Quadratic model for evaluating the hardness of hazelnut shell-polystyrene composite based on input concentration ratio of its constituent materials

Abstract

A quadratic model was derived for evaluating the hardness of hazelnut shell–polystyrene composite (HPC) based on input concentration ratio of the constituent materials. The derived empirical model: Ӈ = - ẞ (ɤ_f /ɤ_m)^N  + Ϧ(ɤ_f /ɤ_m) + Ҽ validated by the core model : Ӈ + ẞ(ɤ_f /ɤ_m)^N ≈ Ҽ + Ϧ(ɤ_f /ɤ_m), in that both sides of the structure are correspondingly near equal. Ӈ, ẞ and ɤ denote the HPC hardness, input concentrations of hazelnut shell and polystyrene. The model-predicted results emphasize similar trend and spread of result points shown in previous research. Correlations between the HPC hardness and input concentration ratio of hazelnut shell and polystyrene were evaluated as 0.99998 and 0.9787 using model-predicted and experimental results. The standard error incurred on predicting the HPC hardness (relative to experimental results) is ˂ 0.3%, for every change in the input concentration ratio of hazelnut shell and polystyrene. This translates to a model confidence level above 99%. The HPC hardness per unit input concentration ratio of hazelnut shell and polystyrene were 6.8215 and 6.9557, using experimental and model-predicted results. The maximum deviation of the model-predicted HPC hardness from experimental results was 2.36%. The derived model shows an exceptional level of functionality, and will predict the HPC hardness, within the experimental results range, on substituting into the model, values of the input concentration ratio of hazelnut shell and polystyrene, providing the boundary conditions are considered.