Statistical models for surface renewal in heat and mass transfer: Part I. Dependence of average transport coefficients on age distribution

AIChE Journal ◽  
1966 ◽  
Vol 12 (5) ◽  
pp. 941-946 ◽  
Author(s):  
L. B. Koppel ◽  
R. D. Patel ◽  
J. T. Holmes
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Statistical Models ◽  
Transport Coefficients ◽  
Age Distribution ◽  
Surface Renewal

scholarly journals A frequency quantum interpretation of the surface renewal model of mass transfer

2017 ◽  
Vol 4 (7) ◽  
pp. 170103 ◽  
Author(s):  
Chanchal Mondal ◽  
Siddharth G. Chatterjee
Keyword(s):  
Mass Transfer ◽  
Steady State ◽  
Frequency Distribution ◽  
Age Distribution ◽  
Gas Absorption ◽  
Bulk Liquid ◽  
Gas Transfer ◽  
Transfer Resistance ◽  
Surface Renewal ◽  
Two Parameter

The surface of a turbulent liquid is visualized as consisting of a large number of chaotic eddies or liquid elements. Assuming that surface elements of a particular age have renewal frequencies that are integral multiples of a fundamental frequency quantum, and further assuming that the renewal frequency distribution is of the Boltzmann type, performing a population balance for these elements leads to the Danckwerts surface age distribution. The basic quantum is what has been traditionally called the rate of surface renewal. The Higbie surface age distribution follows if the renewal frequency distribution of such elements is assumed to be continuous. Four age distributions, which reflect different start-up conditions of the absorption process, are then used to analyse transient physical gas absorption into a large volume of liquid, assuming negligible gas-side mass-transfer resistance. The first two are different versions of the Danckwerts model, the third one is based on the uniform and Higbie distributions, while the fourth one is a mixed distribution. For the four cases, theoretical expressions are derived for the rates of gas absorption and dissolved-gas transfer to the bulk liquid. Under transient conditions, these two rates are not equal and have an inverse relationship. However, with the progress of absorption towards steady state, they approach one another. Assuming steady-state conditions, the conventional one-parameter Danckwerts age distribution is generalized to a two-parameter age distribution. Like the two-parameter logarithmic normal distribution, this distribution can also capture the bell-shaped nature of the distribution of the ages of surface elements observed experimentally in air–sea gas and heat exchange. Estimates of the liquid-side mass-transfer coefficient made using these two distributions for the absorption of hydrogen and oxygen in water are very close to one another and are comparable to experimental values reported in the literature.

Empirical Evaluation of Convective Heat and Moisture Transport Coefficients in Porous Cotton Medium

2002 ◽  
Vol 124 (3) ◽  
pp. 530-537 ◽  
Author(s):  
Kamel Ghali ◽  
Nesreen Ghaddar ◽  
Byron Jones
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Convective Heat ◽  
Transport Coefficients ◽  
Model Parameters ◽  
Moisture Uptake ◽  
Transfer Coefficients ◽  
Mass Transfer Coefficients ◽  
Air Penetration ◽  
Heat And Moisture

The air penetration within a porous clothing system on a moving human being is an important physical process that considerably affects the heat and moisture resistance of the textile material. This effect of the coupled convection heat and mass exchange within the clothing system is experimentally investigated and theoretically modeled to determine the heat and mass transfer coefficients between the air penetrating the void space and the solid fiber as a function of the velocity of penetrating air. Experiments were conducted inside environmentally controlled chambers to measure the transient moisture uptake of untreated cotton fabric samples as well as the outer fabric temperature using an infrared pyrometer. The moisture uptake was conducted at three different volumetric flow rates of 0.0067, 0.018 and 0.045 m3/sec/m2 of fabric area to represent airflow penetrations that could result from slow, medium, and vigorous walking, respectively. The theoretical analysis is based on a two-node adsorption model of the fibrous medium. A set of four coupled differential equations were derived describing time-dependent convective heat and mass transfer between the penetrating air and the solid fiber in terms of relevant unknown transport coefficients. The unknown model parameters were adjusted to fit the experimental data. The outer heat and mass transfer coefficients were found to increase with the air penetration flow rate.

scholarly journals Drying and Heating Processes in Arbitrarily Shaped Clay Materials Using Lumped Phenomenological Modeling

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4294
Author(s):  
Elisiane S. Lima ◽  
João M. P. Q. Delgado ◽  
Ana S. Guimarães ◽  
Wanderson M. P. B. Lima ◽  
Ivonete B. Santos ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Relative Humidity ◽  
Heat And Mass Transfer ◽  
Convective Heat ◽  
Transport Coefficients ◽  
Ceramic Materials ◽  
Raw Material ◽  
Transfer Coefficients ◽  
Mass Transfer Coefficients ◽  
Mass Transfers

This work aims to study the drying of clay ceramic materials with arbitrary shapes theoretically. Advanced phenomenological mathematical models based on lumped analysis and their exact solutions are presented to predict the heat and mass transfers in the porous material and estimate the transport coefficients. Application has been made in hollow ceramic bricks. Different simulations were carried out to evaluate the effect of drying air conditions (relative humidity and speed) under conditions of forced and natural convection. The transient results of the moisture content and temperature of the brick, and the convective heat and mass transfer coefficients are presented, discussed and compared with experimental data, obtaining a good agreement. It was found that the lower the relative humidity is and the higher the speed of the drying air is, the higher the convective heat and mass transfer coefficients are at the surface of the brick and in the holes, and the faster the moisture removal material and heating is. Based on the predicted results, the best conditions for brick drying were given. The idea is to increase the quality of the brick after the process, to reduce the waste of raw material and energy consumption in the process.

Heat and Mass Transfer during Drying of Lentil Based on the Non-Equilibrium Thermodynamics: A Numerical Study

2015 ◽  
Vol 365 ◽  
pp. 285-290 ◽  
Author(s):  
J.C.S. Melo ◽  
Antônio Gilson Barbosa de Lima ◽  
Wilton Pereira Silva ◽  
W.M.P. Barbosa de Lima
Keyword(s):  
Mass Transfer ◽  
Moisture Content ◽  
Heat And Mass Transfer ◽  
Numerical Study ◽  
Transport Coefficients ◽  
Irreversible Processes ◽  
Average Moisture Content ◽  
Convective Boundary ◽  
Vapor Flux ◽  
Oblate Spheroidal

This paper aims to present a mathematical model, based on the thermodynamics of irreversible processes to describe both the heat and mass transfer (liquid and vapor) during the drying of bodies with oblate spheroidal shape. The model was applied to describe drying of lentil grain, considering variables transport coefficients and convective boundary conditions at the surface of the solid. All equations were presented in oblate spheroidal coordinates and numerically solved by using the finite-volume method. Results of the average moisture content, average temperature, liquid flux, vapor flux, and moisture content and temperature distributions inside a lentil kernel during drying process (T=40 oC, RH=50% and v=0.3 m/s) were presented and analyzed.

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