Heat transfer regimes in mantle dynamics using the CitcomCU software.

There are mainly two ways to approach mathematically mantle dynamics: analytically and numerically. The absence of known solutions for the fluid mechanics theory in most of the scenarios makes the analytical approach much challenging to be used in mantle studies. With this in mind, this work presents a study based on the two different main mechanisms responsible for heat transference in a fluid: conduction and convection. Considering an inelastic, incompressible and viscous fluid with infinity Prandtl number in a closed hexahedron, thirty-six simulations were carried to test how well the numerical approach can approximate to the analytical result. With the Rayleigh number and a hexahedron with known geometry, it is possible to predict if the main heat transfer mechanism is through conduction or convection. This work present a good match between the theory and the numerical solution, proving the analytical approach can be well reproduced in a discretized way with the help of a numerical code.