# Optimization of Processing Parameters to Increase Thermal Conductivity of Rice Straw Fiber Film
## 3 Results and Discussion  
### Regression Models  
RSM, which combines mathematics and statistics together, is usually used to analyze the relative significance of different operating parameters even in complicated systems [39; 40; 41; 42]. Therefore, this method was used to optimize the parameters used in this study. The central composite design was  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Basis** & **Neutral Sizing** & **Charcoal** & **Wet Strength** & **Beating** & **Dry Tensile** & **Wet Tensile** & **Thermal** \\  & **Weight** & **Agent Content** & **Addition Ratio** & **Agent Content** & **Degree** & **Strength** & **Strength** & **Conductivity** \\  & & & & & & & **(N)** & **(N)** & **(W/m-K)** \\ \hline
1 & –1 & –1 & –1 & –1 & –1 & 1 & 17.3 & 5.9 & 0.0497 \\
2 & 1 & –1 & –1 & –1 & –1 & –1 & 18.1 & 5.4 & 0.0522 \\
3 & –1 & 1 & –1 & –1 & –1 & 14.3 & 4.1 & 0.0521 \\
4 & 1 & 1 & –1 & –1 & 1 & 17.4 & 6.1 & 0.0521 \\
5 & –1 & –1 & 1 & –1 & –1 & 14.9 & 5.1 & 0.0536 \\
6 & 1 & –1 & 1 & –1 & 1 & 19.3 & 7.8 & 0.0551 \\
7 & –1 & 1 & 1 & –1 & 1 & 16.4 & 5.2 & 0.0552 \\
8 & 1 & 1 & 1 & –1 & –1 & 18.4 & 5.7 & 0.0514 \\
9 & –1 & –1 & –1 & 1 & –1 & 17.7 & 5.1 & 0.0480 \\
10 & 1 & –1 & –1 & 1 & 1 & 33.6 & 12.4 & 0.0626 \\
11 & –1 & 1 & –1 & 1 & 1 & 18.1 & 5.4 & 0.0553 \\
12 & 1 & 1 & –1 & 1 & –1 & 23.4 & 9.1 & 0.0498 \\
13 & –1 & –1 & 1 & 1 & 1 & 15.4 & 4.9 & 0.0574 \\
14 & 1 & –1 & 1 & 1 & 1 & 20.2 & 7.2 & 0.0756 \\
15 & –1 adopted to optimize the process to enhance the thermal conductivity of film made by charcoal and rice straw.  
Thirty-six experiments were carried out to study the effects and interactions of basis weight, neutral sizing agent content, charcoal addition ratio, wet strength agent content, and beating degree on dry and wet tensile strengths and thermal conductivity of films. These are represented in Table 2. Table 2 also shows the values of dry tensile strength, wet tensile strength, and thermal conductivity at each experimental designed condition.  
The regression model results indicated that the best models are the quadratic model for dry and wet tensile strengths, and a linear model for thermal conductivity. Table 3 shows the significance of the regression model parameters.  
The \(R^{2}\) for dry and wet tensile strengths and thermal conductivity models are 0.901, 0.873, and 0.781, respectively. The \(p\) values are all less than 0.001 showing that the models are highly significant, and there is only a 0.01%, 0.01%, and 0.1% chance of occurrence of model \(f\) value because of noise. The lack of fit was not significant with \(p\) values larger than 0.05 for all three models. The three model equations are shown as Equations (2)-(4).  
\[\begin{array}{l}y_{1}=22.56+2.93x_{1}-0.11x_{2}-0.41x_{3}+2.73x_{4}+1.02x_{5}- 0.81x_{1}^{2}-0.99x_{2}^{2}-1.16x_{3}^{2}+1.52x_{1}x_{4}\\ +1.09x_{1}x_{5}+1.62x_{2}x_{3}\\ \end{array} \tag{2}\]  
\[\begin{array}{l}y_{2}=7.27+1.33x_{1}-0.27x_{2}-0.025x_{3}+0.85x_{4}+0.40x_{5} -0.29x_{1}^{2}-0.45x_{3}^{2}+0.75x_{1}x_{4}+0.48x_{1}x_{5}\\ -0.44x_{2}x_{5}-0.40x_{3}x_{4}\\ \end{array} \tag{3}\]  
\[\begin{array}{l}y_{3}=0.055+2.76\times 10^{-3}x_{1}-5.808\times 10^{-4}x_{2}+4. 064\times 10^{-3}x_{3}+2.142\times 10^{-3}x_{4}+1.254\times 10^{-3}x_{5}\\ \end{array} \tag{4}\]  
where, \(y_{1}\), \(y_{2}\), and \(y_{3}\) are dry and wet tensile strengths (N) and thermal conductivity (W/m\(\cdot\)K), respectively; \(x_{1}\), \(x_{2}\), \(x_{3}\), \(x_{4}\), and \(x_{5}\) are basis weight (g/m\({}^{2}\)), neutral sizing agent content (%), charcoal addition ratio (%), wet strength agent content (%), and beating degree (\({}^{\circ}\)SR), respectively.