A Three Dimensional Exact Equation For The Turbulent Dissipation Rate of Generalized Newtonian Fluids

The Flow of inelastic Non-Newtonian fluids is involved in many biological and industrial applications like nanofluids. Despite many years have passed since the beginning of the study of turbulent Non-Newtonian fluids, most of the studies carried out focus the attention on viscoelastic-fluids. In order to make accurate and low-cost prediction on turbulent inelastic Non-Newtonian fluids flow, a RANS Generalized Newtonian Fluid (GNF) turbulence model is required based on exact transport equation of turbulent variables. In a previous paper [52] we achieved the exact transport equations for turbulent kinetic energy and dissipation rate through the introduction of an apparent viscosity transport equation in 2D case for sake of simplicity. The object of this paper is to extend the results given in [52] in 3D case giving the full mathematical demonstration of the exact-equations. The modelling of the unknown terms it is left for a future work.