Heat and mass fluxes in presence of superficial reaction in a not completely developed laminar flow

A mathematical model has been developed in order to study the effect of superficial reaction, the catalytic propane combustion, and its coupling with the fluid flow on mass and energy fluxes between gas and solid phases in a monolithic reactor. Simulations have been performed at different values of the gas inlet temperature and propane mass fraction. The effect of heat produced at the wall by the chemical reaction on fluid flow is studied separately from the entrance effect. A new interpretation of the real driving force is proposed, which is able to correctly predict, in a very simple manner, the values of fluxes independently of the presence of Graetz entrance effects. Also, the dependency of the Nu and Sh numbers with the gas inlet temperature and propane mass fraction is correctly included. This result leads to a different definition of the Nu and Sh numbers and, for the cases investigated numerical correlations are also given.     

圆形自由水射流冲击换热及喷嘴布置

引言 水射流冲击冷却由于具有较高的换热能力,广泛应用于机械和化工行业,以实现工件的快速冷却和控制工件的温度变化.在大型轴类工件(工件直径D=1000～3000 mm)喷水冷却装置中,多喷嘴圆孔自由水射流以特定阵列布置冲击至工件表面,相对短暂的沸腾换热结束后,阵列自由水射流即以强制对流方式实现工件冷却.因此,自由水射流冲击换热特性及多喷嘴布置形式对喷水冷却装置的结构设计至关重要.     

Enhancement of mass transfer from particles by local shear-rate and correlations with application to drug dissolution

We analyze hydrodynamic enhancement of mass (or heat) release rate from small spherical particles within fluid flows from local flow shear-rate, with application to drug dissolution. Combining asymptotic theories in the high/low shear Peclet number limits in Stokes flow with 205 carefully-developed computational experiments, we develop accurate correlations for shear enhancement of Sherwood/Nusselt number (Sh/Nu) as a function of shear Peclet and Reynolds number (S^*, Re _S). The data spanned S^* from 0 to 500 and Re _S from 0 to 10. In Stokes flow our correlations are highly accurate over the entire S^* range, whereas for finite Re _S < 1 accuracy is good for S^* up to a few thousand. Shear enhancement results from highly three-dimensional spiraling flow created by particle spin. We develop a model for particle slip velocity that is inserted into the Ranz/Marshall correlation to show that shear-rate enhancement strongly dominates convection, a result important to drug dissolution.     

Numerical study on the effect of inert region on mass transfer by the segmented electrodes in limiting current method

The effect of inert region on mass transfer has been studied numerically for the cathode package that is used to measure the local mass transfer rate to a solid surface in a flow system. The inert region introduces a considerable error in the limiting current method as the region increased. The overall mean Sherwood number on the cathodic electrodes with the inert region was correlated as follows.Sh _m = 13.96 Re^0.339(1 + RT)^0.444 when RT is the ratio of the inert region to the active region. If RT is less than 0.25, the error of theoretical value to Leveque solution is less than 12%.     

FREE CONVECTIVE DRAFT INDUCED BY THERMAL AND CONCENTRATION GRADIENTS INSIDE AN ISOTHERMAL,VERTICAL CYLINDER†

Laminar, free convective flow through a vertical cylinder induced by the thermal and concentration buoyancy forces is investigated. The numerical studies involve development of a steady-state, two-dimensional heat and mass transfer model for the moist air core of the vertical tube. The stream function-vorticity method is employed to simplify the governing, coupled conservation equations which were then numerically solved by the successive over-relaxation (SOR) and alternating direction implicit ((ADI) methods.

A graphical correlation was found between dimensionless flow rate and dimensionless tube length as a function of the buoyancy force ratio N = Gr/Grc. Excellent agreement was obtained for the dimensionless flow rale results with those of Davis and Perona¹⁶ and Kageyama and Izumi¹³ for the case when only the-thermal buoyancy force is considered.

