Laws Of Mass Transfer Research Articles

A Variable Diffusivity Model for the Drying of Spherical Food Particulates

An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variable effective diffusivity. In order to test the model, experimental data was collected for the drying of green peas in a fluidised bed at three drying temperatures. Through fitting three equation types for effective diffusivity to the data, it was found that a linear equation form, in which diffusivity increased with decreasing moisture content, was most appropriate. The final model accurately described the drying curves of the three experimental temperatures, with an R2value greater than 98.6% for all temperatures.

An inverse problem of Bilayer textile thickness determination in dynamic heat and moisture transfer

An inverse problem of bilayer textile thickness determination in dynamic heat and moisture transfer is presented satisfying the heat–moisture comfort level of human body. Heat and mass transfer law in bilayer textiles is displayed by proving the existence and uniqueness of solution to the coupled partial differential equations with initial-boundary value conditions. The finite difference method is employed to derive the numerical solution to partial differential equations. The regularized solution of the inverse problem is reformulated into solving function minimum problem through the Tikhonov regularization method. The golden section method is applied to solve the direct search problem and achieve the optimal solution to the inverse problem. Numerical algorithm and its numerical results provide theoretical explanation for textile materials research and development.

Development of a qualitative test method for the cleanability of polymer woven filter media

In this paper a new method for cleaning of filter media is presented, and the cleanability with different textures and surface finishes is compared. With the method described, it is possible to evaluate the quality of the cleaning process. According to the German VDMA standard cleaning test, riboflavin and malt extract are applied as model contaminants for evaluation of the cleaning results. To compare the cleanability of filter media with different properties and geometries the results are adapted to the law of mass transfer and to the Sherwood number, a dimensionless parameter describing the quality of a cleaning process.

Dynamic performance limits for a class of multistage chemical power consumption system

A multistage isothermal endoreversible chemical pump system with a finite potential capacity high chemical potential mass reservoir and the linear mass transfer law (g∝Δμ) is investigated in this paper. For the fixed initial time and fixed initial concentration of the key component, the minimum power consumption of the multistage chemical pump system and the corresponding optimal concentration configuration of the key component in the high chemical potential reservoir are derived by applying Hamilton–Jacobi–Bellman optimisation theory analytically, and the obtained results are also compared with those obtained for the maximum power output of the multistage endoreversible chemical engine system. The results in this paper provide a new performance limit for fluid flow energy conversion processes, which is different from that given by conventional classical thermodynamics.

Experimental characterization and modeling of Baker's yeast pellet drying

A contribution to a better understanding and modeling of the drying of a Baker's yeast rod-shaped pellet is proposed. An original experimental setup is developed allowing the characterization of the drying of a Baker's yeast pellet by using a precision balance, a microscope and an infrared camera. Using this experimental setup, the time evolution of the pellets moisture content, dimensions and surface temperature can be obtained in a large set of operating conditions (air temperature, air velocity and initial pellet diameter). The evolution of the fermentative activity of the Baker's yeast during drying as a function of its moisture content can also be investigated through the measurement of its gassing power. In this study, a set of drying experiments of Baker's yeast pellets in this original setup and with a data treatment procedure is presented.A new phenomenological model of the drying of a cylindrical Baker's yeast pellet is built on the basis of heat and mass transfer laws. It includes a description of the shrinkage of the material and it provides a link between the initial drying rate and the Baker's yeast activity at the end of the drying. The unknown parameters are identified by a comparison with experimental results. The combined use of the model and the experimental results leads to four main conclusions: three types of water exists in Baker's yeast pellets (a residual water, a water whose extraction is limited by mass transport phenomena in gas phase inside or outside the pellet, and a third type of water whose extraction is significantly slower); there is an isotropic linear shrinkage during drying which has no significant influence on the drying rate but which appears to be drying rate dependent as, at a same moisture content, a larger drying rate leads to a smaller shrinkage; the time evolution of the pellets surface temperature presents a change of regime at a moisture content of about 0.6 (d.b.); the Baker's yeast activity remains high when its moisture content is larger than 0.75 (d.b.) and the activity at the end of the drying is directly related to the initial Baker's yeast drying rate.

Entransy dissiaption minimization for isothermal throttling process

A class of isothermal throttling process with generalized mass transfer law is investigated, and the optimality condition for the minimum mass entransy dissipation of the process is obtained by applying optimal control theory. The results for special cases with mass transfer laws [g∝(Δp)m] and [g∝Δ(μ)] are further obtained based on the general optimization result, and the obtained results are also compared with other mass transfer strategies of the minimum entropy generation, constant pressure ratio and constant pressure difference. Numerical examples for the cases with the mass transfer laws [g∝(Δp)1/2], [g∝Δ(p)] and [g∝Δ(μ)] are also provided. The results obtained herein can provide some theoretical guidelines for the optimal design and operation of real throttling processes and devices.

