Toward empirical correlations for estimating the specific heat capacity of nanofluids utilizing GRG, GP, GEP, and GMDH

When nanoparticles are dispersed and stabilized in a base-fluid, the resulting nanofluid undergoes considerable changes in its thermophysical properties, which can have a substantial influence on the performance of nanofluid-flow systems. With such necessity and importance, developing a set of mathematical correlations to identify these properties in various conditions can greatly eliminate costly and time-consuming experimental tests. Hence, the current study aims to develop innovative correlations for estimating the specific heat capacity of mono-nanofluids. The accurate estimation of this crucial property can result in the development of more efficient and effective thermal systems, such as heat exchangers, solar collectors, microchannel cooling systems, etc. In this regard, four powerful soft-computing techniques were considered, including Generalized Reduced Gradient (GRG), Genetic Programming (GP), Gene Expression Programming (GEP), and Group Method of Data Handling (GMDH). These techniques were implemented on 2084 experimental data-points, corresponding to ten different kinds of nanoparticles and six different kinds of base-fluids, collected from previous research sources. Eventually, four distinct correlations with high accuracy were provided, and their outputs were compared to three correlations that had previously been published by other researchers. These novel correlations are applicable to various oxide-based mono-nanofluids for a broad range of independent variable values. The superiority of newly developed correlations was proven through various statistical and graphical error analyses. The GMDH-based correlation revealed the best performance with an Average Absolute Percent Relative Error (AAPRE) of 2.4163% and a Coefficient of Determination (R(2)) of 0.9743. At last, a leverage statistical approach was employed to identify the GMDH technique’s application domain and outlier data, and also, a sensitivity analysis was carried out to clarify the degree of dependence between input and output variables.