The combined buoyancy force from thermal and species diffusion provides larger local Nusselt Nu and local Sherwood Sh numbers relative to the case when just one buoyancy force is accounted for. Both local Nu and local Sh are seen to asymptotically approach a constant value as flow develops.     

MASS TRANSFER IN LIQUID FLUIDIZED BEDS AT LOW REYNOLDS NUMBERS

Mass transfer coefficients between fluidized ion exchange resins (Dowex 2 × 8) and dilute solutions of hydrochloric acid and of benzoic were measured in the low Reynolds number range (Re < 1.0). In the case of benzoic acid, the experimental mass transfer coefficients are in agreement with the values predicted by standard correlation Sh = (0.81 ± 0.05) ε^?1 Re ^0.5 Sc ^1/3 in the range 0.1 < Re < 1, but below this value of Re the measured mass transfer coefficients are much lower. With hydrochloric acid the experimental mass transfer data are well correlated by the equation Sh = 1.1 ε^?1 Re Sc ^1/3 in the range Re < 1. The observed decrease of the mass transfer coefficients in the low range of Reynolds numbers is most probably related to the effects which are considered in Nelson and Galloway's theory and in Rowe's modification of the same theory. The theoretical results were found useful in the interpretation of experimental data. The least squares analysis of the experimental data showed that the value of parameter α, with which the best fit between experimental and theoretical results was obtained, was α = 0.62 with benzoic acid and α = 0.7 with hydrochloric acid, in good agreement with the value value proposed by Rowe and established earlier with an NaOH system. Qualitatively, the theory predicts the correct dependence of Sh on Sc as Re → 0.     

Heat and Mass Transfer at the Wall of a Square Mechanically Stirred Gas-Liquid-Solid Catalytic Reactor

Wall mass and heat transfer rates in a square gas-sparged, mechanically stirred reactor were measured by the electrochemical technique under the effect of various geometrical and hydrodynamic variables. For the 45° impeller, the mass transfer data fit the equation Sh = 0.7Sc^0.33Re^0.2Re_g^0.5 with an average deviation of ±6.9 %. For the 90° impeller, the data fit the equation Sh = 0.95Sc^0.33Re^0.14Re_g^0.53 with an average deviation of ±7.5 %. Gas sparging enhanced the wall mass transfer rates by factors of up to 2.61 and 3 for the 90° and 45° impellers, respectively, with a significant decrease in the total power consumption. The contribution of the present results to the operation of multiphase mechanically agitated vessels in different aspects is outlined.     

Local mass transfer measurements from a submerged jet parallel to a flat surface

The local mass transfer rates from a submerged vertical jet parallel to the vertical electrode surface were measured by a limiting current density technique. For these studies, the parameters considered are a plate Reynolds number in the range of 1965 to 136500, electrode height over the orifice of the jet (Y) which varied from 0 to 12 times the jet orifice diameter (d), and the vertical distance of the microelectrode on the electrode plate in the range of 0.7 to 12.5 cm. The system used for measuring the limiting current was the reduction of copper ions. The relationship between the local Sherwood number (Sh) and Reynolds number (Re) was found to be Sh = 0.0004(Re)^1.5 (Sc)^0.33 This relationship is valid for Y/d ≤ 6.0.     

Electrochemical study of mass transfer in decaying annular swirl flow Part II: Correlation of mass transfer data

This paper presents correlations of local mass transfer at the inner rod and the outer wall in annular decaying swirl flow generated by axial vane swirl generators. Four swirl generators with vane angles in the range 15–60° to the duct axis were used and experiments were carried out in a Reynolds number range 3300–50000 and at a Schmidt number of 1650. The results were correlated in the general form Sh _x = 0.0204 Re _x ^0.86 (1 + tan _i )^0.53 Sc ^1/3, for the inner rod, and Sh _x = 0.0224 Re _x ^0.86 (1 + tan _o)^0.55 Sc ^1/3, for the outer pipe. Comparison is made with heat transfer data for work with a similar entry configuration.     

