Table 7 CR model results from Reaction and Diffusion Models for charcoal samples.
AA | Reaction Models | \(ln\left(\frac{g(\alpha )}{{T}^{2}}\right)\) | \(ln\left(\frac{g(\alpha )}{{T}^{2}}\right)\) | \(-\frac{{E}_{a}}{R}\) | \(ln\left(\frac{A.R}{\beta .{E}_{a}}\right)\) | \({E}_{a}\) |
|---|---|---|---|---|---|---|
Diffusion Models | \({350 }\)°C | \({500 }\)°C | \(\beta =10\) | \(kJ/mol\) | ||
1 | 1D diffusion | − 14.99 | − 13.37 | − 5188.94 | − 6.66 | 43.12 |
2 | Diff Control (J) | − 19.14 | − 12.59 | − 21,020.6 | 14.6 | 174.68 |
3 | Diff Control (C) | − 19.25 | − 14.86 | − 14,095.96 | 3.37 | 117.14 |
Reaction order & geometrical contraction models | ||||||
4 | Mampel (1st order) | − 14.93 | − 12.32 | − 8353.96 | − 1.51 | 69.46 |
5 | Second Order | − 14.86 | − 10.71 | − 13,316.16 | 6.51 | 110.66 |
6 | Contracting Cylinder | − 15.65 | − 13.61 | − 6559.72 | − 5.12 | 54.51 |
7 | Contracting Sphere | − 16.05 | − 13.83 | − 7108.61 | − 4.64 | 59.07 |
HM | Reaction Models | \(ln\left(\frac{g(\alpha )}{{T}^{2}}\right)\) | \(ln\left(\frac{g(\alpha )}{{T}^{2}}\right)\) | \(-\frac{{E}_{a}}{R}\) | \(ln\left(\frac{A.R}{\beta .{E}_{a}}\right)\) | \({E}_{a}\) |
|---|---|---|---|---|---|---|
Diffusion Models | \({350 }\)°C | \({500 }\) °C | \(\beta =10\) | \(kJ/mol\) | ||
1 | 1D diffusion | − 14.53 | − 13.32 | − 3881.73 | − 8.30 | 32.26 |
2 | Diff Control (J) | − 18.11 | − 11.33 | − 21,780.82 | 16.85 | 180.99 |
3 | Diff Control (C) | − 18.30 | − 14.60 | − 11,872.43 | 0.76 | 98.66 |
Reaction order & geometrical contraction models | ||||||
4 | Mampel (1st order) | − 14.43 | − 11.94 | − 7993.6 | − 1.60 | 66.43 |
5 | Second Order | − 14.32 | − 9.41 | − 15,764.86 | 10.99 | 131.01 |
6 | Contracting Cylinder | − 15.17 | − 13.45 | − 5517.75 | − 6.31 | 45.85 |
7 | Contracting Sphere | − 15.56 | − 13.62 | − 6236.75 | − 5.55 | 51.83 |
PA | Reaction Models | \(ln\left(\frac{g(\alpha )}{{T}^{2}}\right)\) | \(ln\left(\frac{g(\alpha )}{{T}^{2}}\right)\) | \(-\frac{{E}_{a}}{R}\) | \(ln\left(\frac{A.R}{\beta .{E}_{a}}\right)\) | \({E}_{a}\) |
|---|---|---|---|---|---|---|
Diffusion Models | \({350 }\)°C | \({500 }\)°C | \(\beta =10\) | \(kJ/mol\) | ||
1 | 1D diffusion | − 15.17 | − 13.34 | − 5876.22 | − 5.74 | 48.81 |
2 | Diff Control (J) | − 19.53 | − 11.99 | − 24,207.7 | 19.32 | 201.17 |
3 | Diff Control (C) | − 19.63 | − 14.72 | − 15,764.51 | 5.68 | 131.00 |
Reaction order & geometrical contraction models | ||||||
4 | Mampel (1st order) | − 15.12 | − 12.13 | − 9592.84 | 0.28 | 79.72 |
5 | Second Order | − 15.07 | − 10.12 | − 15,872.24 | 10.41 | 131.90 |
6 | Contracting Cylinder | − 15.84 | − 13.52 | − 7432.79 | − 3.91 | 61.77 |
7 | Contracting Sphere | − 16.24 | − 13.72 | − 8079.23 | − 3.27 | 67.14 |
VP | Reaction Models | \(ln\left(\frac{g(\alpha )}{{T}^{2}}\right)\) | \(ln\left(\frac{g(\alpha )}{{T}^{2}}\right)\) | \(-\frac{{E}_{a}}{R}\) | \(ln\left(\frac{A.R}{\beta .{E}_{a}}\right)\) | \({E}_{a}\) |
|---|---|---|---|---|---|---|
Diffusion Models | \({350 }\)°C | \({500 }\)°C | \(\beta =10\) | (\(kJ/mol\) | ||
1 | 1D diffusion | − 14.01 | − 13.41 | − 1934.69 | − 10.9 | 16.07 |
2 | Diff Control (J) | − 16.84 | − 13.01 | − 12,291.94 | 2.89 | 102.15 |
3 | Diff Control (C) | − 17.18 | − 14.99 | − 7039.28 | − 5.88 | 58.50 |
Reaction order & geometrical contraction models | ||||||
4 | Mampel (1st order) | − 13.82 | − 12.47 | − 4351.42 | − 6.84 | 36.16 |
5 | Second Order | − 13.62 | − 11.10 | − 8089.02 | − 0.64 | 67.22 |
6 | Contracting Cylinder | − 14.61 | − 13.68 | − 2983.26 | − 9.82 | 24.79 |
7 | Contracting Sphere | − 14.98 | − 13.92 | − 3401.91 | − 9.52 | 28.27 |