Entransy Dissipation Minimization for Isothermal Crystallization Processes with Diffusive Mass Transfer Law

A class of isothermal crystallization process with the given total mass of crystals is investigated. The mass transfer process is assumed to obey the diffusive mass transfer law [ g∝Δ(c)], and the optimal concentration configuration for the minimum entransy dissipation of the crystallization process is obtained by applying optimal control theory. Numerical examples are provided, and the obtained results are also compared to those of the minimum entropy generation, constant concentration and constant mass flux operations. The results show that 2/3 power of the net mass of crystals for the minimum entransy dissipation of the process change with the time linearly, and the entransy dissipation rate of the process keeps constant, which coincides with the principle of equipartition of entransy dissipation and is significant different from that obtained for the minimum entropy generation of the process; the entransy dissipation for the mass transfer strategy of constant concentration is smaller than that for the mass transfer strategy of constant mass flux; both the entransy dissipation and the entropy generation for the two mass transfer strategies of the minimum entransy dissipation and the minimum entropy generation are smaller than those for the other two mass transfer strategies. The entropy generation characterizes the irreversibility of energy conversion processes, and the mass entransy dissipation characterizes the irreversibility of mass transfer processes. Since the crystallization process is independent of the energy conversion, so the optimization principle should be entransy dissipation minimization.

Entransy dissipation minimization for one-way isothermal mass transfer processes with a generalized mass transfer law

A class of one-way isothermal mass transfer processes is investigated in this paper. Based on the definition of mass entransy, the entransy dissipation function, which reflects the irreversibility of the mass transfer ability loss, is derived. The optimality condition for the minimum entransy dissipation of the mass transfer process with a generalized mass transfer law is obtained by applying an optimal control theory. Special cases for the linear [g∝Δ(μ)] and the diffusive [g∝Δ(c)] mass transfer laws are obtained based on the general optimization results. The obtained results are also compared with strategies of minimum entropy generation, constant concentration ratio and constant concentration difference operations. The results obtained herein can provide some theoretical guidelines for optimal design and operation of practical mass transfer processes.

Study of the structural parameters of filter cloths with the use of similitude theory and dimensional analysis

This article examines the main laws of filtration on the basis of fundamental laws of hydrodynamics and mass transfer in order to qualitatively evaluate the effect of the structural parameters of filter cloths on the filtration process. The cloths that are examined are largely homogeneous porous structures formed from fibers (for example). Similitude theory and dimensional analysis are used to develop a method of evaluating a structural coefficient that determines the structural parameters of textiles with allowance for their permeability. Values of the coefficient are obtained.

Heat and Mass Transfer at High Speed Filtration in Porous Media and Packed Beds

Packed beds composed of spherical balls are used for the study of transfer processes in porous media at turbulent filtration. The paper summarizes the development of a physical modelling of transfer processes in packed beds. It is shown that the available quantitative measurements of structural characteristics of infiltrated flow in packed beds such as the near-wall zone velocity and temperature profiles and velocity pulsation spectra follow the similarity laws of turbulent separated flows that have been developed by the author and are represented in the first part of the paper. These facts supported by visual observations of flow patterns in packed beds from various authors allow implementing the analogy between transfer processes mechanism in turbulent separated flows and convective transfer processes in near-wall zone of surfaces embedded in grainy layers, or ducts filled with packed bed, at high Reynolds numbers. This approach has resulted in the asymptotic heat and mass transfer law. The universal character of the heat and mass transfer law for the surfaces embedded in grainy layer is confirmed by the authors data and data from many other studies.

Heat and mass transfer at ignition of solid condensed substance with relatively low calorific power by a local energy source

Macroscopic laws of heat and mass transfer at gas-phase ignition of solid condensed substance with relatively low calorific power by a typical local energy source, namely, a small hot metal particle shaped as a parallelepiped, are investigated. The proposed model takes into account a group of interrelated processes of heat and mass transfer with thermal decomposition and chemical reaction in the interaction of solid and a source with limited energy content. The influence of the heat content of a local energy source on the characteristics of the process is analyzed.

