A MATHEMATICAL MODEL FOR PARALLEL FLOW DRYER FOR SLABS WITH HIGH THERMAL DIFFUSIVITY

An analytical model for the process is developed. The thermal diffusivity of the drying slabs is assumed infinite and the moisture diffusivity constant during the entire drying process.

With specified initial and boundary conditions, the mathematical model yields a two-part solution for the diffusion equation. The first part is valid for the initial drying during which the surface moisture content exceeds the value of fiber saturation. This part of the solution is used until the surface moisture content drops to the fiber saturation value. The moisture profile at the end of this period is used as the initial condition for the second period of drying which takes place under hygroscopic conditions.

Two simplifying assumptions are adapted for the hygroscopic region: 1. The dependence between the surface temperature and the moisture content is linear. 2. Constant (average) absorption heat is used during this second drying period.

For both parts of the solution, the surface moisture gradient is proportional to the local temperature difference between the drying air and the slab surface. This temperature difference can be expressed by means of a water mass balance equation for the part of the dryer between the slab in-feed and the point considered and by using the thermodynamic properties of the humid air.     

A MATHEMATICAL MODEL FOR CONTINUOUS DRYING OF GRAINS IN A SPOUTED BED DRYER

ABSTRACT

A mathematical model for a continuous spouted bed dryer has been presented to predict moisture content, air and grain temperatures as well as energy consumption. To better understand the interactive influence of processes in each region of the spouted bed, solution schemes for the spout and downcomer were treated separately. The behavior of dryer was investigated experimentally and found that the dryer behaved differently from an ideal plug flow. The drying rate as simulated by the model is almost constant during grain movement in the dryer. Absence of airflow in the downcomer leads to a tempering process that takes place in the downcomer while intense heat and mass transfer occurs mainly in the spout due to the high airflow rate there. Furthermore, by considering the predicted grain temperature history as one of the indicators of product quality, one can, in principle, design appropriate successive processes in a continuous spouted bed dryer to minimize product damage.     

A MATHEMATICAL MODEL FOR CONTINUOUS DRYING OF GRAINS IN A SPOUTED BED DRYER

A mathematical model for a continuous spouted bed dryer has been presented to predict moisture content, air and grain temperatures as well as energy consumption. To better understand the interactive influence of processes in each region of the spouted bed, solution schemes for the spout and downcomer were treated separately. The behavior of dryer was investigated experimentally and found that the dryer behaved differently from an ideal plug flow. The drying rate as simulated by the model is almost constant during grain movement in the dryer. Absence of airflow in the downcomer leads to a tempering process that takes place in the downcomer while intense heat and mass transfer occurs mainly in the spout due to the high airflow rate there. Furthermore, by considering the predicted grain temperature history as one of the indicators of product quality, one can, in principle, design appropriate successive processes in a continuous spouted bed dryer to minimize product damage.     

A COMPREHENSIVE MATHEMATICAL MODEL FOR A MULTIZONE TUBULAR HIGH PRESSURE LDPE REACTOR

In this study a comprehensive mathematical model of high pressure tubular ethylene polymerization reactors is presented. A fairly general reaction mechanism is employed to describe the complex kinetics of ethylene polymerization. To determine the variation of molecular properties along the reactor length the method of moments is applied to the infinite set of species balance equations to transform it into a low order system of differential equations in terms of the leading moments of the number chain length distribution. Detailed algebraic equations are given describing the variation of kinetic rate constants, thermodynamic and transport properties of the reaction mixture with temperature, pressure and composition. A new correlation is derived to describe the change of reaction viscosity with reactor operating conditions. The model permits a realistic calculation of temperature and pressure profiles, monomer and initiator concentrations, molecular properties of LDPE (i.e. M_n, M_m, LCB and SCB) as well as the variation of inside film heat transfer coefficient with respect to the reactor length. Simulation results are presented illustrating the effects of initiator concentration, inlet pressure, chain transfer concentration and wall fouling on the polymer quality and reactor operation. The present model predictions are in good agreement with experimental observations in industrial high pressure tubular LDPE reactors.     

PSEUDO TWO-DIMENSIONAL MODEL FOR A PNEUMATIC DRYER

Pneumatic drying of chemical products has been frequently used in chemical industries. The increase in the use of this unit operation requires the knowledge of the dynamic of the gas-solid flow in tubes. The mathematical models of vertical pneumatic conveying found in the literature mostly consider the flow steady and one dimensional. However, experimental evidences suggest that radial profiles of the basic variables of the flow exist. In this work a model is proposed for vertical pneumatic conveying considering axial and radial profiles for gas and solids velocities, porosity and pressure. The conservation equations for energy and mass of water were written to extend the model to a pneumatic dryer. The equations of the model were solved using finite difference method and the results show the axial and radial variations of gas and solid temperatures, gas humidity and particle moisture content in the dryer.     

PSEUDO TWO-DIMENSIONAL MODEL FOR A PNEUMATIC DRYER

ABSTRACT

Pneumatic drying of chemical products has been frequently used in chemical industries. The increase in the use of this unit operation requires the knowledge of the dynamic of the gas-solid flow in tubes. The mathematical models of vertical pneumatic conveying found in the literature mostly consider the flow steady and one dimensional. However, experimental evidences suggest that radial profiles of the basic variables of the flow exist. In this work a model is proposed for vertical pneumatic conveying considering axial and radial profiles for gas and solids velocities, porosity and pressure. The conservation equations for energy and mass of water were written to extend the model to a pneumatic dryer. The equations of the model were solved using finite difference method and the results show the axial and radial variations of gas and solid temperatures, gas humidity and particle moisture content in the dryer.     

