engineering and industrial systems, including the cooling of electronic devices, solar collectors, chemical reactors, and combustion chambers. To preserve the mathematical integrity of the model, the coupled nonlinear partial differential equations are transformed into a dimensionless form using appropriate nondimensional variables, thereby ensuring consistency and simplifying the analytical process. The existence and uniqueness of solutions to the model equations are rigorously established via the Lipschitz continuity criterion. The results confirm that a unique solution exists under the satisfaction of the Lipschitz conditions.