An experimental study of a solar-concentrating system based on thermoelectric generators (TEGs) was performed. The system included an electrical generating unit with 6 serially connected TEGs using a traditional semiconductor material, Bi_{2}Te_{3}, which was illuminated by concentrated solar radiation on one side and cooled by running water on the other side. A sun-tracking concentrator with a mosaic set of mirrors was used; its orientation towards the sun was achieved with two pairs of radiation sensors, a differential amplifier, and two servomotors. The hot side of the TEGs at midday has a temperature of around 200°C, and the cold side is approximately 50°C. The thermosiphon cooling system was designed to absorb the heat passing through the TEGs and provide optimal working conditions. The system generates 20 W of electrical energy and 200 W of thermal energy stored in water with a temperature of around 50°C. The hybrid system studied can be considered as an alternative to photovoltaic/thermal systems, especially in countries with abundant solar radiation, such as Mexico, China, and India.

Solar hybrid electric/thermal systems using photovoltaic (PV) panels combined with a water/air-filled heat extracting unit were designed and studied in many laboratories during the last three decades [_{2}Te_{3}, the peak electric efficiency that could be obtained in such a system is 5% [

Chávez-Urbiola et al. [

A schematic of the system is shown in Figure

A schematic of the hybrid system.

Thermoelectric generating (TEG) unit.

The radiation-concentrating block consisted of 55 plane mirrors each having a size equal to that of the TEG array (8 × 12 cm^{2}), providing a concentration ratio (the number of mirrors focused on the heating plate multiplied by the mirror reflecting efficiency) of ~52, and considering a reflection efficiency of 0.95. The mirrors were positioned in a parabolic curve, with the focal point over the heating plate of the TEG assembly; the angle of the inclination of each mirror was calculated to achieve this effect. The block (mirror holder) was attached to the 2-axis sun-tracking system (see [

The TEG array includes 6 generating elements of the type TGM-127-1.4-2.5 based on Bi_{2}Te_{3} (made by Kryotherm, Saint Petersburg, Russia; each element is 4 × 4 × 0.5 cm^{3}). The electrical characteristics of the elements at different temperatures of the operation were given in a previous publication [

For the thermosiphon solar water heaters, the flow rate of the circulating water is conventionally calculated by equating the pressure head and the friction head. Pressure head is caused by density gradients in the loop, and the friction head is caused by friction in the plumbing arrangement.

The pressure head in the thermosiphon causes flow to occur. This flow in the collector is driven by the weight difference between the hot water column in the return pipe passing through the collector and the cold fluid column in the inlet pipe. The temperature conditions are given by the inlet temperature of the fluid

Imagine an opened thermosiphon loop as a U-tube containing a fluid with one column filled with hot fluid and the other with cold fluid. A height difference,

The continuity equations under static equilibrium in case of U-tube can be expressed by

To determine the thermal driving forces, it is necessary to take into account the values of

The friction head, flow rate, and convective coefficient are interrelated, but they also depend on several physical parameters that must be defined, such as piping type, materials, and pipe length, among others.

Using the Bernoulli equation, an energy conservation analysis can be made. For a pipe system [

On the other hand, it is necessary to include the Darcy equation for friction head

As a consequence, it is necessary to take into account the energy losses due to friction (major losses due to friction and minor losses due to changes in the size and direction of the flow path) in the loop.

The friction head can then be expressed for this case in terms of the friction factor and the flow rate

Solving (

Once the flow rate is defined, the convective coefficient can be calculated [

For a thermal length

Once

In order to determine the optimal configuration of the heat exchanger, several configurations were proposed and evaluated using commercial finite element method (FEM) software (COMSOL Multiphysics 4.2a). For the flow rate, the value obtained earlier was used: ^{2}, in correspondence with the 2 × 3 array of TEG elements.

The heat exchanger was designed to be as simple as possible, a flat plate attached to the commercial pipes. In Figure

Computer simulations for different configurations (see text); the colors show the temperature distribution.

After evaluating a wide range of configurations, two options that best meet the conditions were selected and evaluated, and the results are shown in Figure

Computer simulations results for (a)

The actual system studied is shown in the photograph in Figure

Photograph of the system.

The results of the system’s electrical and thermal characterization are presented in Figures

Electric power generation as a function of time of day (a) and as a function of the temperature difference between the TEG plates (b).

Hot water tank temperature (a) and calculated thermal efficiency of the system and the flow rate in the thermosiphon (b).

Figure

The cost-efficiency estimation made in our previous publication for the hybrid system studied [

Performance of the designed hybrid system in the conditions at Queretaro, Mexico at the equinox time of the year has revealed that a systems electrical efficiency of 5% and thermal efficiency of 50% with the estimated cost of the electric energy production are practically equal to those of the traditional photovoltaic/thermal systems. Thus, we conclude that the solar hybrid system with the concentrator and the thermoelectric generator, even with the existing components, can be considered as a reasonable alternative to the traditional electric/thermal solar hybrid system. Taking into account the rapid progress in the development of new nanostructured and highly efficient thermoelectric materials, we can expect that in the near future performance of the TEG-based systems can surpass that of the traditional solar hybrid systems, in particular, in the solar-rich regions having relatively low latitude.

Effective flow area of the piping, m

Specific heat capacity, J/Kg·

Piping diameter, m

Pressure head (thermal driving head), m

Friction factor

Gravity, m/s

Height, m

Energy added to the fluid, J

Cold fluid column height, m

Average convection coefficient, W/m·

Hot fluid column height, m

Friction head inside the piping, m

Energy removed to the fluid, J

Friction coefficient

Thermal conductivity, W/mK

Piping length, m

Equivalent pipig length of the minor losses, m

Thermic inlet length, m

Mas flow, Kg/s

Average Nusselt number

Inlet pressure, N/m

Outlet pressure, N/m

Prandtl number

Heat flux, W

Solar heat input W

Bottoming heat transfer W

Heat transfer to running water W

Reynolds number

Outlet temperature in the fluid of the heating pipe,

Inlet temperature in the fluid of the heating pipe,

Inner surface temperature of the hot pipe,

Flow velocity inside the piping, m/s

Inlet velocity of the fluid, m/s

Outlet velocity of the fluid, m/s

Height at the inlet point, m

Height at the outlet point, m

Thermic efficiency

Fluid density, kg/m

Cold fluid density, kg/m

Hot fluid density, kg/m

Specific weight of the fluid, N/m

Dynamic viscosity, Kg/m·s.

None of the authors of the present work have direct or indirect financial relation with the commercial identity “COMSOL Multiphysics 4.2a” that might lead to a conflict of interests of any kind for any of the authors.

The authors are grateful to CONACYT for financial support of the project and for the Ph.D. scholarship of E. A. Chávez-Urbiola. They would also like to thank Dr. Mike Boldrick of the US Peace Corps for his review of the paper.