The primary focus of the present work is to model the entire casting process from filling stage to complete solidification. The model takes into consideration any phase change taking place during the filling process. An implicit volume of fluid (VOF) based algorithm has been employed for simulating free surface flows during the filling process and the model for solidification is based on a fixed-grid enthalpy-based control volume approach. Solidification modelling is coupled with VOF through User Defined Functions (UDF) developed in commercial fluid dynamics (CFD) code FLUENT 6.3.26. The developed model is applied for the simultaneous filling and solidification of pure metals and binary alloy systems to study the effects of filling process on the solidification characteristics, evolution of mushy zone and the final macrosegregation pattern in the casting. The numerical results of the present analysis are compared with the conventional analysis assuming the initial conditions to be a completely filled mould cavity with uniform temperature, solute concentration and quiescent melt inside the cavity. The effects of process parameters, namely the degree of superheat, cooling temperature and filling velocity etc. are also investigated. Results show significant differences on the evolution of mushy zone and macrosegregation between the present analysis and the conventional analysis. The application of present model to simulate three dimensional sand casting is also demonstrated. The three dimensional competetive effect of filling generated residual flow and the buoyancy-induced convective flow pattern cause significant difference in macrosegregation pattern in casting.

The primary focus of the present work is the development of macro-models for numerical simulation of binary alloy solidification processes, consistent with microscopic phase-change considerations, with a particular emphasis on capturing the effects of non-equilibrium species redistribution on overall macrosegregation behaviour. As a first step, a generalised macroscopic framework is developed for mathematical modelling of the process. The complete set of equivalent single-phase governing equations (mass, momentum, energy and species conservation) are solved following a pressure-based Finite Volume Method according to the SIMPLER algorithm. An algorithm is also developed for the prescription of the coupling between temperature and the melt-fraction. Based on the above unified approach of solidification modelling, a macroscopic numerical model is devised that is capable of capturing the interaction between the double-diffusive convective field and a localised fluid flow on account of solutal undercooling during non-equilibrium solidification of binary alloys. Numerical simulations are performed for the case of two-dimensional transient solidification of Pb-Sn alloys, and the simulation results are also compared with the corresponding experimental results quoted in the literature. It is observed that non-equilibrium effects on account of solutal undercooling result in an enhanced macrosegregation. Next, the model is extended to capture the effects of dendritic arm coarsening on the macroscopic transport phenomena occurring during a binary alloy solidification process. The numerical results are first tested against experimental results quoted in the literature, corresponding to the solidification of an Al-Cu alloy in a bottom-cooled cavity. It is concluded that dendritic arm coarsening leads to an increased effective permeability of the mushy region as well as an enhanced eutectic fraction of the solidified ingot. Consequently, an enhanced macrosegregation can be predicted as compared to that dictated by shrinkage-induced fluid flow alone. For an order-of-magnitude assessment of predictions from the numerical models, a systematic approach is subsequently developed for scaling analysis of momentum, heat and species conservation equations pertaining to the case of solidification of a binary mixture. A characteristic velocity scale inside the mushy region is derived, in terms of the morphological parameters of the two-phase region. A subsequent analysis of the energy equation results in an estimation of the solid layer thickness. It is also shown from scaling principles that non-equilibrium effects result in an enhanced macro-segregation compared to the case of an equilibrium model For the sake of assessment of the scaling analysis, the predictions are validated against computational results corresponding to the simulation of a full set of governing equations, thus confirming the trends suggested by the scale analysis. In order to analytically investigate certain limiting cases of unidirectional alloy solidification, a fully analytical solution technique is established for the solution of unidirectional, conduction-dominated, alloy solidification problems. The results are tested for the problem of solidification of an ammonium chloride-water solution, and are compared with those from existing analytical models as well as with the corresponding results from a fully numerical simulation. The effects of different microscopic models on solidification behaviour are illustrated, and transients in temperature and heat flux distribution are also analysed. An excellent agreement between the present solutions and results from the computational simulation can be observed. The generalised numerical model is subsequently utilised to investigate the effects of laminar double-diffusive Rayleigh-Benard convection on directional solidification of binary fluids, when cooled and solidified from the top. A series of experiments is also performed with ammonium chloride-water solutions of hypoeutectic and hypereutectic composition, so as to facilitate comparisons with numerical predictions. While excellent agreements can be obtained for the first case, the second case results in a peculiar situation, where crystals nucleated on the inner roof of the cavity start descending through the bulk fluid, and finally settle down at the bottom of the cavity in the form of a sedimented solid layer. An eutectic solidification front subsequently progresses from the top surface vertically downwards, and eventually meets the heap of solid crystals collected on the floor of the cavity. However, comparison of experimental observations with corresponding numerical results from the present model is not possible under this situation, since the associated