Impacts of high viscosity variation and internal heating on mantle convection in different aspect ratio cells

<h2>Abstract</h2> This study examines the Rayleigh-Bénard convection model with free slip boundary conditions appropriate for the Earth's mantle in narrow and elongated cells with aspect ratios of 1:2 and 2:1, respectively. The primary goal of this research is to analyze the convection pattern at high Rayleigh number, including internal heating and significant viscosity variation across the mantle depth. Finite element method-based PDE solver is used to solve the model, incorporating viscosity based on both temperature only and temperature and pressure combined. The Nusselt number and Root Mean Square Velocity are computed and presented in tabular form. The stream function contours reveal that splitting of convection cell occurs in narrow cell only with temperature-dependent viscous convection at high internal heating. On the other hand, two square cell convection pattern is the most stable choice for elongated cell for both types of viscosity functions with significant presence of internal heating. Nusselt number vs Rayleigh number graphs indicate that the heat transfer efficiency is highest in narrow cell compared to unit aspect ratio and elongated convection cell.