Computational Study of Magnetohydrodynamics-Based Heat and Mass Transfer Inside Enclosed Systems by Lattice Boltzmann Method

Abstract

Double diffusive convection (DDC) is a form of heat convection that occurs due to two different density gradients (temperature and concentration), which vary under the effect of gravity (Huppert and Turner, 1981). DDC is essential in understanding several systems. Thermal and concentration gradients diffuse with time (may be at the same or different rates), lowering the aptness to propel the convection and also spread these gradients further along the flow regions (Radko, 2013). This phenomenon can be noticed in several broad fields, such as oceanography (salt-fingers), geology (flow of magma), astrophysics (solarcorona), metallurgy (solidification, crystallography) (Huppert and Sparks, 1984). A practical example of DDC is in metallurgical industries. In particular, the solidification of two alloys in which the solute region brings to density difference in the liquid melt, which, jointly with the temperature gradient in the system, develops DDC phenomena (Verhaeghe et al., 2007). The interaction of DDC and the effect of the magnetic field has the potency to modify the fluid circulation, which may be relevant in many instances, like electromagnetic casting and other metal manufacturing processes, cooling of magnetic storage media or electronic devices under magnetic field, geothermal reservoirs, crystal growth, electromagnetic stirring, etc. These types of fluid convection are popularly known as Magneto hydrodynamic convection (Reddy and Murugesan, 2017; Sheikholeslami et al., 2013c; Borjini et al., 2005; Borhan Uddin et al., 2015; Tagawa et al., 2002). Moreover, magnetohydrodynamics (MHD) is the analysis of the interaction of the magnetic field with the electrically conducting fluids, such as plasma, liquid metals, salt water or electrolytes, etc., (Alcala et al., 2015; Manna and Biswas, 2021). The fundamental behind MHD is that the magnetic field induces currents in a moving conductive fluid, creating forces on the fluid and changing the magnetic field. MHD flow has seen an extensive range of applications in the modern past and has gained significant interest owing to geophysical and cosmic fluid dynamics (Hasanuzzaman et al., 2012; Gangawane, 2017a; Gangawane and Bharti, 2018).The application span of MHD for an electrically conducting fluid involves electrical power generation, astrophysical flows, solar power technology, and space vehicle re-entry (Gangawane and Bharti, 2018). Applying a magnetic field to convection processes plays a controlling factor in the convection by damping the flow and temperature oscillations in material manufacturing fields (Sheikholeslami et al., 2013a, 2014b). On the other side, natural convective heat transfer within the enclosure has received considerable attention because of its relevance in various applications, such as thermal insulation, cooling of nuclear reactors, solar panels, ventilation of houses, and petroleum reservoirs, cooling of electronic devices, etc., (Al-Balushi et al., 2019; Ostrach, 1972) more citations. In the last couple of decades, the lattice Boltzmann method (LBM) has evolved into an alternating and promising numerical tool for illustrating the transport processes in various systems and for single and multiphase flows. Rather than solving the mass, momentum, and energy equations, the LBM seeks a solution of the Boltzmann method. LBM was derived from Boolean variables based on lattice gas automata (LGA). The discrete particle kinetics utilizes lattice (space) and time in discretized form (Chen and Doolen, 1998; He and Luo, 1997a; Mohamad and Kuzmin, 2010). Mc Namara and Zanetti (1988) presented LBM to overwhelm the weaknesses of the lattice gas cellular automata (LGA). Whereas the conventional numerical tool depends on the discretization of continuum partial differential equations (e.g., Navier-Stokes energy equations, etc.), LBM is established on microscopic models and mesoscopic kinetic equations. In LBM, the fluid is replaced by the distribution functions of the discrete particles. The fundamental notion of LBM is to build the discrete models over the domain (based upon the Boltzmann equation). Such models encompass the essential physics of microscopic and mesoscopic processes. Lastly, the recovery of relevant macroscopic equations can be achieved by multi-scale Expansion (viz., Chapman-Enskog analysis). Advantages of LBM include simple algorithm, ease in implantation of boundary conditions, making it suitable for complex domain problems, ease in parallel computing, easy estimation of pressure term, etc., (Mohamad, 2011). The objective of the thesis is to explore the hydrodynamics and thermal characteristics in the enclosed systems (i.e., enclosure or cavity) due to DDC associated with MHD. The influence of the aspect ratio of blockage as well as the location of the blockage has been studied. The effect of flow pertinent parameters, such as Hartmann number, Rayleigh number, Prandtl number, Lewis number, and Buoyancy ratio on the convection characteristics, along with the geometric parameters, have been explored. The study was conducted for the general assumptions of steady-state, incompressible, laminar and two-dimensional flows. The simulations are conducted using an LBM solver. The robustness of the solver has been ascertained by a thorough numerical validation and ensuring proper lattice size. Three differen cases have been considered in this work. The first case study explores the combined influence of aspect ratio and blockage on DDC-MHD characteristics and entropy generation for sodium-Potassium alloy liquid metal in the rectangular cavity. The second case study explores the effect of different non-uniform boundary conditions on the MHD-DDC characteristics for similar pertinent parameters. And finally, the third case study explores the influence of different blockage locations at various separation distances from the bottom wall of the cavity for above mentioned hydrodynamic pertinent parameters. Out of this study, some important conclusion has been drawn. The formation of multi-cell flow within the cavity with the increase in the Ra and Le was seen. Moreover, the formation and elongation of vortex cells along either side of the block with the increase in AR was noticed. Higher crowding of temperature and concentration contour lines along the heated/highly concentrated block was noticed for N = 2 compared to N = 2 for a given Ra. The increase in Ra and AR promoted a higher mixing of thermally differential fluid layers. The increase in the Ha restricted the fluid circulation by convection and was also noticed from the contours. The increase in ar and AR enhanced the rate of heat and mass transfer. The augmentation of Ra enhances different irreversibilities. The intensity of increase was noticed to be higher for Sff . The maximum values of Sff were observed to be increasing with the aspect ratios of cavity and blockage. At the same time, the reverse was true for Sth and Sc. When Ra increased from 104 to 105, the STH and SC showed an increase by about 56% and 47%, respectively. The dominance of thermal and species transport irreversibility (Beavg > 0:5) in the cavity was noticed for AR = 2;N = 2. On the other hand, for AR = 4, the significance of flow friction irreversibility within the cavity was observed (Beavg _ 0:5). NuTotal and ShTotal showed an enhancement of about 22% and 21%, respectively, for the sinusoidal profile as compared to linear for AR = 2 of the enclosure. For AR = 4 with sinusoidal boundary treatment, NuTotal and ShTotal showed the augmentation of about 19% and 17% as compared to linear. The variation plots of Nu and Sh demonstrate that a higher; HMT rate was noticed in the sinusoidal boundary condition profile of the enclosure in comparison to the linear boundary condition profile of the enclosure. As the obstruction between the bottom wall of the blockage and the adiabatic bottom wall of the cavity increases, shear force occurs, and the buoyancy-driven flow decreases, which leads to the diminishment in the local HMT rate. When the rectangular block moves farther away from the bottom wall of the cavity (Sd = H=6 and H=4), the buoyancy-driven increases, which tends to the enhancement in the local HMT characteristics. At separation distance (Sd = H=4) higher HMT is observed. The overall HMT rate enhances within the cavity with the augmentation in N and Sd.