Evaluating the Effectiveness of Proportional Nodes Method in Curve Fitting for Surfaces: Application to Data of Dynamic Viscosity of Ammonia-Water Solution

Abstract

This study used the proportional nodes method, a novel curve fitting approach to correlate data for dynamic viscosity of ammonia-water solution. The approach integrates polynomial equations, generated at various temperatures, with those calculated at selected mole fraction nodes. These nodes are scaling factors that account for variations in dynamic viscosity at different temperatures at selected mole fractions. The accuracy of the polynomial equations ensures a high degree of fitting accuracy. The proportional nodes, computed systematically, were integrated into a robust and highly accurate polynomial model to generate correlations that fit the data for the surface. This model exhibited minimal average percentage differences between predicted and actual viscosity values (±0.2614293 for temperature range, 273.15K to 303.15K and ±1.11 for temperature range, 303.15K to 423.15 K), indicating a high level of predictive accuracy. The proportional nodes method offers a significant contribution to both academic research and industry. It provides a more precise and adaptive model for predicting the dynamic viscosity of ammonia-water solution, which is critical for optimizing and designing various industrial applications, including refrigeration systems.