Modeling Transient Free Convection and Nanofluid Effects in Follicular Dynamics: A Delay Differential Equation Approach to Fertility and Endocrine Regulation

Understanding follicular dynamics is critical for advancing fertility treatments and endocrine regulation strategies. This study develops a mathematical model integrating transient free convection, nanofluid effects, heat sources, and chemical reactions in intra-follicular processes and inter-follicular communication. Delay differential equations (DDEs) are employed to capture the delayed responses in follicle wave interactions. The governing equations for momentum, energy, mass transport, and continuity are formulated and transformed using similarity transformation. A numerical approach is implemented to solve the coupled equations, and results are analyzed in terms of velocity, temperature, and concentration profiles. The findings provide insights into the influence of biochemical interactions on follicular wave dynamics, offering potential applications in assisted reproductive technologies (ART) and endocrine therapies.