Mass transfer considerations during pulse plating

This work presents Direct Numerical Simulation of mass transfer from buoyancy-driven bubbles rising in a wall-confined vertical channel, through a multiple markers level-set method. The Navier-Stokes equations and mass transfer equation are discretized using a finite volume method on a collocated unstructured mesh, whereas a multiple markers approach is used to avoid the numerical coalescence of bubbles. This approach is based on a mass conservative level-set method. Furthermore, unstructured flux-limiter schemes are used to discretize the convective term of momentum equation, level-set advection equations, and mass transfer equation, to improve the stability of the solver in bubbly flows with high Reynolds number and high-density ratio. The level-set model is used to research the effect of bubble-bubble and bubble-wall interactions on the mass transfer from a bubble swarm rising in a vertical channel with a circular cross-section.

A multiphase model was developed to simulate heat and mass transfer during the baking process of flat bread (Sangak bread) by considering volume changes. In the proposed model, the equations of heat and mass transfer for liquid (water) and gas (vapor andCO2) phases were developed based onFourier's,Fick's andDarcy's laws, respectively. In addition, the effect of evaporation–condensation phenomenon was considered using the nonequilibrium relation of evaporation rate in the mass and heat transfer equations. The quantity of specific heat and density of each mesh was predicted using series and parallel models, and values of unknown parameters were estimated using the standard least square method. The nonlinear partial differential equations of the model were solved by using the finite element method byCOMSOLMultiphysics software. The changes in bread thickness were determined by ImageJsoftware. The model validation was also accomplished by comparing the predicted temperature and moisture content with the experimental results. The highR2and the low root mean squared error between experimental and predicted data confirmed the validity of the developed mathematical model.Practical ApplicationsThe uniformity of the product quality and the energy loss during the baking process has always been considered as a great challenge in the baking industry. In recent years, there has been increasing demand for minimally processed and near‐fresh quality products. To produce the part‐baked Sangak bread, the dough fully processes and baking occurs to at level in which, the texture properly forms and low color changes occur. Nowadays, it is essential to find methods based on equations, mathematical modeling and engineering principles to improve process control. In order to develop these models, the profound understanding of the procedures during the baking, particularly, mass and energy transfer are essential. Since, there are few researches on evaporation‐condensation and volume change in contact baking; it is important to understand its mechanism for exploiting this phenomenon in the food industries.

Numerical investigation of oxidation and dissolution behavior in the fuel cladding using MPS-CV method

Analysis of heat, mass and pressure transfer in starch based food systems

Effects of Pulse Plating on lithium electrodeposition, morphology and cycling efficiency

A mathematical model of simultaneous heat and moisture transfer is developed for convective drying of building material. A rectangular brick is considered for sample object. Finite-difference method with semi-implicit scheme is used for solving the transient governing heat and mass transfer equation. Convective boundary condition is used, as the product is exposed in hot air. The heat and mass transfer equations are coupled through diffusion coefficient which is assumed as the function of temperature of the product. Set of algebraic equations are generated through space and time discretization. The discretized algebraic equations are solved by Gauss–Siedel method via iteration. Grid and time independent studies are performed for finding the optimum number of nodal points and time steps respectively. A MATLAB computer code is developed to solve the heat and mass transfer equations simultaneously. Transient heat and mass transfer simulations are performed to find the temperature and moisture distribution inside the brick.

The role of the diffuse double layer in leaching of calcium from the surface of flyash particles

Concentration gradient driven mixed convective flow in a horizontal rectangular enclosure with concentrated top wall is studied in this work. The continuity, momentum and mass transfer equations are discretized by using the hybrid finite volume method. The innovative thought in this work is to examine the sole effect of the concentration gradient on the mass transfer between the top wall and the fluid within the horizontal rectangular enclosure. The dimensionless parameters such as the Reynolds number (Re), the Schmidt number (Sc) are appropriately chosen to calculate the Richardson numbers (Ri) for specific fluids such as ammonia gas (Sc = 0.78) and methanol liquid (Sc = 556) at low (Re = 25) and high (Re = 25000) Reynolds numbers at different mass transfer Rayleigh numbers (Ram,L) in the range of 3x105 < Ram,L) < 7x109. In accordance with these calculated Richardson numbers revealed as Ri>>1 and Ri<<1 respectively, it is found that pure and negligible free convection effects prevails between the top wall and the fluid within the horizontal rectangle. When Ri~1 mixed convection results between the top wall to these fluids within the horizontal rectangle. A novel empirical correlation for calculating the average Sherwood numbers (Sh) for specific fluids at different mass transfer Rayleigh numbers as mentioned above is suggested in this research and thereby the mass transfer from the top wall to these fluids within the horizontal rectangle is examined and validated. Since this correlation is novel in nature, the conclusions regarding the mass transfer from the top wall to these fluids within the horizontal rectangle justified and comparison or improvement over the existing correlations is unnecessary. It is found that for all the boundary values of the mass transfer Rayleigh number, there is a substantial increase in the average Sherwood numbers Sh and hence the mass transfer from the top wall to the fluid (ammonia gas or methanol liquid) substantially increases within the horizontal rectangle.

