# Thermal Analysis of the Receiver of a Standalone Pilot Solar Dish–Stirling System

^{*}

## Abstract

**:**

## 1. Introduction

^{2}year. The solar hours in this area are almost 2800 h/year [2]. A standalone pilot solar dish–Stirling system was set up under the meteorological conditions specific to Kerman City. The power produced was to be applied in remote areas where accessing the electrical grid is very difficult. The proposed module consists of a collector with a parabolic dish diameter of 3 m. It was manufactured using identical square 0.08 × 0.08 m glass/silver mirror panels 2-mm thick. The receiver aperture had a diameter of 0.12 m (i.e., C = 625), and a rim angle of 45°. A directly illuminated tube type was used for the receiver, so it can only be operated during the daytime (solar-only type). A free piston Stirling engine with a nominal capacity of 1 kW was installed in the Kerman pilot facility. The engine working fluid was helium, and the system was subjected to maximum temperature and pressure of 800 K and 10 bars, respectively. Figure 1 shows the receiver and the engine installed on the Kerman pilot.

## 2. Methodology

#### 2.1. The Collector Parameters

_{d}). This shape can also be defined by the rim angle. A schematic of the system is illustrated in Figure 2.

#### 2.2. Thermal Modeling of the Receiver

#### 2.2.1. The Conduction Losses

#### 2.2.2. The Convection Losses

#### 2.2.3. The Radiation Losses

#### 2.2.4. The Total Thermal Loss

_{conc}), the receiver efficiency (η

_{rec}), the Stirling engine efficiency (η

_{SE}), and the generator efficiency (η

_{gen}) as below:

#### 2.3. Solar Radiation Model

## 3. Results and Discussion

#### 3.1. The Receiver Incident Flux Intensity

#### 3.2. Conduction Loss through the Receiver

#### 3.3. Convection Loss through the Receiver

#### 3.4. Radiation Loss through the Receiver

#### 3.5. Total Thermal Losses through the Receiver

#### 3.6. Thermal Efficiency of the Receiver and the System Performance

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A | area [m^{2}] |

C | concentration ratio [-] |

d | diameter [m] |

f | focal distance [m] |

G | beam solar irradiance [W/m^{2}] |

Gr | Grashof number [-] |

h | convective heat transfer coefficient [W/(m^{2} K)] |

k | thermal conductivity [W/(m K)] |

L | length [m] |

Nu | Nusselt number [-] |

Q | distance between the surface of the concentrator and the focal point [m] |

$\dot{\mathrm{Q}}$ | heat transfer rate [W] |

T | temperature [K] |

v | wind speed [m/s] |

Greek symbols | |

α | absorptivity [-] |

δ | thickness [m] |

ε | emissivity [-] |

η | efficiency [-] |

θ | incident angle [deg] |

σ | Stefan–Boltzmann constant [W/(m^{2} K^{4}] |

ψ_{rim} | rim angle [deg] |

Subscripts | |

amb | ambient |

ap | aperture |

cav | receiver cavity |

conc | concentrator |

d | dish |

eff | effective |

insul | insulation |

rec | receiver |

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**Figure 5.**Receiver aperture incident flux intensity during the daytime hours on an average day of each month.

**Figure 10.**Thermal efficiency of the receiver during the daytime hours on an average day of each month.

**Figure 11.**Power output of the Kerman pilot during the daytime hours on an average day of each month.

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**MDPI and ACS Style**

Gholamalizadeh, E.; Chung, J.D. Thermal Analysis of the Receiver of a Standalone Pilot Solar Dish–Stirling System. *Entropy* **2018**, *20*, 429.
https://doi.org/10.3390/e20060429

**AMA Style**

Gholamalizadeh E, Chung JD. Thermal Analysis of the Receiver of a Standalone Pilot Solar Dish–Stirling System. *Entropy*. 2018; 20(6):429.
https://doi.org/10.3390/e20060429

**Chicago/Turabian Style**

Gholamalizadeh, Ehsan, and Jae Dong Chung. 2018. "Thermal Analysis of the Receiver of a Standalone Pilot Solar Dish–Stirling System" *Entropy* 20, no. 6: 429.
https://doi.org/10.3390/e20060429