Convection means the movement happens inside a fluid by the cause of too much heat and lesser density to rise, and also the colder cause denser materials to sink.
Thus, Solid cannot undergo convection because the molecules inside the solid are closer and can hardly move unlike liquid.
So, when the temperature got hotter or colder, the molecules on solid will only vibrate and not convert.
Therefore, this concludes that the solid do not undergo convection rather conduction of heat.