Results and discussions

1.1. Pressure losses

From an engineering point of view an important parameter is the pressure drop within the channel as this parameter determines the requirements for the pumping power. To determine the pressure drop, it is convenient to work with the friction factor of Darcy [6], defined as:

image085 image086 image087

If the pressure variation is isolated from the equation 1 and integral transformation is carried, out the pressure drop is obtained as:

Where p is the fluid density, Vm is the mean fluid velocity, D is the hydraulic diameter and (x2-x1) is the pipe length.

image088 Подпись: (Eq. 3)

If we analyze the equation 2, it is noticed that the pressure drop is highly affected by the hydraulic diameter, which is directly linked to the shape factor (the bigger the Dh is, the smaller the AP). Once the pressure drop is know, the pumping power can be determined as:

Ignoring the effect of temperature on the cell performance, the efficiency of the electrical conversion of the cells is 20%. Therefore, for the cell surface area under investigation (0.01m2) and with an irradiation of 15000 W/m2, the electrical power produced by the cells is predicted to be 30 W.

Taking into account the necessary pumping power and the electrical power produced by the cells, the net electrical power is defined as:

pnet electrical Pelec, PV Pelec, pumping (Eq. 4)

In the figure 4, the variation of the net P with the Re and the defined aspect ratios is shown,

image090

In the figure 4, it can be noticed that the maximum net electrical efficiency has a quadratic form, and increases with growing aspect ratio. On the other hand, the slope of the parabola in the region which describes the power in the laminar regime is much greater in tubes with smaller aspect ratio.