On the Prandtl or Schmidt number dependence of the turbulent heat or mass transfer coefficient

Numerical experiments using a direct numerical simulation (DNS) of turbulent flow between two parallel plates in conjunction with Lagrangian scalar tracking (LST) of trajectories of thermal markers in the flow field are conducted for Prandtl or Schmidt numbers between 0.01 and 50,000. The LST methodology is used to generate mean temperature profiles as a function of the entry distance in the case of a step change in heat or mass flux at the walls of the channel. The heat transfer coefficient and the Nusselt number ratio, Nu(x)/Nu(x→∞), downstream from the step change in the wall flux are determined for the range of Pr or Sc fluids examined. Relations between the heat or mass transfer coefficient at the fully developed part of the channel and Pr or Sc are proposed for low and high Pr or Sc cases. Finally, unified correlations, which provide the heat or mass transfer coefficient for all Pr or Sc, in the Reynolds number range examined, are proposed. Also, the exponent of the asymptotic dependence of the eddy diffusivity close to the wall is obtained.     

Systematic mesh development for 3D CFD simulation of fixed beds: Single sphere study

To develop and validate meshes for computational fluid dynamics (CFD) simulations of transport in fixed beds, a single particle is often used as a test case. We present results for drag coefficient (C_D) and heat transfer Nusselt number (Nu) for flow past a sphere, focusing on high flow rates typical of industrial steam reformers (400 < Re < 20,000). Over this range, good predictions of C_D were obtained using large eddy simulation (LES) to capture vortex shedding and wake dynamics, with a mesh refined downstream from the sphere. The small time-steps and high cell count required make this too expensive for fixed beds. Nu can be accurately calculated using a Reynolds-averaged Navier-Stokes (RANS) method with shear-stress transport (SST) k-ω closure provided the mesh at the particle surface is fine enough and covers most of the boundary layer. Single sphere simulations of heat transfer are more useful for fixed bed mesh development than drag coefficient calculations.     

Mass transfer at rotating cone electrodes

Upright and inverted rotating cone electrodes (apex half angle 52°) have been studied using electrodeposition of copper from an acid electrolyte (Sc=1770) by means of limiting current mass transport techniques. The behaviour suggests that it is appropriate to regard these electrodes as modified disc electrodes. The upright rotating cone electrode exhibits a flow transition atRe=1×10⁵. In laminar flowSh=4.5Re ^0.48 and in turbulent flowSh=0.04Re ^0.95. The inverted rotating cone electrode exhibits a flow transition atRe=6×10⁴. In laminar flowSh=4.5Re ^0.45 and in turbulent flowSh=0.04Re ^0.88. The data have been interpreted in terms of a coating thickness affected by throwing power effects and the use of a conical cathode cell for control of high speed electrodeposition processes is indicated.Nomenclature A electrode area (cm²) - C _b concentration (of bulk solution) (mol cm^–3) - c concentration difference (mol cm^–3) - D diffusion coefficient (cm² s^–1) - f/2 friction factor - F Faraday's constant (96485 A s mol^–1) - i _L limiting current density (A cm^–2) - J mass transfer flux (mol s^–1 cm^–2) - K _L mass transfer coefficient (cm s^–1) - l slant height of the cone (cm) - U peripheral velocity (cm s^–1) - x local condition coordinate (cm) - z no. of electrons - apex half-angle of cone - angular velocity (rad s^–1) - wall shear stress (dyn cm^–2) - kinematic viscosity (cm² s^–1) - Re Reynolds number=Ud/v - Sc Schmidt number=v/D - Sh Sherwood number=K _L d/D     

Combined buoyancy effects of thermal and mass diffusion on laminar forced convection in the thermal entrance region of horizontal square channels

Heat and mass transfer in laminar mixed convection in the thermal entrance region of horizontal square channels is investigated by using the vorticity-velocity formulation of the Naiver-Stokes equations. The numerical results, including the developments of temperature and concentration contours, Nu_z and friction coefficient ratios, fRe / (fRe)₀, are presented for an air-water system. The effects of bottom wall temperature and the relative humidity on the momentum, heat and mass transfer in the flow are examined in detail. Results show that the influences of the evaporation of the water vapor along the wetted wall on the heat and mass transfer and the ratio fRe / (fRe)₀ are rather substantial.     

