Finite Difference Modeling of the Temperature Profile during the Biodrying of Organic Solid Waste
Abstract
:1. Introduction
2. Materials and Methods
2.1. Source of Data
2.2. Considerations for the Heat Transfer and Microbial Heat Generation
2.3. Distribution of the Node Network
3. Results
3.1. Development of the Equations in Explicit form for Determining the Temperature at Each of the Nodes
3.1.1. Conduction Heat Transfer and Microbial Heat Generation
3.1.2. Convection Heat Transfer
3.1.3. Incident Solar Radiation
3.1.4. Calculation Procedure
3.2. Comparison between the Modeling and the Experimental Results
3.2.1. Cell Growth
3.2.2. Temperatures at the Center, C, and Midpoints of the pile Lm, Rm, Bm, Um
3.2.3. Temperatures on the Surface Faces of the Pile: L, R, B, U
- Temperature at the base (B) face of the pile
- Temperatures on the left and right faces of the pile: L and R
- Temperature at the upper face of the pile: U
3.3. Suggestions for Future Research
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
Appendix A
The Node Equation | Can Be Extended for the Nodes | Number of Nodes |
---|---|---|
1 | 30, 31, 32, 34, 35, 37, 38 and 39; 49, 50, 51, 54, 55, 56, 59, 60 and 61 74, 75, 76, 79, 80, 81, 84, 85 and 86 | 8 9 9 |
0 | 29 and 36; 48, 53 and 58; 73, 78 and 83 | 8 |
2 | 33 and 40; 52, 57 and 62; 77, 82 and 87 | 8 |
3 | 27 and 28; 44, 45 and 46; 69, 70 and 71 | 8 |
4 | 41 and 42; 64, 65 and 66; 89, 90 and 91 | 8 |
5; 6; 7; 8 | 43 and 68; 47 and 72; 87 and 92; 63 and 88 | 8 |
9 | 112, 113 and 114; 116, 117; 119, 120 and 121 | 8 |
10 | 96, 97 and 98; 100, 101; 103, 104 and 105 | 8 |
11; 12; 13; 14 | 109 and 110; 93 and 94; 107 and 108; 123 and 124 | 8 |
15 to 22 | No correspondence | 0 |
23; 24; 25; 26 | 95 and 102; 99 and 106; 111 and 118; 115 and 122 | 8 |
Total = 27 | Total = 98 |
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Node Type | Node Number | Cut of the Volume Element at the Boundary | Areas Perpendicular to the x, y, z Axes | ||
---|---|---|---|---|---|
x Axis | y Axis | z Axis | |||
Internal | 1 | None | |||
Surface | 0 and 2 | ||||
3 and 4 | |||||
9 and 10 | |||||
Edge | 5, 6, 7, 8 | ||||
11, 12, 13, 14 | |||||
23, 24, 25, 26 | |||||
Vertex | 15, 16, 17, 18 19, 20, 21, 22 |
Time (Days) | Biomass (kg/kg Dry Pile) | Substrate (kg/kg Dry Pile) |
---|---|---|
0 | 0.0120 | 0.94 |
7 | 0.0239 | 0.92 |
14 | 0.0340 | 0.91 |
21 | 0.0453 | 0.84 |
28 | 0.0470 | 0.86 |
35 | 0.0465 | 0.82 |
42 | 0.0480 | 0.83 |
49 | 0.0460 | 0.82 |
Date | Surface Direction | Average Incident Solar Radiation on the Surface (W/m2) | |||||||
---|---|---|---|---|---|---|---|---|---|
6:00 | 8:00 | 10:00 | 12:00 | 14:00 | 16:00 | 18:00 | 20:00 | ||
October–December | N | 0 | 40 | 77 | 90 | 77 | 40 | 0 | 0 |
E | 0 | 626 | 505 | 97 | 87 | 40 | 0 | 0 | |
S | 0 | 321 | 711 | 847 | 711 | 321 | 0 | 0 | |
W | 0 | 40 | 87 | 97 | 505 | 626 | 0 | 0 | |
Horizontal | 0 | 156 | 509 | 640 | 509 | 156 | 0 | 0 | |
Direct | 0 | 643 | 884 | 927 | 884 | 643 | 0 | 0 |
Date | Surface Direction | R = Ratio of the Solar Radiation on the Surface to the Direct Solar Radiation | |||||||
---|---|---|---|---|---|---|---|---|---|
6:00 | 8:00 | 10:00 | 12:00 | 14:00 | 16:00 | 18:00 | 20:00 | ||
October–December | nor | 0 | 0.06 | 0.09 | 0.10 | 0.09 | 0.06 | 0 | 0 |
eas | 0 | 0.97 | 0.57 | 0.10 | 0.10 | 0.06 | 0 | 0 | |
wes | 0 | 0.50 | 0.80 | 0.91 | 0.80 | 0.50 | 0 | 0 | |
sou | 0 | 0.06 | 0.10 | 0.10 | 0.57 | 0.97 | 0 | 0 | |
Upper horizontal | 0 | 0.24 | 0.69 | 0.69 | 0.58 | 0.24 | 0 | 0 | |
Direct | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Time Period (Days) | Center and Midpoints of the Pile | Pile Surfaces or Faces | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Node 1 Center (C) | Node 55 Left Midpoint (Lm) | Node 80 Right Midpoint (Rm) | Node 31 Upper Midpoint (Um) | Node 38 Base Midpoint (Bm) | Node 9 Left (L) | Node 10 Right (R) | Node 3 Upper (U) | Node 4 Base (B) | ||
Biodrying: Microbial activity and Ambient drying | 0 to 10 | −4 | −10 | +4 | +8 | no record | −10 | −10 | −15 | no record |
11 to 20 Turning at 10 | 0 | −13 | −13 | −10 | −8 | −7 | −7 | −7 | −15 | |
21 to 30 Turning at 20 | −25 | −25 | −25 | −25 | −25 | −2 | −2 | −10 | Recoding error | |
31 to 35 Turning at 30 | −36 | −36 | −36 | −36 | −36 | −3 | −3 | −5 | −8 | |
Ambient drying | 36 to 42 No Turning | 0 | 0 | 0 | 0 | 0 | −3 | −3 | −5 | no record |
43 to 50 Turning at 42 | +10 | +2 | +2 | 0 | +10 | −3 | −3 | −5 | no record |
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Orozco-Álvarez, C.; Díaz-Megchún, J.; Osorio-Mirón, A.; García-Salas, S.; Hernández-Sánchez, E.; Palma-Orozco, G.; Robles-Martínez, F. Finite Difference Modeling of the Temperature Profile during the Biodrying of Organic Solid Waste. Sustainability 2022, 14, 14705. https://doi.org/10.3390/su142214705
Orozco-Álvarez C, Díaz-Megchún J, Osorio-Mirón A, García-Salas S, Hernández-Sánchez E, Palma-Orozco G, Robles-Martínez F. Finite Difference Modeling of the Temperature Profile during the Biodrying of Organic Solid Waste. Sustainability. 2022; 14(22):14705. https://doi.org/10.3390/su142214705
Chicago/Turabian StyleOrozco-Álvarez, Carlos, Javier Díaz-Megchún, Anselmo Osorio-Mirón, Sergio García-Salas, Enrique Hernández-Sánchez, Gisela Palma-Orozco, and Fabián Robles-Martínez. 2022. "Finite Difference Modeling of the Temperature Profile during the Biodrying of Organic Solid Waste" Sustainability 14, no. 22: 14705. https://doi.org/10.3390/su142214705