Unsteady mass transfer from/to a drop accompanied by a reversible second-order chemical reaction on the surface of the drop

Unsteady mass transfer between a drop and a surrounding fluid flow with reversible second-order chemical reaction on the surface of the drop has been analysed. The dispersed phase reactant and product are insoluble in the continuous phase. The continuous phase reactant and product are insoluble in the dispersed phase. Creeping flow in both phases was assumed. The mass balance equations were solved numerically in spherical coordinates system by a finite difference nonlinear multigrid method. For moderate Pe numbers (Pe1000), the computations focused on the influence of the chemical reaction on the mass transfer rates in both phases and on the chemical composition on the surface of the drop.     

The effect of surface mass transfer on buoyancy-induced darcian flow adjacent to a horizontal heated surface

The effect of uniform surface mass transfer on the buoyancy-induced flow in a porous medium adjacent to a horizontal heated surface with a power law variation of wall temperature, T_wαx^λ, is considered in this paper. It is found that a similarity solution exists for the problem when $\text{λ = 2}$. Approximate solutions based on the local nonsimilarity method are obtained for other values of λ. Numerical solutions were carried out up to the third-level of truncation and results are presented for a wide range of massflux parameter and wall temperature distributions.     

Pressure drop and point mass transfer in a rectangular microchannel

This paper describes the pressure drop and local mass transfer in a rectangular microchannel having a width of 3.70 mm, height of 0.107 mm and length of 35 mm. The pressure measurements were carried out with distilled water as working fluid at Reynolds numbers in the range of 100–845, while mass transfer measurements with a chemical solution at Reynolds numbers in the range of 18–552 by using the electrochemical limiting diffusion current technique (ELDCT). Experimental friction factors were slightly higher than those calculated by theoretical correlation. The Sherwood number correlation was also obtained.     

Conjugate mass transfer to a spherical drop accompanied by a second-order chemical reaction inside the drop

Conjugate mass transfer between a drop and a surrounding fluid flow with second-order (inclusive the particular case - pseudo-first-order), irreversible chemical reaction in the dispersed phase has been analyzed. The dispersed phase reactant is insoluble in the continuous phase and its complete depletion is allowed. Two sphere models were considered: the rigid sphere and the fluid sphere with internal circulation. For each sphere model two hydrodynamic regimes were employed: creeping flow and moderate Re numbers. Slow and fast chemical reactions were analyzed. A single, constant value was considered for Pe, Pe=100. The influence of the diffusivity ratio on the particle average concentrations, total mass transferred and enhancement factor is studied. The values obtained for the enhancement factor of the pseudo-first-order chemical reaction are compared with solutions provided by published predictive equations. The chemical reaction enhances the mass transfer rate even for values of the modified Hatta modulus smaller or considerably smaller than one. For the flow patterns and sphere models considered in this work, the enhancement factor is independent on hydrodynamics.     

Free convection effect on mhd coupled heat and mass transfer of a moving permeable vertical surface

The purpose of this paper is to consider numerically the free convection effect on magnetohydrodynamic heat and mass transfer of a continuously moving permeable vertical surface. The surface is maintained at linear temperature and concentration variations. The similar equations were solved by using a suitable variable transformation and employing an implicit finite difference method. Numerical results were graphically given for the Nusselt number and the Sherwood number for various parameters. Generally, it is found that the Nusselt number and the Sherwood number increase for the suction case, increasing the buoyancy ratio N and the buoyancy parameter Gr_T/Re² and for the decrease of magnetic parameter M. Furthermore, the Nusselt (Sherwood) number increases for the decrease (increase) of Schmidt number Sc.     

Heat/mass transfer from a drop translating in steady and time-periodic electric fields: External problem

Enhancement of heat or mass transport from a spherical drop of a dielectric fluid translating in another dielectric fluid in the presence of steady and time periodic electric fields (both uniform and non-uniform) is investigated in this paper. The external problem or the limit of the majority of the transport resistance being in the continuous phase is considered. Using a finite volume formulation, the transient energy (species) conservation equation is solved for Peclet numbers (Pe) varying from 10 to 1000 and dimensionless electric field frequency (ω¹) from 10 to 50,000 using a fully implicit method. To map the infinite domain in the radial direction, an exponential transformation is employed that provides a fine grid spacing near the drop surface where sharp variations are expected and a coarser grid in the far field where low gradients prevail. The transient temperature distribution and the local and the average Nusselt numbers are obtained and the heat/mass transfer enhancement due to the application of electric field is determined. The effect of electric field is expressed in terms of L, the ratio of the maximum electric-field-induced surface velocity to the translation-induced surface velocity. For the steady and time-periodic electric fields, the heat transfer enhancement increases monotonically with Pe and with L. Also, the heat transport rate is higher when the continuous phase is more viscous compared to the dispersed phase. The steady uniform electric field gives the highest average Nusselt number for heat transfer from the drop surface to the continuous phase, followed by the non-uniform time periodic electric field and then the time periodic uniform electric field. The enhancement relative to pure translation exhibits a non-monotonic dependence on electric field frequency but the highest value is obtained at ω¹ = 0. Earlier studies have shown that there is significant enhancement in the heat/mass transfer in the drop interior with a time periodic electric field compared to a steady uniform electric field when the majority of the transport resistance is in the drop. The results presented here show that an opposite behavior is obtained in the drop exterior, i.e. a steady electric field provides higher heat/mass transfer enhancement compared to a time periodic electric field, when the bulk of the transport resistance is in the continuous phase. Therefore whether the steady or the time periodic electric field provides the most enhancement of heat/mass transfer for a conjugate problem will depend on the relative transport resistance in the two phases.     