Mass transfer from highly soluble cylinders in cross flow: Some experimental results

Mass transfer coefficients from highly soluble cylinders in cross flow orientation have been determined experimentally. The separate contributions arising from the different parts of the cylinder, namely, the front, plane sides and the rear have been delineated by masking various parts of the test specimen. Simple empirical expressions are devised for the components as well as for the total mass transfer coefficient. The present results compare favourably with the literature data in the following ranges of conditions: 90 ≤ Re_p ≤ 850; 600 ≤ Sc ≤ 1100 and 70 ≤ Sh < 210.     

Mass transfer to volumetric electrodes with two-phase flow

Experimental studies of mass transfer were conducted in stacked screens with a gas-liquid mixture flowing through the bed. Depending on the gas and liquid flow rates and on the geometric characteristics of the screens, different flow regimes are obtained. In the heterogeneous flow regime the gas phase controls mass transfer, meanwhile in the transition and bubbling flow regimes the influence of the liquid flow prevails. Appropriate dimensionless groups correlate the mass transfer coefficients with the pertinent variables for the different regimes.Nomenclature A electrode area (cm²) - A ₁ surface area of one screen (cm²) - c _o bulk concentration (mol cm^–3) - D diffusivity (cm²s^–1) - d particle or wire diameter (cm) - F Faraday's constant - i limiting current (A) - k mass transfer coefficient (cm s^–1) - N distance between wires (cm) - Re _g Reynolds number for gas flow,Re _g=u _g R _h v _g ^–1 - Ré _g Reynolds number for gas flow,Re ₁=u ₁ R _h v ₁ ^–1 - Re ₁ Reynolds number for liquid flow,Re' ₁=u ₁ dv ₁ ^–1 - Ré ₁ Reynolds number for liquid flowRe ₁=u ₁ R _h v ₁ ^–1 - R _h hydraulic radius of screen bed (cm) - S _c Schmidt number,Sc=v ₁ D ^–1 - Sh Sherwood number,Sh=kdD ^–1 - Sh ₀ Sherwood number without gas,Sh ₀ =kdD ^–1 - u _g superficial gas velocity (cm s^–1) - u ₁ superficial liquid velocity (cm s^–1) - screen thickness (cm) - porosity - v kinematic viscosity (cm²s^–1) - specific area (cm^–1)     

Mixed convection heat and Mass transfer in a vertical channel with film evaporation

Numerical results are presented for effects of latent heat transport associated with film vaporization on laminar mixed convection heat and mass transfer in a vertical channel with a half channel width b = 0.01 m. The influences of the inlet liquid mass flowrate and wall temperature on the film vaporization and the associated heat and mass transfer characteristics are examined for air-water and air-ethanol systems with gas Reynolds number Re_g = 2000. Predicted results obtained by including transport in the liquid film are contrasted with those where liquid film transport is neglected, showing that the assumption of an extremely thin film made in Lin et al. (1988) and Yan and Lin (1989) is only valid for systems having small liquid mass flow rates. Additionally, it is found that the interfacial heat flux is predominantly determined by latent heat transfer connected with film evaporation.     

