Mathematical Model of Coupled Heat and Mass Transfer in Unsaturated Soils

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CONJUGATE MODEL FOR HEAT AND MASS TRANSFER OF POROUS WALL IN THE HIGH TEMPERATURE GAS FLOW

Heat and mass transfer of a porous permeable wall in a high temperature gas dynamical flow is considered. Numerical simulation is conducted on the ground of the conjugate mathematical model which includes filtration and heat transfer equations in a porous body and boundary layer equations on its surface. Such an approach enables one to take into account complex interaction between heat and mass transfer in the gasdynamical flow and in the structure subjected to this flow. The main attention is given to the impact of the intraporous heat transfer intensity on the transpiration cooling efficiency.

Establishment and Application of UFC-ACC Heat Transfer Coefficient Model

Based on medium plate runout table ultra-fast cooling( UFC)-accelerated cooling equipment( ACC) system,a heat transfer coefficient model was constructed. Firstly,according to the measured data,heat transfer coefficients under different roll speed and water volume were calculated by using an inverse heat conduction method. Secondly,a monofactorial heat transfer coefficient calculation formula was obtained. Finally,the heat transfer coefficient model based on medium plate runout table UFC-ACC system was constructed by intercept function,slope function,interaction influence function and linear or nonlinear influencing factors. The precision of these models was validated by comparing model prediction value with measured data,and the results were in good agreement with practical needs,and the average deviation was less than 5%.

Surface-particle-emulsion heat transfer model between fluidized bed and horizontal immersed tube

A mathematical model, surface-particle-emulsion heat transfer model, ispresented by considering voidage variance in emulsion in the vicinity of an immersed surface. Heattransfer near the surface is treated by dispersed particles touching the surface and through theemulsion when the distance from the surface is greater than the diameter of a particle. A film withan adjustable thickness which separates particles from the surface is not introduced in this model.The coverage ratio of particles on the surface is calculated by a stochastic model of particlepacking density on a surface. By comparison of theoretical solutions with experimental data fromsome references, the mathematical model shows better qualitative and quantitative prediction forlocal heat transfer coefficients around a horizontal immersed tube in a fluidized bed.

Mathematic Model of Unsteady Penetration Mass Transfer in Randomly Packed Hollow Fiber Membrane Module

Based on the membrane-based absorption experiment of CO2 into water, shell-side flow distribution and mass transfer in a randomly packed hollow fiber module have been analyzed using subchannel model and unsteady penetration mass transfer theory. The cross section of module is subdivided into many small cells which contains only one hollow-fiber. The cross sectional area distribution of these cells is presented by the normal probability density distribution function. It has been obtained that there was a most serious non-ideal flow in shell side at moderate mean packing density, and the large amount of fluid flowed and transferred mass through a small number of large voids. Thus mass transfer process is dominated by the fluid through the larger void area. The mass transfer process in each cell is described by the unsteady penetration theory. The overall mass transfer coefficient equals to the probability addition of the mean mass transfer coefficient in each cell. The comparisons of the values calculated by the model established with the empirical correlations and the experimental data of this work have been done.The predicted overall mass transfer coefficients are in good agreement with experimental data.

Numerical modeling of multiphase flow,heat transfer and titanium flow behavior in blast furnace hearth

Understanding the complex phenomena in BF hearth is essential to increase furnace productivity and to extend furnace campaign.We have developed several continuum-based mathematical/numerical models to simulate the multi-phase flow,heat transfer and chemical reactions in the BF hearth.These models have generated an improved insight on the mechanisms for liquid drainage efficiency,lining erosion and wall protection in BF hearth under operational conditions.The current paper gives an overview of these studies in three aspects:Gas flow and pressure on the liquid surface,and their effect on the drainage characteristics;The flow and temperature distributions of liquid iron in BF hearth,and the temperature distribution in the refractories;Finally,titanium behaviors due to titania injection to form Ti(C,N) -rich scaffold on the hearth surface,to protect the hearth from erosion.

Heat and Mass Transfer in Process of Fluidized-Bed Spray Granulation

This article presents a mathematical model of heat and mass transfer for the process of fluidized-bed spray granulation, which can be applied in the analysis of bed temperature profile, temperature and humidity of outlet gas and moisture content of particles. Effects of operation parameters on the batch granulation are investigated. The theoretical calculation agrees reasonably well with the experimental data.

Modeling of Heat Transfers in Bioreactive Household Waste Storage Facilities: Spatial and Temporal Distributions

In order to enhance the production of biogas and to study the thermal behavior of waste, a numerical study of fluid flows and heat transfers within household waste was developed to predict the distributions of thermal fields. The mathematical model is based on the conservation of mass and energy equations. The resulting system of equations is discretized using the finite volume method and solved using the Thomas algorithm. The results of the model studied are compared with the numerical and site measurements results from other authors. The results have been found to be in good agreement. The results show that the mathematical model is able to reproduce the thermal behavior in anaerobic phase in landfills. The isotherms revealed that temperatures are lower in the upper part of the waste cell, very high in the core and decrease slightly in the bottom of the cell due to the biodegradation of waste.

