Influence of non-linear motion on mixed convection in viscous fluids with temperature-dependent thermal conductivity and oscillating thermal wave

This study investigates the effects of non-linear motion on mixed convection viscous fluid flow, incorporating thermal conductivity inversely proportional to a linear function of temperature under the influence of oscillating thermal waves. To provide a comprehensive understanding, the research explores convective heat transfer in the presence of vorticity. The governing equations, including continuity, momentum, and heat equations, are formulated to represent the intricate non-linear dynamics of fluid flow and heat transfer. These equations are rendered dimensionless using appropriate scaling variables and subsequently transformed into steady and unsteady forms to address varying thermal and flow conditions. A Gaussian elimination approach, combined with a primitive variable formulation, is employed for numerical computation, alongside the finite difference method. Computational solutions are developed using FORTRAN Laher-90, with graphical and tabular results presented via Tecplot-360 to analyze transient shear stress (τ_s​) and transient heat transfer (τ_t) influenced by oscillating thermal waves. The findings reveal critical insights into the interplay between vorticity, non-linear fluid behavior, and thermal oscillations, contributing to advancements in optimizing convective heat transfer mechanisms. The findings show that in steady-state conditions, temperature distribution and flow velocity increase with higher values of the thermal conductivity variation parameter (ς). In the unsteady state, transient shear stress τₛ exhibits higher wave amplitude at ς = 0.2, followed by slight changes in phase angle at different values. However, transient heat transfer τ_t decreases in wave magnitude as ς increases.