1.1. Governing equations

Under consideration of the natural convection flow of Newtonian fluid in a vertical cylinder domain and after introducing the Boussinesq approximation, the phenomenon is governed by mass, momentum and energy equations written in dimensionless form:

*

where, t dimensionless time step, dimensionless temperature, p* dimensionless pressure and V* dimensionless velocity.

In the model, laminar flow and constant physical properties except density variations in buoyancy terms of the momentum equations (Boussinesq approximation) have been assumed. The flow field and the heat transfer are determined by the following dimensionless parameters: aspect ratio H/D, Prandlt number Pr and Rayleigh number Ra.