Convective Heat Transfer in the Strongly Viscous Mantle in Different Aspect Ratio Cells

Mantle convection, a fundamental mechanism controlling the dynamics of the Earth’s surface and interior, shows different behaviors caused by different factors such as viscosity variation, viscous dissipation, internal heating, and so on. In this paper, the effects of temperature-dependent viscosity, temperature and pressure-dependent viscosity and viscous dissipation on mantle convection are investigated in elongated and narrow cells. The Rayleigh-B´enard convection model is solved numerically with the full form of the Arrhenius viscosity function at a high Rayleigh number for viscosity contrasts up to 1030. The root mean square velocity and Nusselt number are computed and tabulated. The thermal characteristics and flow dynamics inside the convection cell are presented by temperature profiles and stream function contours. These simulated results indicate that increasing viscosity contrasts with the incorporation of viscous dissipation weakens the convection vigour and heat transfer in the mantle. The selected narrow cell remains stable for a very high viscosity contrast at different viscous pressure number μ, whereas the selected elongated cell with temperature-dependent viscosity and strong viscous dissipation becomes unstable and single-cell pattern breaks down at high viscosity variation. J. Bangladesh Math. Soc. 44.2 (2024) 077–096