There are some contributions to the heat losses from conduction phenomena. One of those is the heat that comes out from the solar tube, mainly from the junction between the two cylinders, external and internal, and from the support structures at the bottom of the two cylinders in the evacuated area. This is not a relevant effect (see Figure 1, conduction loss to external). The other is the thermal resistance between the cermet layer and the vector fluid that maintains the cermet at a higher temperature than the fluid with the creation of a temperature gradient between the surface and the fluid itself. In the results of the certified collectors in accordance with EN-12975-2:2006 the efficiency curve depends on irradiance, external temperature and fluid average temperature, but indirectly depends on the unmeasured cermet layer temperature. So, if there’s a temperature gradient from the cermet layer and the vector fluid of several degrees, the measured efficiency curve suffers from such results. The temperature gradient comes out from the geometry of the tube, the material used, the vector fluid and fluid dynamic applied to the circuit.

Another problem is the convection heat transferred from the copper tube to the fluid, in our case water. A laminar flow with low Reynolds number involves a low heat transfer coefficient and the increasing of the temperature gradient between the cermet and the fluid at the steady state. For example, for a commercial sample reported in the Figure 2, the vector fluid, water, flows in a copper tube with internal diameter of 6 mm at the average velocity of 0,056 m/s. At a temperature of 70°C it has a Reynolds number of 815, sign for a laminar flow. The calculated heat transfer coefficient, based on Nusselt number obtained from the Bohm expression, becomes 92,50 (W/m2-K). Such value may be critical in the convection from the cermet to the fluid.

2. Modelling

2.1. Real case modelling

To have a more accurate analysis of the previous model description, it has been simulated a partial three-dimensional model of a real evacuated solar tube with some initial hypothesis and some approximations:

• 313 K temperature on the vector fluid at the inlet;

• modelization of a partial section of the tube (20 cm);

• air layer between the glass and the aluminium profile;

• the influence of the air layer with different thicknesses;

• approximated model with no computation for the external borosilicate glass tube and the evacuated area;

• the Multiphysic analysis combining heat transfer (conduction and convection) and fluid dynamic (incompressible Navier-Stokes).

The solar tube have been modelled correlating the heat transfer to the fluid dynamic. Fluid dynamic models only the vector fluid, in our case water. Heat transfer works on all the layers and calculate conduction and convection phenomena.

The relation assumes that mass is always conserved, which means that density and velocity must be related through:

(8)

The FE modelling uses Fourier’s law of conduction which states that the conductive heat flux, q, is proportional to temperature gradient:

(9)

Not considering the viscous heating and pressure work, the heat equation can be derived in a more similar form:

(10)

When only the conduction heat transfer in solid material is active in the modelling, the convective term рС? лі * Vr is equal to zero.

In the modelling it has been considered the inward heat flux in the cermet surface:

(11)

The modelling has reported the following results in terms of data, for the model of 20 cm in length:

• net heat flux: 9,1 W

• temperature gradient between income and outcome of the vector fluid: 3,25 K

• cermet Average Temperature: 315,6 K

•

temperature gradient between the cermet layer and the outward vector fluid flow (average