# Mathematical modeling of the geometrical sizing and thermal performance of a Dish/Stirling system for power generation

## Highlights

Mathematical modeling of a Dish/Stirling system integrating different calculation methodologies proposed by other authors.

Numerical simulation by varying the opto-geometric parameters to find maximum operating conditions.

Thermal balance analysis, to evaluate how thermal losses affect the output operating conditions.

Model validation Dish/Stirling with real technologies presented in the specialized publications.

## Abstract

This paper proposes a mathematical model for a solar Dish/Stirling system. Firstly, it is presented a methodology to calculate the appropriate angles and characterize the solar tracking control system for the city of Itajubá-MG/Brazil, in order to maximize the heat flow on the cavity of the receiver. Secondly, it was developed an algorithm for sizing and to determine the effects of opto-geometric parameters on the overall efficiency of the Dish/Stirling system. The model allows defining different configurations and geometric distances between the concentrator and the receiver, in order to obtain the desired heat in the receiver cavity. Finally, it is carried out a thermal balance for the evaluation of the maximum efficiency and overall efficiency of the system.

The results obtained for a concentrator with a diameter of 10.5 [m] and solar irradiation of 1000 W/m2 are: theoretical maximum working temperature in the receiver surface of 1596 K and a maximum thermal efficiency of 68%. It is observed that for collectors between 10 and 20 m of diameter, the overall efficiency variation is not significant (23–25%), since the variation of the temperature of the receiver and the thermal losses in the cavity are minimal for the evaluated conditions.

## Keywords

• Solar energy;
• Solar concentrator;
• Stirling engine;
• Maximum efficiency;
• Energy conversion;
• Thermal analysis