Transient heat and mass transfer in a drop experiencing absorption with internal circulation

Transient heat and mass transfer associated with a moving liquid during absorption was numerically studied in this work. The roles played by the internal circulation inside the droplet and the exorthermic heat effect were demonstrated. The numerical results reveal that the significant absorption enhancement by internal circulation becomes neglible with the increase of exothermic absorption heat. The highly exotermic system of , which is used as a typical refrigerant/absorbent combination in commercial absorption heat pump (AHP), was selected as an example to illustrate this point.     

The effect of heat transfer on the pressure drop through a heat exchanger for aero engine applications

This work is focused on the experimental study of the performance of a heat exchanger designed for aero engine applications. The heat exchanger is operating as a heat recuperator by taking advantage of the thermal energy of the exhaust gas of the aero engine in order to obtain a better combustion with less pollutant emissions. The experimental study has been performed in a wind-tunnel by taking detailed flow and thermal measurements on a 1:1 model of the heat exchanger under various operating conditions described by the hot gas inlet mass flow rates and its spatial direction (different angles of attack and inclination) towards the heat exchanger. The hot gas has been modeled with preheated air. Six sets of measurements have been carried-out for different hot gas inlet and outlet temperatures, including also isothermal measurements without any heat transfer in order to have a reference point for the pressure drop of the flow through the device. The experimental results showed that the effect of the angle of attack on the pressure drop is significant while the effect of the angle of inclination is negligible. Additionally, the pressure drop through the heat exchanger is greatly affected by the heat transfer.     

Heat or mass transfer from a moving drop — Some approximate relations for the Nusselt number

The external problem of heat/mass transfer for a steadily moving surfactant-free spherical drop is considered. Simple approximate relations for the maximum velocity at the surface of the drop and the Nusselt (Sherwood) number are derived on the basis of the boundary-layer-type estimates. The relations contain adjustable 0(1) numerical factors, which are chosen so as to give the best fit to the results of the previously obtained accurate numerical solutions of the Navier-Stokes and convective-diffusion equations for Re ≤ 200 and Pe ≤ 1000. It is also indicated how the knowledge of the maximum surface velocity allows one to reduce the problem to the well-documented case or low Reynolds number.     

Evaporation of a volatile-liquid lens floating on the surface of a stagnant immiscible liquid

The paper presents experimental results of evaporation of isolated lenses on n-pentane or R 113 (C₂C?₃F₃) at a horizontal interface between a hot water and the common vapors of the two fluid substances. n-Pentane lenses often became unstable and even split into smaller lenses during evaporation process, while R 113 lenses were always stable. Corresponding to this fact, the evaporation rate of n-pentane lenses was typically 10 times higher than that of R 113 lenses under the same temperature driving force. A variation in the water layer thickness exhibited no appreciable effect on the evaporation rate. These findings indicate that the primary factor for enhancing the heat transfer from the water to lenses is such an interfacial turbulence, with an unidentified mechanism, as to give lenses the unstable behavior rather than a buoyancy-driven convection in the water bulk.     

Endwall effect on the mass transfer in a square open cavity

In a lid-driven flow over a square open cavity with confined endwalls, a naphthalene sublimation technique was employed to measure the local mass transfer rates over the bottom surface of the cavity for the Reynolds numbers ranging from 2,000 to 4,000. The tested cavity has a span-to-width ratio (SAR) of 8 and a width-to-depth ratio (AR) of 1. The measured results are compared with predictions based on a deterministic vortex method with the assumption of two-dimensional cavity flow. The numerical results indicate an increase in mass transfer rate on the bottom surface of the cavity with an increase in the Reynolds number. The experimental results show the similar trend in the mass transfer rate with the presence of endwalls. In addition, a large variation in the spanwise direction of the measured local mass transfer rates implies the existence of Taylor-Görtler-like (TGL) vortices in the cavity. Furthermore, a correlation is derived between the measured overall averaged Sherwood number and the Reynolds number.     

