Mathematical modelling of nanofluid thermophysical properties using compulas

Abstract

In this dissertation, mathematical research is performed to model nanofluid thermophysical properties in terms of multivariate probability density functions utilizing copulas from known verified and validated experimental data for water/alumina nanofluid mixtures. A comprehensive review of the available data from the open scientific literature is undertaken to first understand the accuracy limits of the combination of available experimental and theoretical data for nanofluids. The nanofluid data is then processed using multivariate statistical analysis techniques in order to mathematically incorporate the input process parameter’s intrinsic measurement uncertainties. Having analysed the verified data, optimal functional expressions for the effective thermal conductivity are then determined. This mathematical analysis is inclusive of estimates of the process parameter’s respective experimental statistical uncertainties through stochastic based Monte Carlo simulations by incorporating information of the nanoparticle morphology such as the nanoparticle size and volume fraction, and the nanofluid temperature. Numerical simulations are performed for the resulting copula-based PDF’s with custom developed multivariate sampling strategies which are derived and tested. These model predictions were verified and validated by comparing them to a MLP-NN scheme to check for consistency. Quantitative results from these simulations indicate that the copula mathematical model is able to achieve an 𝐴𝐴𝑅𝐷 = 3.0953% accuracy for predicted behaviours of the developed thermal conductivity database compared to an 𝐴𝐴𝑅𝐷 = 4.2376% accuracy for a conventional MLP neural network. The proposed mathematical modelling approach is a new novel original research technique that has been developed which is able to incorporate physical experimental measurement uncertainties such that the model is able to adaptively refine the predicted nanofluid model quantitative uncertainties in sub-domains of the input metaparameters which is not presently mathematically possible with existing neural network modelling approaches.