# Simulation of Coupled Heat-Mass Transfer in Sea Cucumbers with Heat Pump Drying

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Materials

#### 2.2. Instruments and Equipment

#### 2.3. Experimental Steps

- (a)
- For pretreatment, a fresh sea cucumber was boiled in water for 10 min.
- (b)
- The boiled sea cucumber was weighed and its initial size was measured.
- (c)
- The sea cucumber was put into the drying equipment, and the air outlet temperature was set to one of the above temperatures in turn. Two temperature measuring points were arranged on the surface and inside of the sample. After the drying machine was running, the sea cucumber was weighed and measured every 20 min. The length of the test was set at 600 min.
- (d)
- The above steps were repeated three times, and their average results were analyzed.

#### 2.4. Test Quantity and Calculating Formulas

- (1)
- Dry-base moisture

- (2)
- Relative deviation rate$${E}_{MD}=\frac{{y}_{1}-{y}_{2}}{{y}_{1}}\times 100\%$$

- (3)
- Correlation coefficient$${R}^{2}=1-\frac{{{\displaystyle \sum}}_{i=1}^{m}\frac{{\left({y}_{i}-\widehat{{y}_{i}}\right)}^{2}}{m-j-1}}{{{\displaystyle \sum}}_{i=1}^{m}\frac{{\left({y}_{i}-\overline{{y}_{i}}\right)}^{2}}{m-1}}\times 100\%$$

#### 2.5. Physical Model

#### 2.6. Governing Equations

_{w}and the air saturation S

_{g}are defined as the volume fractions of water and gas in the pore volume, respectively.

#### 2.7. Boundary Condition

## 3. Results and Discussions

#### 3.1. Analysis of Temperature and Dry Basis Moisture Content Changes

#### 3.2. Effect of Wind Speed on Heat and Mass Transfer Process

#### 3.3. Internal Heat and Mass Transfer Law

^{3}at the upwind. At the downwind of the sea cucumber, the dry-base moisture content is 4.65, and the concentration is 27,500 mol/m

^{3}. The difference in the dry-base moisture content and internal concentration between the two positions is 50% and 2500 mol/m

^{3}, respectively. The difference in the dry-base moisture content increases continuously with drying. At the same time, the air velocity distribution affects temperatures in the materials. The temperature on the windward end is higher than the windward end, which also affects the moisture uniformity in the material during the drying process.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

C | Molar concentration, mol/m^{3} |

${C}_{\epsilon}$ | Model constants |

c_{p} | Heat capacity, J/(kg·K) |

c | Mass concentration, kg/m^{3} |

c_{v,sat} | Saturated vapor concentration, kg/m^{3} |

D | Mass diffusivity, m^{2}/s |

D_{cap} | Capillary diffusion coefficient, m^{2}/s |

D_{va} | Vapor diffusion coefficient, m^{2}/s |

F | Relaxation function |

h_{evap} | Latent heat, J/kg |

n | Mass flux, kg/(m^{2}·s) |

K_{evap} | Evaporation rate constant, 1/s |

M | Molecular weight, kg/mol |

M_{db} | Moisture content on dry basis,1 |

P | Pressure, pa |

R | Gas constant, kJ/kmol K |

R_{evap} | Evaporation rate, kg/(m^{3}·s) |

S | Saturation |

t | Time, s |

T | Temperature, K |

T_{in} | Inlet temperature, K |

u | Velocity, m/s |

u_{in} | Inlet velocity, m/s |

Greek symbols | |

$\mathsf{\lambda}$ | Thermal conductivity, W/(m·K) |

$\mu $ | Dynamic viscosity, Pa·s |

${\mu}_{T}$ | Turbulent dynamic viscosity, Pa·s |

$\mathsf{\nu}$ | Kinematic viscosity, kg/(m$\xb7$s) |

$\mathsf{\rho}$ | Density, kg/m^{3} |

$\varphi $ | Porosity |

Subscripts | |

a | Air |

db | Dry basis |

eff | Effective |

g | Gas |

i | Initial |

l | Liquid |

s | Solid |

v | Vapor |

sat | Saturated |

w | Water |

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**Figure 1.**Heat pump dryer (

**a**) schematic diagram and (

**b**) T-S diagram of heat pump. Note: 1—compressor, 2—condenser, 3—throttle valve, 4—receiver, 5—evaporator, 6—first bypass valve, 7—s bypass valve, 8—drying oven, 9—circulating fan. a—compressor inlet, b—condenser inlet, c’—throttle valve inlet, c—condenser outlet, d—evaporator inlet.

**Figure 2.**Schematic diagram of two-dimensional axisymmetric model of sea cucumber in drying oven. Note: Figure 2 shows the cross-section view of the desiccating box and the model of the sea cucumber; the middle line is the axis of symmetry, the desiccating box is 24 cm wide, 30 cm high, the long axis of the sea cucumber is 7 cm, and the short axis is 4 cm.

**Figure 7.**Variation in velocity, dry base moisture content, temperature, and concentration in the drying chamber.

(1) | (2) | (3) | (4) | (5) | |
---|---|---|---|---|---|

Velocity | 0 | u_{in} | 0 | - | $\left(\nabla u\right)\xb7\mathrm{n}=0$ |

Temperature | $\left(\nabla \mathrm{T}\right)\xb7\mathrm{n}=0$ | T_{in} | $\left(\nabla \mathrm{T}\right)\xb7\mathrm{n}=0$ | - | $\left(\nabla \mathrm{T}\right)\xb7\mathrm{n}=0$ |

Mass concentration of vapor | $\left(\nabla {c}_{v}\right)\xb7\mathrm{n}=0$ | ${c}_{v}\left(\mathrm{RH}\right)$ | $\left(\nabla {c}_{v}\right)\xb7\mathrm{n}=0$ | - | $\left(\nabla {c}_{v}\right)\xb7\mathrm{n}=0$ |

Mass concentration of water | - | - | - | $\left(\nabla c\right)\xb7\mathrm{n}=0$ | - |

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**MDPI and ACS Style**

Zhao, H.; Dai, J.; Wu, K.
Simulation of Coupled Heat-Mass Transfer in Sea Cucumbers with Heat Pump Drying. *Appl. Sci.* **2022**, *12*, 5508.
https://doi.org/10.3390/app12115508

**AMA Style**

Zhao H, Dai J, Wu K.
Simulation of Coupled Heat-Mass Transfer in Sea Cucumbers with Heat Pump Drying. *Applied Sciences*. 2022; 12(11):5508.
https://doi.org/10.3390/app12115508

**Chicago/Turabian Style**

Zhao, Haibo, Jiaao Dai, and Kun Wu.
2022. "Simulation of Coupled Heat-Mass Transfer in Sea Cucumbers with Heat Pump Drying" *Applied Sciences* 12, no. 11: 5508.
https://doi.org/10.3390/app12115508