Comparison of fuel and emission properties of petro diesel and sunflower biodiesel prepared by optimized production variables

Effect of Fiber Chemical Treatments on Performance of Date Palm Fibers Using Response Surface Methodology

“…The other combinations showed the least effect on the dependent variables. Because each model has four independent variables, two variables were held constant at the center level for each plot .…”

“…The fibers were immersed in the (3–7%) and (2–6%) by weight of sodium hydroxide (NaOH) and hydrogen peroxide (H 2 O 2 ) solution for 14–18 h at 30–46°C. An experimental design was done with CCD . According to the study of Alsaeed et al .…”

“…The variables were included the weight percent of hydrogen peroxide ( X 1 ), weight percent of sodium hydroxide ( X 2 ), treatment time ( X 3 ), and temperature ( X 4 ). In RSM technique, a codification of independent variables is done to eliminate the effect of variables magnitude on the estimation of regression coefficients . The relation between the coded and actual values is expressed as follows: where ( x i ) is the code value of the i th independent variable, ( X i ) is the uncoded value of the i th independent variable, and ( X 0 ) is the value of the i th independent variable at the center point.…”

“…In addition, to analyze the goodness‐of‐fit of the model, the regression coefficients ( R 2 ), and adjusted and predicted ( R 2 ) were also evaluated. where ( β k 0 ) indicates the intercept constant, ( β ki ) show the coefficients of linear terms, ( β kii ) represent the coefficients of quadratic terms, ( β kij ) show the coefficients of interaction terms, and ( k ) represents the number of independent variables. The values of X 1 , X 2 , X 3 , and X 4 that correspond to the minimum value of Y L were solved by setting the partial derivatives of the functions to zero and solving . The number of experiments, N , needed for optimization experiments was calculated by the following relationship: where k is the number of independent parameters, 2 k is the number of experiments which must be performed with variables having a code value equal to ±1 (factorial points); 2 k is the number of experiment which must be performed using the variables with a code value equal to ±2 (axial points), and c p is the number of experiments which must be done with variables having a code value equal to 0 (central point).…”

“…When a quadratic equation (Equation ) is used as the response model, the optimal values for the independent variables are found by taking the first partial derivatives of this equation and equating them to zero . Equation can be presented by the following matrix form: where Y , β 0 , and b are the response, offset, and linear effect vectors, respectively.…”