Temperature modulation effects on chaos and heat transfer in Darcy–Bénard convection using a local thermal non-equilibrium model

This article investigates the effect of temperature modulation on convective heat transport in a fluid-saturated porous layer under local thermal non-equilibrium (LTNE) conditions. The boundary temperatures are modulated to have two parts: a steady part and an externally imposed time-dependent oscillatory part. An extended Darcy model with a time derivative term is used for the momentum equation for porous medium. A fifth-order Lorenz model is derived using a truncated Fourier series representation involving only two terms. The resulting heat transfer is calculated in terms of thermal Nusselt number by solving finite-amplitude equations numerically. The influence of the governing physical parameters on heat transport is analyzed and depicted graphically. It has been found that heat transfer can be effectively controlled by appropriately adjusting the external thermal mechanisms of the system. A study of streamlines and isotherms has also been conducted to get an insight of the flow phenomena under LTNE conditions. The plots of bifurcation diagrams and the largest Lyapunov exponent are also reported in the paper to describe the chaotic behavior of the fifth-order, non-autonomous system.