The mathematical formulation is based on the principles of conservation of mass, linear momentum and energy in incompressible flows. In an arbitrary spatial region of volume V, bounded by a closed surface S’, these conservation principles can be written as [19]:

(1)

я

TOC o "1-5" h z J vpv ■ dS = J —pS ■ dS + j ^(7 + pSj ■ dS + j gpdV (2)

.4 .4 .4 V’

j hpdV + j hpv ■ dS = — j q ■ dS + j q„dV (3)

V’ .4 .4 V’

where the following main hypothesis are assumed: symmetry of the stress tensor <r, which is a consequence of the conservation of angular momentum; transient effects in the momen­tum equation are negligible; all body forces actuating are due to the gravitational accelera­tion; effects of kinetic energy and pressure in the energy equation are negligible; the effects of the work of the body forces in the energy balance are negligible.

In equation 2, the stress forces have been divided into the forces due to pressure at the boundary of the volume S and the forces due to flow resistance, which are respectively the two first terms on the right of the equality of equation 2.

The model is based on the division of the whole thermosyphon system and its com­ponents into strategically distributed control volumes (CVs). At each one of the CVs the simplified general governing equations 1,2 and 3, are integrated assuming local averaged fluid variables. In this step, some further simplifications are applied at each CV according to the physical phenomena which is taking place.

The tank is divided into n equal sized CV in a similar way as is done in the well known multinode model [11,7], the collector in a single CV (assuming an exponential distribution from the inlet to the outlet according to [7] for the modelling of the body forces), and the pipes in n different CV.

This model requires some information to be provided from experimental data of the com­ponents as the efficiency curve of the collector, the heat loss coefficient of the tank, the pressure drop in the pipes and in the collector due to fluid flow resistance… This information can also be provided from higher level numerical models.

This is the level of modelling of thermosyphon systems typically used, see [9, 14, 6, 18].