Use of a fictitious Marangoni number for natural convection simulation

• A new approach for natural convection simulation based on a fictitious Marangoni number is proposed.
• The approach is most useful when the relevant Nusselt number correlation is not known.
• The approach allows the simulation of natural convection via mass flow simulation.

In this paper, a method based on the use of a fictitious Marangoni number is proposed for the simulation of natural thermocapillary convection as an alternative to the traditional effective diffusivity approach. The fundamental difference between these two methods is that the new method adopts convective mass flows in simulating natural convection. Heat transfer in the natural convection simulation is calculated through the mass transport. Therefore, empirical Nusselt numbers correlations required in the effective diffusivity method are eliminated. This represents a clear advantage in the context of design studies where flexibility in varying the geometry unconstrained by the availability of appropriate correlations is highly desirable. The new method is demonstrated using a simple geometrical model. An analytical expression of the fictitious Marangoni number associated with convection between vertical plates is derived and a computational fluid dynamics (CFD) simulation is performed to study the efficacy of the proposed method. The results show that the new method can approximate real natural convection quite accurately and can be used to simulate the convective flow in complex, obstructed or finned structures where the specific Nusselt correlation is not known.