# Heat Pump Dryer Design Optimization Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- 1.
- Changes in drying air properties;
- 2.
- Heat flow within dryer;
- 3.
- Product moisture content.

#### 2.1. Stage 1 of the Algorithm

#### 2.2. Stage 2 of the Algorithm

#### 2.3. Stage 3 of the Algorithm

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Roman characters | ||

$A$ | Total exposed heat exchanger area | [m²] |

$H$ | Enthalpy | [kJ/kg * K] |

$h$ | Convection heat transfer coefficient | [W/m² * K] |

$k$ | Heat transfer coefficient of material | [W/m² * K] |

$l$ | Thickness of the heat exchanger’s walls | [m] |

$T$ | Absolute temperature | [K] |

$U$ | Mean global heat flux coefficient | [W/m² * k] |

$V$ | Air’s speed | [m/s] |

$w$ | Absolute humidity | [kg water/kg air] |

Greek characters | ||

α | Thermal diffusivity | [m²/s] |

$\rho $ | Mixture density | [kg/m³] |

$\tau $ | Kinematic viscosity | [m²/s] |

$v$ | Specific volume | [m³/kg] |

$\varnothing $ | Relative humidity | |

Subscripts | ||

$Ap$ | Plaque’s area | [m²] |

${c}_{p}$ | Specific heat | [kJ/kg * K] |

${D}_{ab}$ | Air diffusion coefficient | [m²/s] |

${k}_{ar}$ | Thermal conductivity of the humid air | [W/m² * K] |

${m}_{l}$ | Total water mass removed | [kg/s] |

$\dot{m}$ or $\frac{\partial m}{\partial t}$ | Mass flow rate | [kg/s] |

${\mu}_{mix}$ | Dynamic viscosity | [N * s/m²] |

$Pv$ | Air’s vapor pressure | [Pa] |

${P}_{vs}$ | Vapor saturation pressure | [Pa] |

${T}_{dp}$ | Dew point | [K] |

$\Delta {T}_{ml}$ | Logarithmic mean temperature difference | [K] |

${x}_{v}$ | Vapor molar fraction |

## References

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**Figure 1.**Scheme of a specific prototype of a heat pump food dryer tested for this algorithm where the thin line represents the refrigerant circuit while the thick arrows represent the airflow circuit.

**Figure 3.**Stage 2 of algorithm. Heat flow analysis between components, air and food. Component design derived from Equations (18)–(24).

**Figure 4.**Stage 3 of algorithm. Food humidity calculus and verification as demonstrated from Equations (25)–(33).

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## Share and Cite

**MDPI and ACS Style**

Andrade, B.; Amorim, I.; Silva, M.; Savosh, L.; Frölén Ribeiro, L. Heat Pump Dryer Design Optimization Algorithm. *Inventions* **2019**, *4*, 63.
https://doi.org/10.3390/inventions4040063

**AMA Style**

Andrade B, Amorim I, Silva M, Savosh L, Frölén Ribeiro L. Heat Pump Dryer Design Optimization Algorithm. *Inventions*. 2019; 4(4):63.
https://doi.org/10.3390/inventions4040063

**Chicago/Turabian Style**

Andrade, Bernardo, Ighor Amorim, Michel Silva, Larysa Savosh, and Luís Frölén Ribeiro. 2019. "Heat Pump Dryer Design Optimization Algorithm" *Inventions* 4, no. 4: 63.
https://doi.org/10.3390/inventions4040063