Non-isothermal dynamics of thin-film free-surface and channel flows of non-Newtonian nanofluids

Numerical modelling of the dynamic behaviour of generalized-viscoelastic-fluidbased nanofluids (GVFBNs) and viscoelastic-fluid-based nanofluids (VFBNs) has a number of industrial applications such as in new battery technologies and phasechange heat transfer devices. The computational results have shown that for certain flow parameters values, some of the non-Newtonian fluids also known as complex fluids (e.g. worm-like micellar solutions, granular flows, polymer solutions and some polymer melts) reveal flow instabilities within the flow field, such as the emergence of regions of different shear bands due to the flow induced material non-homogeneities. It has also been observed that it is becoming increasingly clear that the thermal runway phenomenon should not be ignored in polymers or other complex fluids since it may, in some instances, be as important as the complex rheology in differentiating susceptibility order for different types of nanofluids, for instance Newtonian fluid Based Nanofluids (NFBN), Generalized Newtonian Fluid-Based Nanofluids (GNFBN), Viscoelastic-fluid based nanofluids (VFBN) and Generalized viscoelastic fluid based nanofluids (GVFBN). These computational observations laid the foundation of this thesis. We have investigated the improvement of heat transfer for GVFBN and VFBN by homogenously mixed spherical shape nanoparticles. To incorporate the nanoparticles in the governing equations we use a single phase nanofluid modelling approach. Our mathematical models are governed by a system of non-linear, highly coupled, time-dependent Partial Differential Equations (PDEs). We developed computational solutions in Matlab software for the resulting system of equations by using an efficient semi-implicit finite-difference method, combined with a Crank-Nicolson scheme. In addition, the effects of nanoparticles on fluid velocity, extra stresses, temperature, and thermal conductivity are explored. Comparisons of the numerical results for the nanofluids with those from the literature without nanoparticles show excellent agreement