transport process involves a complex combination of a number of closely interconnected physical mechanisms, many of which are yet to be resolved. Subsequent to the development of the mathematical model and experimental arrangements for macroscopic transport processes during an alloy solidification process, some of the important modes of double-diffusive instability are analytically investigated, as a binary alloy of any specified initial composition is directionally solidified from the top. By employing a close-formed solution technique, the critical liquid layer heights corresponding to the onset of direct mode of instability are identified, corresponding two a binary alloy with three different initial compositions. In order to simulate turbulent transport during non-equilibrium solidification processes of binary alloys, a modified k-8 model is subsequently developed. Particular emphasis is given for appropriate modelling of turbulence parameters, so that the model merges with single-phase turbulence closure equations in the pure liquid region in a smooth manner. Laboratory experiments are performed using an ammonium chloride-water solution that is solidified by cooling from the top of a rectangular cavity. A good agreement between numerical and experimental results is observed. Finally, in order to study the effects of three-dimensionality in fluid flow on overall macrosegregation behaviour, the interaction between double-diffusive convection and non-equilibrium solidification of a binary mixture in a cubic enclosure (cooled from a side) is numerically investigated using a three-dimensional transient mathematical model. Investigations are carried out for two separate model systems, one corresponding to a typical metal-ally analogue system and other corresponding to an actual metal-alloy system. As a result of three-dimensional convective flow-patterns, a significant solute macrosegregation is observed in the transverse sections of the cavity, which cannot be captured by two-dimensional simulations.

Multiphase transport phenomena primarily encompass the fundamental principles and applications concerning the systems where overall dynamics are precept by phase change evolution. On the other hand, multiscale transport phenomena essentially corroborate to a domain where the transport characteristics often contain components at disparate scales. Relevant examples as appropriate to multiphase and multiscale thermofluidic transport phenomena comprise solid-liquid phase change during conventional solidification process and hydrodynamics through narrow confinements. The additional effect of superimposed magnetic field over such multiphase and multiscale systems may give rise to intriguing transport characteristics, significantly unique in nature as compared to flows without it. The present investigation focuses on multiphase, multi-scale transport phenomena in physical systems subjected to the superimposed magnetic field, considering four important and inter-linked aspects. To begin with, for a multiphase system concerning binary alloy solidification, a normal mode linear stability analysis has been carried out to investigate stationary and oscillatory convective stability in the mushy layer in the presence of external magnetic field. The stability results indicate that the critical Rayleigh number for stationary convection shows a linear relationship with increasing Ham (mush Hartmann number). Magnetohydrodynamic effect imparts a stabilizing influence during stationary convection. In comparison to that of stationary convective mode, the oscillatory mode appears to be critically susceptible at higher values of  (a function of the Stefan number and concentration ratio), and vice versa for lower  values. Analogous to the behaviour for stationary convection, the magnetic field also offers a stabilizing effect in oscillatory convection and thus influences global stability of the mushy layer. Increasing magnetic strength shows reduction in the wavenumber and in the number of rolls formed in the mushy layer. In multiscale paradigm, the combined electroosmotic and pressure-driven transport through narrow confinements have been firstly analyzed with an effect of spatially varying non–uniform magnetic field. It has been found that a confluence of the steric interactions with the degree of wall charging (zeta potential) may result in heat transfer enhancement, and overall reduction in entropy generation of the system under appropriate conditions. In particular, it is revealed that a judicious selection of spatially varying magnetic field strength may lead to an augmentation in the heat transfer rate. It is also inferred that incorporating non–uniformity in distribution of the applied magnetic field translates the system to be dominated by the heat transfer irreversibility. Proceeding further, a semi-analytical investigation has been carried out considering implications of magnetohydrodynamic forces and interfacial slip on the heat transfer characteristics of streaming potential mediated flow in narrow fluidic confinements. An augmentation in the streaming potential field as attributable to the wall slip activated enhanced electromagnetohydrodynamic transport of the ionic species within the EDL has been found. Furthermore, the implications of Stern layer conductivity and magnetohydrodynamic influence on system irreversibility have been shown through analysis of entropy generation due to fluid friction and heat transfer. The results being obtained in this analysis have significant scientific and technological consequences in the context of novel design of future generation energy efficient devices, and can be useful in the further advancement of theory, simulation, and experimental work. Finally, the combined consequences of interfacial electrokinetics, rheology, and superimposed magnetic field subjected to a non-Newtonian (power-law obeying) fluid in a narrow confinement are studied in this work. The theoretical results demonstrate that the applied magnetic field imparts a retarding influence in the induced streaming potential development, whereas, triggers the heat transfer magnitude. Moreover, additional influences of power law index show reduction in heat transfer as well as the streaming potential magnitude. It is unveiled that the optimal combinations of power law index and the magnetic field lead to the minimization of the global total entropy generation in the system.