Mass transfer mathematical model for one-side plate steady-state ultrafiltration

A mass transfer mathematical model was developed based on one-side plate steady-state ultrafiltration(UF), and the numerical solution was obtained by Crank-Nicolson finite difference method. The effects of the feed concentration, channel length, axial velocity, and diffusion coefficient on the concentration at membrane surface and the concentration profiles were investigated. Furthermore, the operation parameters and the parameters of membrane module were all transformed into dimensionless ones, and the parameter rejection was included in the mass transfer model, therefore, it can be used to calculate the steady-state ultrafiltration with different rejections. The model was used for the calculation of the ultrafiltration of metal-cutting oil emulsion. The results show that the concentration polarization can be reduced by increasing the axial velocity to some extent, but the reduction of concentration polarization is very small when the resistance of ultrafiltration is very great.

Effects of thermophoresis particle deposition and of the thermal conductivity in a porous plate with dissipative heat and mass transfer

Network simulation method（NSM） is used to solve the laminar heat and mass transfer of an electricallyconducting,heat generating/absorbing fluid past a perforated horizontal surface in the presence of viscous and Joule heating problem. The governing partial differential equations are non-dimensionalized and transformed into a system of nonlinear ordinary differential similarity equations,in a single independent variable,畏. The resulting coupled,nonlinear equations are solved under appropriate transformed boundary conditions. Computations are performed for a wide range of the governing flow parameters,viz Prandtl number,thermophoretic coeffcient（a function of Knudsen number）,thermal conductivity parameter,wall transpiration parameter and Schmidt number. The numerical details are discussed with relevant applications. The present problem finds applications in optical fiber fabrication,aerosol filter precipitators,particle deposition on hydronautical blades,semiconductor wafer design,thermo-electronics and problems including nuclear reactor safety.

Study on mass transfer of ethyl acetate in polymer adsorbent by experimental and theoretical breakthrough curves

A new polymeric adsorbent with highly hypercrosslinked structure was developed for the removal of VOCs from polluted air. The purpose of this work is to obtain the intraparticle mass transfer coefficient of the adsorbent particles. Adsorption experiments for obtaining breakthrough curves were carried out with a fixed bed system. A dynamic mathematical model for the fixed bed adsorption system was developed.By model fitting, the overall mass transfer coefficient was determined when the deviation error was minimum. Then, the intraparticle mass transfer coefficient of the adsorbent was determined when the external mass transfer resistance was eliminated at higher velocities. Furthermore, a linear relationship of the intraparticle mass transfer coefficient and equilibrium coefficient at lower inlet gas concentrations range was correlated. Moreover, an equation for predicting external mass transfer coefficient at low Reynolds number range at room temperature was obtained.

Mathematical Simulation of Dynamic Heat Transfer in a Human-Clothing-Environment System

A mathematical model has been developed to describe the dynamic heat transfer in the clothing microclimate under transient wear conditions. This model is solved numerically by the implicit finite difference method. If the physical activity and ambient conditions are specified, the model can predict the thermoregulatory response of the body. Experimental measurements with garments made of fibers with different levels of hygroscopicity are compared with predictions by the model. There is good agreement between prediction and experiment for the temperature of the clothing microclimate.

Heat-transfer model on the improvement of continuous casting slab temperature

A heat transfer model on the solidification process has been established onthe basis of the technical conditions of the slab caster in No.3 steel works of Wuhan Iron & SteelCorporation, and the temperature field in the solidifying slab was calculated which was verified bythe measured slab surface temperature. The influences of the main operating factors includingcasting speed, spray cooling patterns, superheat of melt and slab size on the solidification processwere analyzed and the means of enhancing the slab temperature was brought forward. Raising thecasting speed to 1.3 m/min, controlling the flowrate of secondary cooling water and improving thecooling pattern at the lower segments of secondary cooling zone could improve the slab temperatureeffectively. And the increasing the superheat is adverse to the production of high temperature slab.

Mathematical model and general laws of wet compression

Wet compression is an effective way to enhance the performance of gas turbines and it has attracted a good deal of attention in recent years. The one sidedness and inaccuracy of previous studies,which took concentration gradient as mass transfer potential are discussed. The mass transfer process is analyzed from the viewpoint of non equilibrium thermodynamics,by taking generalized thermodynamic driving force as mass transfer potential,and the corresponding mass transfer coefficient is obtained using the heat and mass transfer equilibrium occurring between moist air and water droplets at wet bulb temperature for the sake of avoiding complex tests and providing more accurate formulas. A mathematical model of wet compression is therefore established,and the general laws of wet compression are investigated. The results show that the performance of atomizer is critical for wet compression and wet compression is more suitable for compressors with higher pressure ratio and longer compression time.

