During solidification of non-eutectic alloys, non-isothermal phase change causes dendritic growth of solid front with liquid phase entrapped within the dendritic network producing the mushy region. Solidification causes rejection of solute at the solid-liquid interface and within the mushy zone, causing a sharp concentration gradient to build up across the mushy region. At the same time, a temperature gradient is present as a result of externally imposed boundary conditions as well as due to evolution of latent heat, giving rise to the so-called “double-diffusive” or thermo-solutal convection. Depending on the relative density of the solute being rejected in the liquid phase during solidification process, thermal and solutal buoyancy can either aid or oppose each other. Rejection of a heavier solute leads to aiding thermo-solutal convection situation whereas the rejection of lighter solute causes the thermal and solutal buoyancy to oppose each other. If the thermal and solutal buoyancies oppose each other, flow instability arises adjacent to the mush-bulk liquid interface regions. Thus, there may be a wide variety of convection situations present in the solidifying domain for different combinations of solution concentrations and externally imposed boundary conditions. The situation becomes even more complex if the solid phase movement along with the bulk flow is involved in the process, leading to multiphase convection. Detachment of solid phase from the solid/liquid interface can be caused by remelting (solutal and/or thermal) and shearing action of a convecting liquid adjacent to the interface. Depending on the drag of the bulk flow and the density of the solid phase relative to that of the bulk liquid, these detached particles can either float or sediment. The redistribution of the rejected solute by means of diffusion (at a local scale) and thermo-solutal convection (at system level length scales) causes heterogeneous orientation of mixture constituents over the solidifying domain popularly known as macro-segregation. From the point of view of manufacturing, severe form of macro-segregation or heterogeneous species distribution is an undesirable phenomenon and hence, a thorough understanding of the species redistribution by means of diffusion and convection during solidification process is very important. Most of the earlier studies on double diffusive convection during solidification involved fixed dendrites. However, the advection of solid particles during the solidification process can generate major instability in the flow pattern while modifying the solid front growth, and hence the macro-segregation pattern considerably. With this viewpoint in mind, the overall objective of the present work is to address these wide-varieties of single phase and multi phase flow situations and their effect on solid front growth and macro-segregation during directional solidification of non-eutectic binary alloys, numerically as well as experimentally. Different configurations of directional solidification processes involving double diffusive convection have been studied for two different kinds of non-eutectic solutions. While solidification of hypoeutectic solutions leads to aiding type double diffusive convection, the solidification of hyper-eutectic solutions is characterized by opposing type double diffusive convection. Solidification of hypo-eutectic solution generally involves single phase flow, while most of the hyper-eutectic solidification involves movement of solid phase (i.e. multiphase flow). As far as the modeling part is concerned, transport phenomena during solidification with multiphase convection are not common in existing literature. This work is a first attempt to develop a solidification model with multiphase flow based entirely on macroscopic parameters. As a first step, a generalized macroscopic framework has been developed for mathematical modeling of multiphase flow during solidification of binary alloy systems. The complete set of equivalent single-domain governing equations (mass, momentum, energy and species conservation) are coupled with the phase (solid and liquid) velocities. A generalized algorithm has been developed to determine solid detachment and solid advection phenomena, based on two critical parameters, namely: critical solid fraction and critical velocity. While the first of these two parameters (critical solid fraction) represents the strength of the dendritic bond, the second (critical velocity) stands for the intensity of flow to create drag force and solutal remelting at the dendrite roots. A new approach for evaluating liquid/solid fraction by using fixed grid enthalpy updating scheme, that accounts for multiphase flow and, at the same time, handles equilibrium and non equilibrium solidification mechanisms, has been proposed. The newly developed model has been validated with existing literatures as well as with experimental observations performed in the present work. The experimental results were obtained by using PIV as well as laser scattering techniques. Side cooled as well as top cooled configurations are studied. Single phase convection is observed for the case of hypo-eutectic solution, whereas hyper-eutectic solutions involve convection with movement of solid phase. For the case of bottom cooled hyper-eutectic solution, finger-like convection leading to freckle formation is observed. For all the hyper-eutectic cases, solid phase movement is found to alter the convection pattern and final macrosegregation significantly. The numerical results are compared with experimental observations both qualitatively as well as quantitatively.

The problem of laminar and turbulent conjugate mixed convection flow and heat transfer in shallow enclosures with a series of block-like heat generating components is studied numerically for a Reynolds number range of zero (pure natural convection) to typically 106, Grashof number range of zero (pure forced convection) to 1015 and various block-to-fluid thermal conductivity ratios, with air as the working medium. The shallow enclosure has modules consisting of heat generating elements, air admission and exhaust slots. Two problems are considered. In the first problem, the enclosure has free boundaries between the modules and in the second problem, there are partitioning walls between the different modules. The flow and temperature distributions are taken to be two-dimensional. Regions with the same velocity and temperature distributions can be identified assuming repeated placement of the blocks and fluid entry and exit openings at regular distances, neglecting end wall effects. One half of such rectangular region is chosen as the computational domain taking into account the symmetry about the vertical centreline. On the basis of the assumption that mixed convection flow is a superposition of forced convection flow with finite pressure drop and a natural convection flow with negligible pressure drop, the individual flow components are delineated. The Reynolds number is based on forced convection velocity, which can be determined in practice from the fan characteristics. This is believed to be more meaningful unlike the frequently used total velocity based Reynolds number, which does not vanish even in pure natural convection and which makes the fan selection difficult. Present analysis uses three models of turbulence, namely, standard k-ε (referred to as Model-1), low Reynolds number k-ε (referred to as Model-2) and an SGS kinetic energy based one equation model (referred to as Model-3). Results are obtained for aiding and opposing mixed convection, considering also the pure natural and pure forced convection limiting cases. The results show that higher Reynolds numbers tend to create a recirculation region of increasing strength at the core region and that the ranges of Reynolds number beyond which the effect of buoyancy becomes insignificant are identified. For instance, in laminar aiding mixed convection, the buoyancy effects become insignificant beyond a Reynolds number of 500. Results are presented for a number of quantities of interest such as the flow and temperature distributions, local and average Nusselt numbers and the maximum dimensionless temperature in the block. Correlations are constructed from the computed results for the maximum dimensionless temperature, pressure drop across the enclosure and the Nusselt numbers.