Evaporative heat and mass transfer from the free surface of a liquid wicked into a bed of spheres

Evaporation of ethanol from square packed arrays of 3.95 mm diameter copper spheres in a transparent, enclosed chamber is investigated. The enclosure ensures that relatively saturated vapor conditions exist near the free surface. The desired heat flux is imposed on the copper substrate upon which the copper spheres are mounted, and the liquid level in the bed is maintained by wicking from a continuous supply of liquid provided by a syringe pump. Transparent windows in the enclosure allow for visualization of the evaporating liquid meniscus shape, which is recorded for different liquid feeding rates and heat fluxes. Experimentally measured meniscus profiles are compared to analytical results based on surface-energy minimization. A meniscus microregion is defined from the contact line to the length where the liquid thickness reaches 10 μm. An approximate kinetic theory-based analysis estimates that up to ～55% of the total meniscus mass transfer occurs in this microregion.     

Natural convection heat and mass transfer along a vertical wavy surface

A numerical study of natural convection heat and mass transfer along a vertical wavy surface has been performed. The wavy surface is maintained at uniform wall temperature and constant wall concentration. A simple coordinate transformation is employed to transform the complex wavy surface to a flat plate. A marching finite-difference scheme is used for the analysis. The buoyancy ratio N, amplitude-wavelength ratio α, and Schmidt number Sc are important parameters for this problem. The numerical results, including the developments of skin-friction coefficient, velocity, temperature, concentration, Nusselt number as well as Sherwood number along the wavy surfaces are presented. The effects of the buoyancy ratio N and the dimensionless amplitude of wavy surface on the local Nusselt number and the local Sherwood number have been examined in detail.     

Mixed convection heat and mass transfer along a vertical wavy surface

A numerical study of mixed convection heat and mass transfer along a vertical wavy surface has been carried out numerically. The wavy surface is maintained at uniform wall temperature and constant wall concentration that is higher than that of the ambient. A simple coordinate transformation is employed to transform the complex wavy surface to a flat plate. A marching finite-difference scheme is used for present analysis. The buoyancy ratio N, amplitude-wavelength ratio α, and Richardson number (Gr/Re²) are important parameters for this problem. The numerical results, including the developments of skin-friction coefficient, velocity, temperature, concentration, Nusselt number as well as Sherwood number along the wavy surface are presented. The effects of the buoyancy ratio N and the dimensionless amplitude of wavy surface on the local Nusselt number and the local Sherwood number have been examined in detail.     

Experimental study of laminar forced convective mass transfer and pressure drop in microtubes

The investigation of laminar convective mass transfer and friction factor was performed experimentally for the circular tubes with the diameter of 0.20 mm and the L/d values in the range of 100–500 for a Reynolds number range of 40–1400. The pressure drop experiments were conducted with distilled water, and the mass transfer experiments were carried out with an electrochemical solution by using the electrochemical limiting diffusion current technique. The friction factor results showed good agreement with the classical Poiseuille flow theory, while Sherwood numbers are smaller than those obtained by conventional correlations.     

Resident time of a compound drop impinging on a hot surface

The resident time of a water-in-diesel compound drop impinging on a hot surface at a temperature higher than the Leidenfrost temperature was investigated experimentally. Past experimental evidence suggested that the resident time of a pure liquid drop was independent of the impact velocity. And this independency could also be seen for compound drops. For both pure drops and compound drops, the resident time became longer with increasing outer diameter of the drop. For water-in-diesel compound drops of a given outer diameter, the resident time decreased as the volume of the core water drop increased. By using a modified Weber number which took into account of the two interfaces of the compound drop, a correlation of the non-dimensional resident time was obtained and was in good agreement with the experimental data.     

Steady and time-periodic electric field-driven enhancement of heat or mass transfer to a drop: Internal problem

Transient heat or mass transfer to a spherical drop of a dielectric fluid suspended in another dielectric fluid in the presence of steady and time periodic electric fields (both uniform and non-uniform) is investigated in this paper. The internal problem or the heat (mass) transfer limit that corresponds to the bulk of the resistance being in the dispersed phase is addressed. Using a finite volume formulation, the energy conservation equation is solved to obtain the transient temperature distribution and the overall Nusselt number for the drop Peclet numbers from 0 to 10,000 and the dimensionless frequency (ω¹) from 0 to 50,000 using a fully implicit method. Application of steady and time-periodic fields leads to fluid circulation in the drop which provides an increase in the heat (mass) transfer rate. At first glance one might expect that the time-periodic field, which gives rise to a continuously varying flow field, might provide better mixing and improved heat (mass) transfer enhancement compared to time invariant one which gives rise to a steady flow field. However results show that for low to moderate Peclet numbers, the steady electric field is more effective in heat transfer enhancement compared to non-uniform time periodic field which in turn is more effective than the uniform time-periodic field. This counterintuitive heat (mass) transfer behavior is explained in detail in the paper. On the other hand, at high Peclet numbers, the non-uniform time periodic field provides significant improvement in heat (mass) transfer relative to steady uniform electric field. We show that at high Peclet numbers the maximum heat (mass) transfer enhancement is obtained when the dimensionless electric field frequency is of the order of Peclet number or ω¹ ～ O(Pe). By tracking Lagrangian fluid particles, it is revealed that application of non-uniform unsteady electric field results in chaotic advection at high Pe whereas steady and unsteady uniform electric fields do not.