scholarly journals Mathematical models of the process of submlimationand optimization of lyophilization modes

2018 ◽  
Vol 17 (3) ◽  
pp. 20-28
Author(s):  
E. V. Blynskaya ◽  
S. V. Tishkov ◽  
K. V. Alekseyev ◽  
S. V. Minaev
Keyword(s):  
Heat Transfer ◽  
Energy Balance ◽  
Mathematical Models ◽  
Side Wall ◽  
Factors Affecting ◽  
Mass Transfer Processes ◽  
Transient Energy ◽  
Mathematical Formulas ◽  
Adsorption Desorption ◽  
Energy Balances

The purposeof this study is to analyze methods of mathematical modeling for calculating the stage of primary sublimation, as the most important stage in lyophilization technology. Presented are mathematical formulas, equations for the calculation of heat and mass transfer processes, during the removal of 90 % of all frozen ice. A model is considered that takes into account the contribution of all thermal effects, including the transient energy balance, taking into account the heat transfer through the side wall of the vial and radiation, even if they are present in a small amount. The mathematical model can be used to optimize the lyophilization cycle, and also as tools for technological monitoring (using sensors based on models). The model considered in the article is a one-dimensional nonstationary state model in which the correct comprehensive transient energy balance has been introduced to describe the heat transfer through the glass of the vial, and the results are estimated using experimental data. The equations used in the simulation describe the mass and energy balances in the dried layer, taking into account the rate of adsorption/desorption of water at the interface, mass and heat transfer at the sublimation interface, as well as the energy balance of heat transfer in the wall of vials, shelf and other factors affecting the process of sublimation. Conclusions are made on the presented mathematical models and the characteristic of the direction of the process of optimization of primary sublimation in lyophilization technology is given.

scholarly journals Averaged energy-balance analysis of wavy micro-channels

2021 ◽  
Vol 2116 (1) ◽  
pp. 012080
Author(s):  
Roxana Durantes ◽  
Justin Moon ◽  
J Rafael Pacheco ◽  
Arturo Pacheco-Vega
Keyword(s):  
Heat Transfer ◽  
Energy Balance ◽  
Channel Model ◽  
Heat Rate ◽  
Operating Conditions ◽  
Temperature Fields ◽  
Global Energy ◽  
Single Wave ◽  
Micro Channels ◽  
Energy Balances

Abstract This study presents numerical simulations of the convective heat transfer on wavy micro-channels to investigate heat transfer enhancement in these systems. The goal is to extend the analysis of our previous work [1, 2], by proposing a methodology based on local and global energy balances in the device instead of the commonly used Nusselt number. The analysis is performed on a single-wave baseline micro-channel model that is exposed to a heat influx. The governing equations for an incompressible laminar flow and conjugate heat transfer are first built, and then solved, for representative models, under several operating conditions, by the finite element technique. From computed velocity, pressure and temperature fields, local and global energy balances based on cross-section-averaged velocities and temperatures enable calculating the heat rate at each section. Results from this study show that this so-called averaged energy-balance methodology enables an accurate assessment of the channel performance.

Innovative energy and mass balance of a continuous evaporating crystallizer

2019 ◽  
pp. 646-654
Author(s):  
Jan Iciek ◽  
Kornel Hulak ◽  
Radosław Gruska
Keyword(s):  
Energy Balance ◽  
Mass Balance ◽  
Working Conditions ◽  
Crystallization Process ◽  
Heat Losses ◽  
Inert Gas ◽  
Gas Removal ◽  
Energy Balances ◽  
Heat Released ◽  
Mass And Energy Balances

The article presents the mass and energy balances of the sucrose crystallization process in a continuous evaporating crystallizer. The developed algorithm allows to assess the working conditions of the continuous evaporating crystallizers and the technological and energy parameters. The energy balance algorithm takes into account the heat released during the crystallization of sucrose, which was analyzed in this study, heat losses to the environment and heat losses due the vapor used for inert gas removal.

Methodology of Research in Micropollutants – Heavy Metals

1982 ◽  
Vol 14 (12) ◽  
pp. 107-125 ◽  
Author(s):  
Roland Wollast
Keyword(s):  
Heavy Metals ◽  
Mathematical Models ◽  
Aqueous Phase ◽  
Suspended Matter ◽  
Solid Phase ◽  
Aquatic Organisms ◽  
Biological Processes ◽  
Particulate Phase ◽  
Sources Of Pollution ◽  
Adsorption Desorption

A comparison of the concentration of dissolved and of particulate heavy metals in the aquatic system indicates that these elements are strongly enriched in the suspended matter. The transfer between the aqueous phase and the solid phase may be due to dissolution-precipitation reactions, adsorption-desorption processes or biological processes. When these processes are identified, it is further possible to develop mathematical models which describe the behaviour of these elements. The enrichment of heavy metals in the particulate phase suspended or deposited and in aquatic organisms constitutes a powerful tool in order to evaluate sources of pollution.

Heat Transfer and Flow Phenomena in a Swirl Chamber Simulating Turbine Blade Internal Cooling

1998 ◽  
Author(s):  
C. R. Hedlund ◽  
P. M. Ligrani ◽  
H.-K. Moon ◽  
B. Glezer
Keyword(s):  
Heat Transfer ◽  
Turbine Blade ◽  
Flow Characteristics ◽  
Leading Edge ◽  
Internal Cooling ◽  
Vortex Pairs ◽  
Nusselt Numbers ◽  
Swirl Chamber ◽  
Flow Phenomena ◽  
Energy Balances

Heat transfer and fluid mechanics results are given for a swirl chamber whose geometry models an internal passage used to cool the leading edge of a turbine blade. The Reynolds numbers investigated, based on inlet duct characteristics, include values which are the same as in the application (18000–19400). The ratio of absolute air temperature between the inlet and wall of the swirl chamber ranges from 0.62 to 0.86 for the heat transfer measurements. Spatial variations of surface Nusselt numbers along swirl chamber surfaces are measured using infrared thermography in conjunction with thermocouples, energy balances, digital image processing, and in situ calibration procedures. The structure and streamwise development of arrays of Görtler vortex pairs, which develop along concave surfaces, are apparent from flow visualizations. Overall swirl chamber structure is also described from time-averaged surveys of the circumferential component of velocity, total pressure, static pressure, and the circumferential component of vorticity. Important variations of surface Nusselt numbers and time-averaged flow characteristics are present due to arrays of Görtler vortex pairs, especially near each of the two inlets, where Nusselt numbers are highest. Nusselt numbers then decrease and become more spatially uniform along the interior surface of the chamber as the flows advect away from each inlet.

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