The heat flux distribution across the ingot surfaces can be evaluated from the heat balances and the calculated temperatures. The top heat flux shows the distribution across the ingot top which is used as the top boundary condition.

These transverse heat flux distributions can be plotted along the ingot length from start to end of melting as illustrated below for the top and base fluxes in an ESR and VAR ingot. As would be expected, the base heat flux is very high at the start of melting and diminishes rapidly as the ingot grows. The top heat flux is also high at the start of melting, but then remains more or less constant throughout the extent of melting until the hottop cycle starts, after which the heat flux diminishes until melting is completed.

The side heat flux combined with the specified cooling water flow rate can be used to estimate the change in water temperature along the crucible length.