Liquid‐Solid Mass Transfer Behavior of a Vertical Array of Closely Spaced Horizontal Tubes in Relation to Catalytic and Electrochemical Reactor Design

The rates of mass transfer at a vertical array of closely spaced horizontal tubes were measured by the limiting‐current technique under single‐phase flow, gas sparging and two‐phase flow. The single‐phase flow data were correlated by the equation: Sh = 0.75 Sc^0.33 Re^0.59. The gas sparging data with no net solution flow were correlated by the equation: J = 0.31(Re_g.Fr)^–0.22. For two‐phase flow, the gas flow was found to enhance the rate of array mass transfer by a factor ranging from 1.25 to 5.25, depending on Re_g and Re. The enhancement ratio increases with decreasing Re and increasing Re_g. For Re ≥ 2500, the rate of mass transfer approaches the value of single‐phase flow, regardless of the value of Re_g, which ranged from 7 to 41. The importance of the present geometry in building electrochemical and catalytic reactors, where exothermic liquid‐solid diffusion‐controlled reactions take place, is highlighted. The present geometry offers the advantage that the outer surface acts as a turbulence promoter while the inner surface acts as a heat exchanger.     

Mass transfer characteristics of wire-mesh honeycomb reactors

The mass transfer characteristics in honeycombs made of catalyst-deposited metal wire meshes (wire-mesh honeycomb; WMH) were studied to test the prediction that WMH has better flow distribution and a higher rate of interphase mass transfer than the conventional ceramic type of honeycomb module. The WMH module was constructed from alternating layers of flat and corrugated wire-mesh sheets packed within a frame. Wire-mesh sheets were coated with aluminum particles using electrophoretic method. Thermal sintering at 800°C and then calcinations at 500°C yielded a porous layer of Al/Al₂O₃ composite particles that were firmly attached on the wire surface. The alumina-protected wire meshes were further deposited with Pt/TiO₂ catalyst powder by washcoating method. The oxidation of ethyl acetate was monitored as model reaction. A one-dimensional model was established and the parameters of intrinsic first-order kinetics were regressed from the reaction results obtained in the region controlled by chemical reaction, after which interphase mass transfer coefficients were regressed in other region. Three expressions for the Sherwood number that are typically used for honeycomb, wire-mesh gauze and packed bed reactors were examined to determine the optimal expression for WMHs. The mass transfer coefficient in the WMH was found to be quite different from that in the conventional ceramic honeycomb reactor and much higher than that in the wire-mesh gauze reactor. The best-fit results were obtained with packed-bed expression, Sh=1.06Re^0.50Sc^1/3, indicating the mechanism of reaction in the WMH is most similar to that in a packed bed. The optimal Sh expression was then used to predict the behavior of systems with a larger channel size or longer bed; the model predictions showed good agreement with experimental results from real WMH reactors.     

Improvement of heat removal in solid‐state fermentation tray bioreactors by forced air convection

BACKGROUND: Heat removal is one of the major constraints in large‐scale solid‐state fermentation (SSF) processes. The effect of internal air circulation by forced convection on heat and water transfer has not been studied in SSF tray bioreactors. Formulation of a mathematical model for SSF requires a good estimation of the mass and heat transfer coefficients. RESULTS: A stainless steel tray bioreactor (80.6 L capacity) was used. Aspergillus niger C28B25 was cultivated under SSF conditions on an inert support. Temperature, moisture content, biomass and substrate concentrations were measured. Water and energy integral balances were used to estimate the heat and mass transfer coefficients involved in the process. The Reynolds number (N_Re) in the headspace of the tray bioreactor ranged from 2.5 to 2839, which increased the global heat transfer coefficient from 4.2 to 6.9 (W m^?2 K^?1) and the mass transfer coefficient from 1.0 to 2.1 (g m^?2 s^?1). Mathematical model predictions of the temperature and moisture content of the fermentation bed showed a high goodness‐of‐fit with the experimental results. CONCLUSIONS: This is the first report describing the effect of N_Re of air in the headspace of a SSF tray bioreactor on the heat and mass transfer coefficients and temperature regulation in SSF. Copyright © 2011 Society of Chemical Industry