Reverse pulse electrodeposition of Zn–Ni alloys from a chloride bath

In the study of multi-component mass transfer it is common to use the film model, in which all the resistance to mass transfer towards a catalytic surface is assumed to be localized in a diffusion layer in front of the surface. At the surface one furthermore assumes that the temperature and chemical potentials are continuous, while the coupling of a possible heat flux to the mass fluxes is assumed to be negligible. Both these assumptions are questionable. Using nonequilibrium thermodynamics we discuss how to integrate the coupling between heat and mass fluxes in the description of the film. Furthermore, following Gibbs, we introduce the surface as a separate thermodynamic system where the coupling between the vectorial heat flux and the scalar reaction rate is allowed and can be significant in heterogeneous catalysis. Non-equilibrium thermodynamic theory for surfaces allows one to find the proper rate equations. It allows for a consistent and complete description of mass and heat transfer through the film and subsequently from the film to the surface where the reaction takes place. Fast endo- or exothermic surface reactions in heterogeneous catalysis may give significant temperature gradients between a catalyst surface and the media, which will, when not accounted for, lead to an incorrect evaluation of the activity, stability and selectivity of a catalyst. Non-equilibrium thermodynamics is a useful tool for predicting the surface temperature as well as for analyzing the system. In this contribution we sketch how to systematically set up the complete description, in which the film and the surface "sum up" to one effective surface.

Analysis of the effect of particle size and residence time distributions on heat or mass transfer with linear source in particulate systems

The effect of axialacoustic Ž elds on the evaporationof individualdroplets is investigatedboth experimentallyand theoretically. A setup was developed in which images of droplets moving through an acoustic Ž eld were acquired using a state-of-the-art, high-speed, intensiŽ ed video system. The evaporation rates of droplets were determined from the droplet diameters measured from these images. Experimental investigations using methanol droplets showed that the presence of an acoustic Ž eld signiŽ cantly enhances the evaporation of droplets. The evaporation rate is a strong function of the acoustic amplitude, but increases only slightlywith frequency. The effect of acoustic oscillations on water and methanol droplet evaporation was theoretically modeled by numerically integrating the differential equations for droplet mass, momentum,and heat transfer. The model uses quasisteady correlations for momentumheat and mass transfer. The model predicted the measured trends correctly. However, the quantitative agreement of these predictions with the experimental data depends strongly on the correlations for Nussult and Sherwood numbers used to model the energy and mass transfer, respectively.

Mass transfer of dissolved oxygen (DO) across a sediment–water interface was investigated using laboratory experiments and a numerical simulation model. DO concentration profiles and velocity profiles were measured with high resolution in a recirculating flume with water flowing at cross-sectional average velocities from 3.5 to 11.5 cm/s over a flat and hydrodynamically smooth organic sediment bed. Parameters extracted from the measurements included (1) the DO penetration depth, (2) the effective diffusion coefficient in the sediment layer, (3) the thickness of the turbulent diffusive boundary layer, and (4) the diffusion coefficients in the diffusive boundary layer. DO penetration depths were less than 1 mm, and diffusive boundary layer thicknesses were less than 8 mm. Diffusion in the sediment porewater system was shown to be essentially molecular. The laboratory data were compared to results from a deterministic simulation model. The model included explicit descriptions of (1) mass transfer through the diffusive boundary layer above the sediment/water interface, (2) the boundary layer development over the sediment bed of finite length, (3) diffusive transfer in the sediment porewater system, and (4) microbial uptake of DO in the sediment. The model included both water-side and sediment-side mass transport limitations. The control of DO flux could alternate between water-side and sediment-side without discontinuity. Monod-type kinetics was adopted for DO uptake in the sediment. Organic substrate availability in the sediment did not vary over the course of an experiment. A kinetic limitation for organic matter (substrate) was not considered, and microbial activity in the sediment was parameterized by biomass density. Measured and simulated DO concentration profiles showed satisfactory agreement, with some discrepancies at the interface caused by roughness and porosity effects of the sediment surface.

Heat and mass transfer to blood flowing through a tapered overlapping stenosed artery

This study presents an extended fractional-order mathematical model for blood flow through a stenosed artery under the combined effects of a magnetic field, porous medium, chemical reaction, and nanoparticle diffusion. The study aims to provide a more accurate and physiologically relevant representation of nanoparticle transport in pathological arterial flow conditions. The governing nonlinear equations for momentum and mass transfer were formulated and solved using a semi-analytical approach involving modified Bessel and Mittag–Leffler functions. Model validation through comparison with existing results showed excellent agreement, confirming the reliability of the proposed formulation. The parametric analysis revealed that increasing the chemical reaction parameter and Schmidt number reduced nanoparticle concentration, whereas a higher fractional order enhanced mass transport by weakening memory effects. The study concludes that the fractional-order framework offers an improved description of nanoparticle transport in stenosed arterial blood flow and contributes to the advancement of mathematical modeling for physiologically realistic hemodynamic analysis.