Mathematical Modeling of Heat Flux Distribution in Raw Cotton Stored in Bunt

The scientific article examines the physical and mechanical properties of raw cotton stored in buntings in cotton palaces. Because during the storage of raw cotton in bunts, some of its properties deteriorate, some improvements. Therefore, the mathematical modeling of storage conditions of raw cotton in bunts and the physical and mechanical conditions that occur in it is of great importance. In the developed mathematical model, the main factor influencing the physical and mechanical properties of raw cotton is the change in temperature. Due to the temperature, kinetic and biological processes accumulated in the raw cotton in Bunt, it can spread over a large surface, first in a small-local state, over time with a nonlinear law. As a result, small changes in temperature lead to a qualitative change in physical properties. In determining the law of temperature distribution in the raw cotton in Bunt, Laplace’s differential equation of heat transfer was used. The differential equation of heat transfer in Laplace’s law was replaced by a system of ordinary differential equations by approximation. Conditions are solved in MAPLE-17 program by numerical method. As a result, graphs of temperature changes over time in raw cotton were obtained. In addition, the table shows the changes in density, pressure and mass of cotton, the height of the bun. As the density of the cotton raw material increases from the top layer of the bunt to the bottom layer, an increase in the temperature in it has been observed. This leads to overheating of the bottom layer of cotton and is the main reason for the deterioration of the quality of raw materials.

Turbulence flow and heat transfer of aluminum melt in tip cavity in process of thin-gauge high-speed casting

The uniformity of flow distribution of aluminum melt in tip cavity is a precondition to decide whether or not thin-gauge high-speed casting can be accomplished smoothly. The laws of aluminum melt flow and heat transfer in tip cavity can be found out through numerical simulation, which gives theoretical basis for solving the problem of the flow distribution of melt in tip cavity. A mathematical model with a low Reynolds number k—ε model for turbulence flow and heat transfer of aluminum melt in tip cavity was developed. The finite difference method was used to calculate the flow field and temperature field of aluminum melt in tip cavity. The phenomena and characteristics of turbulence flow and heat transfer were analyzed, including the characteristics of temperature distribution of turbulence similar to that of laminar flow. The simulation results are in good agreement with the experimental results for flow velocities and temperature at the exit of tip, which verifies the validity of the simulation results.

HEAT TRANSFER BEHAVIOR OF SUPERALLOY DROPLETS DURING SPRAY FORMING

Based on the Newtonian heat transfer formulation and classical heterogeneous nucleation theory, a mathematical model has been established to predict the profile of flight velocity, heat transfer coefficient, temperature, solid fraction and cooling rate of atomizing droplets for a superalloy. The results indicated that above parameters change with different droplet size and flight distance. The changing trend as well as the mechanism for the change are described and discussed.

Zonal method solution of radiative heat transfer in a one-dimensional long roller-hearth furnace in CSP

A radiative heat transfer mathematical model for a one-dimensional long furnace was set up in a through-type roller-hearth furnace （TTRHF） in compact strip production （CSP）. To accurately predict the heat exchange in the furnace, modeling of the complex gas energy-balance equation in volume zones was considered, and the heat transfer model of heating slabs and wall lines was coupled with the radiative heat transfer model to identify the surface zonal temperature. With numerical simulation, the temperature fields of gas, slabs, and wall lines in the furnace under one typical working condition were carefully accounted and analyzed. The fundamental theory for analyzing the thermal process in TI＇RI-IF was provided.

Numerical method and model for calculating thermal storage time for an annular tube with phase change material

For calculating the thermal storage time tor an annular tube with phase change material(PCM),a novel method is proposed.The method is suitable for either low-temperature PCM or high-temperature PCM whose initial temperature is near the melting point.The deviation fit is smaller than 8%when the time is below 2×10~4 s.Comparison between the predictions and the reported experimental data of thermal storage time at same conditions is investigated and good agreements have been got.Based on this method,the performance of the thermal storage unit and the role of natural convection are also investigated.Results show a linear relation between the maximum amount of stored heat and thermal storage time,and their ratio increases with the height of the thermal storage unit.As the thickness of the cavity increases,natural convection plays an increasingly important role in promoting the melting behavior of paraffin.When the thickness of the cavity is small,natural convection restrains the melting behavior of paraffin.

Transfer and Reaction Performances of Selective Catalytic Reduction of N2O with CO over Monolith Catalysts

This work tries to identify the relationship between geometric configuration of monolith catalysts, and transfer and reaction performances for selective catalytic reduction of N2O with CO. Monolith catalysts with five different channel shapes (circle, regular triangle, rectangle, square and hexagon), was investigated to make a comprehensive comparison of their pressure drop, heat transfer Nu number, mass transfer Sh number and N2O conversion. It was found that monolith catalysts have a much lower pressure drop than that of traditional packed bed, and for monolith catalysts with different channel shapes, pressure drop decreases in the order of regular triangle > rectangle > square > hexagon > circle. The order of Nu is in regular triangle > rectangle ≈ square > hexagon > circle, similar to that of Sh. N2O conversion follows the order of regular triangle > rectangular ≈ square ≈ circle > hexagon. The results indicate that chemical reaction including internal diffusion is the controlling step in the selective catalytic reduction of N2O removal with CO. In addition, channel size and gas velocity also have influence on N2O conversion and pressure drop.