# Modeling and Thermal Analysis of a Moving Spacecraft Subject to Solar Radiation Effect

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## Abstract

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## 1. Introduction

## 2. Heat Transfer Modeling of a Rotating Spacecraft Under Solar Radiation

## 3. Numerical Procedure: Meshless Method

#### 3.1. Theoretical Background

**b**determines the approximation properties of the kernels. From the mathematical point of view, the invertibility of matrix $\mathbf{A}$ depends entirely on that of the Vandermode matrix $\mathbf{V}$.

#### 3.2. Generation of the Point Cloud

#### 3.3. Explicit Solver

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic showing the incident solar rays and rotating coordinate system of spacecraft: an infinitely long and hollow cylindrical shape rotating at constant angular speed $\omega $.

**Figure 2.**Node distribution over the simulated domain: (

**a**) boundary nodes, (

**b**) full set of nodes, (

**c**) interior and boundary nodes.

**Figure 3.**A boundary stencil for enforcing no flux boundary conditions. The stencil is based at the one center located on the boundary. Base center marked with a square (green) and supporting centers with a circle (red).

**Figure 4.**Temperature variations of outer vehicle surface for varying spinning speeds: comparison between current simulations and FDM results [9].

**Figure 5.**Temperature variations of the internal vehicle surface ($\frac{r}{{r}_{o}}=0.8$) for varying spinning speeds: comparison between current simulations and FDM results.

**Figure 6.**Variations of the temperature extrema (maximum and minimum) at the outer surface with the spinning speed: current simulations.

**Figure 7.**Temperature contours obtained for different spinning speeds: current simulations. (

**a**) $\omega =0$ rad/h, (

**b**) $\omega =0.02$ rad/h, (

**c**) $\omega =0.1$ rad/h, (

**d**) $\omega =1$ rad/h, (

**e**) $\omega =10$ rad/h, (

**f**) $\omega =1000$ rad/h.

**Figure 9.**Temperature contours obtained for different spinning speeds: current simulations. (

**a**) $\omega =0$ rad/h, (

**b**) $\omega =0.1$ rad/h, (

**c**) $\omega =1$ rad/h, (

**d**) $\omega =10$ rad/h.

**Table 1.**Numerical values of the parameters used for the rotating spacecraft [9].

Parameter | Symbol | Numerical Value |
---|---|---|

Outer radius | ${r}_{o}$ | 0.3048 m |

Inner radius | ${r}_{i}$ | 0.1524 m |

Inclination of the vehicle | $\psi $ | $\frac{\pi}{2}$ |

Intensity of the sloar radiation | ${f}_{s}$ | 1.4 kW/m^{2} |

Thermal conductivity | K | 0.173 W/m K |

Absorptivity | $\alpha $ | 1 |

Emissivity | $\u03f5$ | 1 |

Characteristic temperature | ${T}_{o}$ | 297.46 K |

Non-dimensional radius | $\xi $ | 0.8 and 1 |

Spinning speed | $\omega $ | 0–1000 rad/h |

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**MDPI and ACS Style**

Gadalla, M.; Ghommem, M.; Bourantas, G.; Miller, K.
Modeling and Thermal Analysis of a Moving Spacecraft Subject to Solar Radiation Effect. *Processes* **2019**, *7*, 807.
https://doi.org/10.3390/pr7110807

**AMA Style**

Gadalla M, Ghommem M, Bourantas G, Miller K.
Modeling and Thermal Analysis of a Moving Spacecraft Subject to Solar Radiation Effect. *Processes*. 2019; 7(11):807.
https://doi.org/10.3390/pr7110807

**Chicago/Turabian Style**

Gadalla, Mohamed, Mehdi Ghommem, George Bourantas, and Karol Miller.
2019. "Modeling and Thermal Analysis of a Moving Spacecraft Subject to Solar Radiation Effect" *Processes* 7, no. 11: 807.
https://doi.org/10.3390/pr7110807