Evaporation of water droplets containing carbon nanotubes

The evaporation of water droplets containing carbon nanotubes has been experimentally studied. The droplets were evaporated in a flow of dry air at temperatures in a range of T0 = 20−200°C and Reynolds numbers designed on the initial diameter were Re = 500−2000. The results of measurements of the droplet surface temperature and evaporation rate show that the addition of ∼0.1 wt % nanoparticles to the base liquid (water) virtually does not change the laws of heat and mass transfer.

Unified Description of Isothermal Endoreversible Chemical Cycles with Linear Mass Transfer Law

An isothermal endoreversible four-reservoir chemical pump cycle operating between a finite potential capacity high-chemical-potential mass reservoir and three infinite potential capacity mass reservoirs is established in this paper. Optimal control theory is applied to determine the optimal cycle configuration corresponding to the maximum energy output per cycle for the fixed total cycle time and transferred energy of high-chemical-potential mass reservoir in which the mass transfer between working fluid and mass reservoirs obey linear mass transfer law. The optimal cycle configuration is an isothermal endoreversible four-reservoir chemical pump cycle, in which the chemical potential (the concentration) of the key component in the finite potential capacity high-chemical-potential mass reservoir and that in the working fluid change nonlinearly with time and the difference between the chemical potential (the ratio of the concentration) of the key component in the finite potential capacity mass reservoir and (to) that in the working fluid is a constant, and the chemical potentials (the concentration) of the key component in the working fluid at the infinite potential capacity mass reservoir sides are also constants. Moreover, the numerical example is provided to reveal the influences of concentration and chemical potential change of the finite potential capacity high-chemical-potential mass reservoir on the optimal configuration of the four-reservoir chemical pump cycle. Then, a unified description of various isothermal endoreversible chemical cycles with linear mass transfer law is obtained. They include ten type of isothermal endoreversible chemical cycles: four-reservoir chemical pumps with finite potential capacity mass reservoirs and infinite potential capacity mass reservoirs, four-reservoir chemical potential transformers with finite potential capacity mass reservoir and infinite potential capacity mass reservoirs, three- reservoir chemical pumps with finite potential capacity mass reservoirs and infinite potential capacity mass reservoirs, three-reservoir chemical potential transformers with finite potential capacity mass reservoir and infinite potential capacity mass reservoirs, two-reservoir chemical pump with infinite potential capacity mass reservoirs, and chemical engine with infinite potential capacity mass reservoirs. The results can provide some guidelines for optimal design and operation of real chemical cycles and devices.

A model of heat and mass transfer inside a pressure cooker

A model has been developed to describe steam cooking in a pressure cooker. The physical and thermal characteristics of commercial pressure cookers and of the food cooked in them, heat and mass transfer laws and various phenomena (conduction in solids, liquid and gas free convection, undercooled and emitted steam boiling, condensation and also valve opening laws) were all taken into account. Gas and water were considered to be two homogeneous fluid compartments. The hot plate was also modelled. This model enabled the prediction of heat and mass fluxes and pressures, the composition of gas, the temperature in the fluid compartment and temperature pattern in food under non-steady conditions during the three periods of cooking (pressure increase, pressure regulation and pressure decrease). The model was validated experimentally using an instrumented device containing a model foodstuff (PTFE cube). The fluxes generated by the model enabled the description of pressure and temperature increases, and allowed us to suggest better methods for energy-saving and rapid steam cooking.

Dynamic Modeling and a Parametric Study of an Indirect Solar Cabinet Dryer

A dynamic mathematical model for drying of agricultural products in an indirect cabinet solar dryer is presented. This model describes the heat and mass transfer in the drying chamber and also considers the heat transfer and temperature distribution in a solar collector under transient conditions. For this purpose, using conservation laws of heat and mass transfer and considering the physical phenomena occurring in a solar dryer, the governing equations are derived and solved numerically. The model solution provides an effective tool to study the variation of temperature and humidity of the drying air, drying material temperature, and its moisture content on each tray. The predicted results are compared with available experimental data. It is shown that the model can predict the performance of the cabinet solar dryer in unsteady-state operating conditions well. Furthermore, the effect of some operating parameters on the performance and efficiency of dryer is investigated and compared with selected published data.

Cooling process of iron ore pellets in an annular cooler

A 3-D mathematical model was presented for the cooling process of iron ore pellets based on the laws of mass, momentum, and heat transfer. The flow, pressure, and temperature fields were obtained by numerical simulation with the commercial software FLUENT. In order to verify the model, a mass and energy balance field test was systematically carried out on an annular cooler in Shougang Mining Company. The maximum relative errors of temperature, pressure, and velocity between computational and testing results are 2.87%, −8.11%, and 7.14%, respectively, indicating the validity of the model. Further, the effects of process parameters, such as pellet diameter, bed thickness, air velocity, and temperature, on the pellet bed temperature profiles were studied.

