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Register a new userA mathematical Study of Magnetohydrodynamic Casson Fluid via Special Functions with Heat and Mass Transfer embedded in Porous Plate
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This article is proposed to investigate the impacts of heat and mass transfer in magnetohydrodynamic casson fluid embedded in porous medium. The generalized solutions have been traced out for the temperature distribution, mass concentration and velocity profiles under the existence and non-existence of transverse magnetic field, permeability and porosity. The corresponding solutions of temperature distribution and mass concentration, velocity profiles are expressed in terms of newly defined generalized Robotnov-Hartley function, wright function and Mittage-Leffler function respectively. All the corresponding solutions fulfill necessary conditions (initial, natural and boundary conditions) as well. Caputo Fractionalized solutions have been converted for ordinary solutions by substituting {zeta}=1. Some similar solutions for the temperature distribution, mass concentration and velocity profiles have been particularized form generalized solutions. Owing to the rheology of problem, graphical illustrations of distinct parameters are discussed in detail by depicting figures using Mathcad software (15).
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Immiscible fluid displacement in porous media is fundamental for many environmental processes, including infiltration of water in soils, groundwater remediation, enhanced recovery of hydrocarbons and carbon geosequestration. Microstructural heterogeneity, in particular of particle sizes, can significantly impact immiscible displacement. For instance, it may lead to unstable flow and preferential displacement patterns. We present a systematic, quantitative pore-scale study of the impact of spatial correlations in particle sizes on the drainage of a partially-wetting fluid. We perform pore-network simulations with varying flow rates and different degrees of spatial correlation, complemented with microfluidic experiments. Simulated and experimental displacement patterns show that spatial correlation leads to more preferential invasion, with reduced trapping of the defending fluid, especially at low flow rates. Numerically, we find that increasing the correlation length reduces the fluid-fluid interfacial area and the trapping of the defending fluid, and increases the invasion pattern asymmetry and selectivity. Our experiments, conducted for low capillary numbers, support these findings. Our results delineate the significant effect of spatial correlations on fluid displacement in porous media, of relevance to a wide range of natural and engineered processes.
The surface texture of materials plays a critical role in wettability, turbulence and transport phenomena. In order to design surfaces for these applications, it is desirable to characterise non-smooth and porous materials by their ability to exchange mass and momentum with flowing fluids. While the underlying physics of the tangential (slip) velocity at a fluid-solid interface is well understood, the importance and treatment of normal (transpiration) velocity and normal stress is unclear. We show that, when slip velocity varies at an interface above the texture, a non-zero transpiration velocity arises from mass conservation. The ability of a given surface texture to accommodate for a normal velocity of this kind is quantified by a transpiration length. We further demonstrate that normal momentum transfer gives rise to a pressure jump. For a porous material, the pressure jump can be characterised by so called resistance coefficients. By solving five Stokes problems, the introduced measures of slip, transpiration and resistance can be determined for any anisotropic non-smooth surface consisting of regularly repeating geometric patterns. The proposed conditions are a subset of effective boundary conditions derived from formal multi-scale expansion. We validate and demonstrate the physical significance of the effective conditions on two canonical problems -- a lid-driven cavity and a turbulent channel flow, both with non-smooth bottom surfaces.
We numerically study the Rayleigh-Benard (RB) convection in two-dimensional model emulsions confined between two parallel walls at fixed temperatures. The systems under study are heterogeneous, with finite-size droplets dispersed in a continuous phase. The droplet concentration is chosen to explore the convective heat transfer of both Newtonian (low droplet concentration) and non-Newtonian (high droplet concentration) emulsions, the latter exhibiting shear-thinning rheology, with a noticeable increase of viscosity at low shear rates. It is well known that the transition to convection of a homogeneous Newtonian system is accompanied by the onset of steady flow and time-independent heat flux; in marked contrast, the heterogeneity of emulsions brings in an additional and previously unexplored phenomenology. As a matter of fact, when the droplet concentration increases, we observe that the heat transfer process is mediated by a non-steady flow, with neat heat-flux fluctuations, obeying a non-Gaussian statistics. The observed findings are ascribed to the emergence of space correlations among distant droplets, which we highlight via direct measurements of the droplets displacement and the characterisation of the associated correlation functions.
We develop a two-fluid model (TFM) for simulation of thermal transport coupled to particle migration in flows of non-Brownian suspensions. Specifically, we propose a closure relation for the inter-phase heat transfer coefficient of the TFM as a function of the particle volume fraction, particle diameter, magnitude of the particle phases shear-rate tensor, and the thermal diffusivity of the particles. The effect of shear-induced migration in the particulate phase is captured through the use of state-of-the-art rheological closures. We validate the proposed interphase heat transfer coupling by calibrating it against previous experiments in a Couette cell. We find that, when the shear rate is controlled by the rotation of the inner cylinder, the shear and thermal gradients aid each other to increase the particle migration when temperature difference between the inner and outer walls, $Delta T = T_mathrm{in} - T_mathrm{out} < 0$. Meanwhile, for $Delta T > 0$, the shear and thermal gradients oppose each other, resulting in diminished particle migration, and a more uniform distribution of the particulate phase across the gap. Within the TFM framework, we identify the origin and functional form of a thermo-rheological migration force that rationalizes our observations. We also investigate the interplay of shear and thermal gradients in the presence of recirculating regions in an eccentric Couette cell (with offset axis and rotating inner cylinder). Simulations reveal that the system Nusselt number increases with the eccentricity $E$ for $Delta T > 0$, but a maximum occurs for $Delta T < 0$ at $E = 0.4$. This observation is explained by showing that, for $E>0.4$ and $Delta T < 0$, significant flow recirculation enhances particle inhomogeneity, which in turn reduces heat transfer in the system (compared to $Delta T > 0$).
Direct Numerical Simulations are used to solve turbulent flow and heat transfer over a variety of rough walls in a channel. The wall geometries are exactly resolved in the simulations. The aim is to understand the effect of roughness morphology and its scaling on the augmentation of heat transfer relative to that of skin friction. A number of realistic rough surface maps obtained from the scanning of gas turbine blades and internal combustion engines as well as several artificially generated rough surfaces are examined. In the first part of the paper, effects of statistical surface properties, namely surface slope and roughness density, at constant roughness height are systematically investigated, and it is shown that Reynolds analogy factor (two times Stanton number divided by skin friction coefficient) varies meaningfully but moderately with the surface parameters except for the case with extremely low slope or density where the Reynolds analogy factor grows significantly and tends to that of a smooth wall. In the second part of the paper, the roughness height is varied (independently in both inner and outer units) while the geometrical similarity is maintained. Considering all the simulated cases, it is concluded that Reynolds analogy factor correlates fairly well with the equivalent sand roughness scaled in inner units and asymptotically tends to a plateau.
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