Multivariate Analysis of Variance (MANOVA) and Multivariate Regression in Determining Thermal Conductivity of Nanofluid for Use in Mechanical Systems

Statistical methods are used in the analysis of all types of data. In this paper, using multivariate analysis of variance and multivariate regression, the data related to the thermal conductivity of nanofluids have been analyzed and the results of the two methods have been compared. A two-step method was used to prepare ethylene glycol-magnesium oxide nanofluid. In order to prepare the nanofluid by suspending the nanoparticles in the base fluid, an ultrasonic homogenizer was used. For this purpose, nanoparticles with diameters of 20, 50, and 100 nm in volume fractions of 0.25, 0.5, 0.75, 1, and 1.25% have been used at temperatures of 25, 30, 35, 40, 45, and 50 degrees Celsius. Transient hot wire method was used to measure thermal conductivity in different volume fractions. Then the obtained experimental values were analyzed using SPSS.26 software. The coefficient of determination and the graphs of the errors obtained in the two methods showed that when the independent variables are defined as grouped, the use of multivariate analysis of variance can better describe the dispersion of the thermal conductivity.