Magnetorheological fluids involve multi-physics phenomena which are manifested by interactions between structural mechanics, electromagnetism and rheological fluid flow. In comparison with analytical models, numerical models employed for magnetorheological fluid applications are thought to be more advantageous, as they can predict more phenomena, more parameters of design, and involve fewer model assumptions. On that basis, the state-of-the-art numerical methods that investigate the multi-physics behaviour of magnetorheological fluids in different applications are reviewed in this article. Theories, characteristics, limitations and considerations employed in numerical models are discussed. Modelling of magnetic field has been found to be rather an uncomplicated affair in comparison to modelling of fluid flow field which is rather complicated. This is because, the former involves essentially one phenomenon/mechanism, whereas the latter involves a plethora of phenomena/mechanisms such as laminar versus turbulent rheological flow, incompressible versus compressible flow, and single- versus two-phase flow. Moreover, some models are shown to be still incapable of predicting the rheological nonlinear behaviour of magnetorheological fluids although they can predict the dynamic characteristics of the system.

In this study, we numerically investigated the effect of swirl inserts with and without nanofluids over a range of Reynolds numbers for parabolic trough collectors with non-uniform heating. Three approaches were utilized to enhance the thermal-hydraulic performance—the variation of geometrical properties of a single canonical insert to find the optimized shape; the use of nanofluids and analysis of the effect of both the aforementioned approaches; the use of swirl generators and nanofluids together. Results revealed that using the straight conical strips alone enhanced the Nusselt number by 47.13%. However, the use of nanofluids along with the swirl generators increased the Nusselt number by 57.48%. These improvements reduced the thermal losses by 22.3% for swirl generators with nanofluids, as opposed to a reduction of only 15.7% with nanofluids alone. The investigation of different swirl generator designs showed various levels of improvements in terms of the overall thermal efficiency and thermal exergy efficiency. The larger swirl generator (H30mm-θ30°-N4) with 6% SiO₂ nanofluids was found to be the optimum configuration, which improved the overall collector efficiency and thermal exergy by 14.62% and 14.47%, respectively.