Non‐isothermal modelling of H2S removal in a biofilter

In this study the biodegradation of H2S in the air in a biofilter is modelled in the non‐isothermal operating condition. For this purpose, using conservation laws of heat and mass transfer and considering the physical and chemical phenomena occurring in a biofilter, the governing equations in non‐isothermal, isothermal, steady, and unsteady‐state operations are obtained and solved numerically. The model results are compared with the available experimental data and also with the results of the isothermal model. The comparisons are made both in steady and unsteady‐state situations. The results show that considering the heat effects on the modelling of a biofilter improves the accuracy of the model results. Furthermore, the effects of some operating parameters on the removal efficiency of biofilter are investigated.

Entransy dissipation minimization for a class of one-way isothermal mass transfer processes

A class of one-way isothermal mass transfer processes with Fick’s diffusive mass transfer law [g ∝ Δ(c)] is investigated in this paper. Based on the definition of the mass entransy, the entransy dissipation function which reflects the irreversibility of mass transfer ability loss is derived. The optimal concentration allocations of the key components corresponding to the highand low-concentration sides for the minimum entransy dissipation of the mass transfer process are obtained by applying optimal control theory and compared with the strategies of the minimum entropy generation, constant mass transfer flux (constant concentration difference), and constant concentration ratio (constant chemical potential difference). The results are as follows. For the optimal mass transfer strategy of the minimum entransy dissipation, the product of the square of the key component concentration difference between the high- and the low-concentration sides and the inert component concentration at the low-concentration side is a constant, while for that of the minimum entropy generation, the ratio of the square of the key component concentration difference between the high- and the low-concentration sides to the key component concentration at the low-concentration side is a constant; when the mass transfer process is not involved in energy conversion process, the optimization principle should be the minimum entransy dissipation; the mass transfer strategy of constant concentration difference is superior to that of constant concentration ratio. The results obtained in this paper can provide some theoretical guidelines for optimal designs and operations of practical mass transfer processes.

Maximum Power Output of Multistage Continuous and Discrete Isothermal Endoreversible Chemical Engine System with Linear Mass Transfer Law

The maximum power output of a multistage isothermal endoreversible chemical engine system operating between a finite potential capacity high-chemical-potential reservoir and an infinite potential capacity low-chemical-potential environment with the linear mass transfer law is investigated in this paper. For the fixed initial time and fixed initial concentration of the key component in the high-chemical-potential reservoir, the continuous model is optimized by applying Hamilton-Jacobi-Bellman (HJB) theory and Euler-Lagrange equation, respectively, and the discrete model is optimized by applying dynamic programming method and discrete maximum principle, respectively. Numerical examples for the discrete model with three different boundary conditions are provided, and the results are also compared with those for the continuous model. The results show that both of the maximum power outputs of the limiting continuous and multistage discrete isothermal endoreversible chemical engine systems are equal to the difference between their classical reversible thermodynamic performance limits and a dissipation term. The relative concentration of the key component in the high-chemical-potential reservoir for the maximum power outputs of the continuous and discrete models decreases with the increase of time linearly. The relationships among the maximum power output of the system, the process period and the final concentration of the key component in the high-chemical-potential fluid reservoir are discussed in detail.

Maximum Power Output of Multistage Continuous and Discrete Isothermal Endoreversible Chemical Engine System with Linear Mass Transfer Law

The maximum power output of a multistage isothermal endoreversible chemical engine system operating between a finite potential capacity high-chemical-potential reservoir and an infinite potential capacity low-chemical-potential environment with the linear mass transfer law is investigated in this paper. For the fixed initial time and fixed initial concentration of the key component in the high-chemical-potential reservoir, the continuous model is optimized by applying Hamilton-Jacobi-Bellman (HJB) theory and Euler-Lagrange equation, respectively, and the discrete model is optimized by applying dynamic programming method and discrete maximum principle, respectively. Numerical examples for the discrete model with three different boundary conditions are provided, and the results are also compared with those for the continuous model. The results show that both of the maximum power outputs of the limiting continuous and multistage discrete isothermal endoreversible chemical engine systems are equal to the difference between their classical reversible thermodynamic performance limits and a dissipation term. The relative concentration of the key component in the high-chemical-potential reservoir for the maximum power outputs of the continuous and discrete models decreases with the increase of time linearly. The relationships among the maximum power output of the system, the process period and the final concentration of the key component in the high-chemical-potential fluid reservoir are discussed in detail.