Determination of Nusselt Number of Herschel Bulkley Nanofluids by Using CMA-ES Algorithm

Drilling muds are the most applicable fluids in drilling. Two basic types of drilling fluids are used, water based muds (WBM) and oil based muds (OBM). Water based muds are more applicable than oil based muds. One of the most important applications of this fluid is cooling a bit. Chemical engineers try to change drilling mud’s rheological property in order to increase heat transfer to the bit. Rheological properties of drilling muds are well described by the Herschel Bulkley model. Adding polyacrylic acid to water changes its rheological property to Herschel Bulkley fluid. Standard equations like Shah and London and Hausen correlations were not able to predict local Nusselt number of non-Newtonian fluids.This study concerns estimating parameters of a local Nusselt number of Herschel Bulkley fluids with CuO nanoparticles in four concentrations of 0.1, 0.3, 0.6 and 0.05% in constant heat flux and laminar region. A nonlinear optimization algorithm (CMA-ES) was used to estimate local Nusselt number. There is good agreement between experimental data and those predicted by proposed correlations with R^2 greater than 0.99.