An approximate symbolic solution for convective instability flows in vertical cylindrical tubes

The convective flow in vertical cylindrical tubes is investigated and a new formula for its velocity is derived. The Ostroumov problem is briefly discussed, and the relevant fourth-order ordinary differential equation referring to this problem is solved directly in its complete form and within a frame of an allowed simplification, as well. The result obtained for the velocity function is in good qualitative agreement with earlier simulation calculations.