DYNAMIC MATHEMATICAL MODEL OF A ROTARY DRYER: METHOD OF CHARACTERISTICS

A mathematical model for the dynamic behavior of a countercurrent rotary dryer has been developed and solved. The model consists of four hyperbolic partial differential equations with split boundary conditions. The equations are solved numerically using an algorithm based on the method of characteristics. The solution is stable and rapid. Sample results of a dryer simulation are presented.     

喷雾干燥设备设计的数学模拟法

系统论述了喷雾干燥器内粒子的运动状态与风场流动特性及其数学模型的建立过程,在传递理论的基础上根据马歇尔方程计算了干燥过程中粒子与干燥介质之间的传质传热,通过求解粒子在干燥室内的运动方程而进行喷雾干燥设备设计的粒子运动轨迹法及设计计算程序的计算机实现过程,并用实验数据及理论解对程序的可靠性进行了论证。     

A MATHEMATICAL MODEL OF HIGH INTENSITY PAPER DRYING

High intensity drying occurs when one web surface is heated to the thermodynamic saturation temperature corresponding to the local hydraulic pressure. Rapid vapor generation causes the process to be driven by a total pressure gradient, so vapor leaves the web by a bulk flow mechanism rather than a slower diffusion mechanism. Vapor pressure build-up promotes rapid web heating and offers the opportunity for liquid removal by displacement. Lower energy usage can result if only a part of the moisture is evaporated.     

煤炭优化组合的数学模型

本文提出了一种可以使低质煤炭通过优化组合代替优质煤在某些生产部门应用的数学模型，并根据部分数据给出了计算结果。     

A MATHEMATICAL MODEL OF HIGH INTENSITY PAPER DRYING

High intensity drying occurs when one web surface is heated to the thermodynamic saturation temperature corresponding to the local hydraulic pressure. Rapid vapor generation causes the process to be driven by a total pressure gradient, so vapor leaves the web by a bulk flow mechanism rather than a slower diffusion mechanism. Vapor pressure build-up promotes rapid web heating and offers the opportunity for liquid removal by displacement. Lower energy usage can result if only a part of the moisture is evaporated.     

MATHEMATICAL MODEL DEVELOPMENT AND SIMULATION OF HEAT PUMP FRUIT DRYER

ABSTRACT

A mathematical model of a heat pump fruit dryer was developed to study the performance of heat pump dryers. Using the moisture content of papaya glace' drying, the refrigerant temperature at the evaporator and condenser and the performance, was verified. It was found that the simulated results using closed loop heat pump dryer were close to the experimental results. The criteria for evaluating the performance were specific moisture extraction rate and drying rate. The results showed that ambient conditions affected significantly on the performance of the open loop dryer and the partially closed loop dryer. Also, the fraction of evaporator bypass air affected markedly on the performance of all heat pump dryers. In addition, it was found that specific air flow rate and drying air temperature affected significantly the performance of all heat pump dryers.     

A MATHEMATICAL MODEL FOR A YANKEE HOOD

Drying of thin paper sheet on a Yankee cylinder equipped with a steam heated high velocity hood is examined. When possible infiltration of air from the surroundings is considered, then the process is fully determined by twelve variables. One of these can be chosen as an independent variable. An equation group of eleven equations is derived. The method of solution is iterative. Finally, a numerical demonstration example is presented.     

A MATHEMATICAL MODEL AND SIMULATION FOR NON ISOTHERMAL GAS ABSORPTION WITH CHEMICAL REACTION

In this paper, the principles of mass and heat transfer for a non-isothermal gas absorption with chemical reaction have been described. The examples of carbon monoxide complexing with aluminum cuprous tetrachloride solution and carbon dioxide absorbed by monoethanolamine aqueous solution in packed column have been simulated and computed with a mathematical model which considered of both mass and heat transfer, gas and liquid resistance. The fundamental differential equations of the process are treated with forth order Runge-Kutta method. Through simulating and computing, the temperature profiles and concentration profiles of both gas and liquid phase along the packed height have been visualized. The results are reasonably accurate and conform with pilot plant experimental data.     

AN APPROXIMATIC MATHEMATICAL MODEL FOR DESIGN OF INDUSTRIAL CRYSTALLIZERS WITH ELUTRIATORS

Introduetion Crystallization has bee一1 widely aPPlied to ehemieal,Pharmaeeutieal and Petroleunl indus-tries.Various Produets are manufaetured by erystallization,for examPle,Potassium ehloride.sodium ehloride,sugar,ammonium sulfate, MSG,glueose,etc.Crysta…     

MATHEMATICAL SIMULATION OF A NEWLY-DEVELOPED SEED-COTTON DRYER

The basic analitical method for so-called expression operation, the separation of liquid from solid-liquid systems by compression, are presented in view of the flow through compressible porous media. It has become evident that the expression mechanism consists of two flow phenomena. These types of phenomena can be analyzed by consideration of the flow mechanism through compressible porous beds, first by the filtration theory and second by the so-called consolidation theory. A simplified equation is also presented. It is shown that the simplified equation is well applicable to industrial expression problems even when the creep effects of matarials to be expressed are appreciable     

THERMAL DYNAMICS OF A DRUM DRYER

The thermal dynamics of a top-loading drum dryer is studied with a view of deriving the transfer function for the thermal process involved. The drum which initially operates at a steady state, is subjected to a step change in the steam pressure and the response of the temperature of the outer surface of the drum is recorded. The normalised time domain response of the temperature T is analysed using the least squares method to a non-linear function. The time domain response is also transformed into the frequency domain using Fourier transforms and the transfer function is derived.