Mathematical modeling of an aqueous film coating process in a Bohle Lab-Coater: Part 2: Application of the model

For the prediction of the air and product temperatures, the product moisture, and the air humidity during a coating process in a Bohle Lab-Coater, a model was developed. The purpose of this work was to determine the limit moisture, the critical moisture, and the constant for the exchange rate between both zones and to use these values for other sets of experiments to test the model. The adaptation of the 3 parameters (limit moisture, critical moisture, and exchange rate constant), was done by calculation of the product temperature in both zones for several sets of parameters in order to minimize the sum of square deviation between the calculated and the measured product temperatures. This set of parameters was used to test the validity of the model. By applying the model, the product temperature could be predicted based on the product, process, and equipment-related parameters. Hence, the model can be used to theoretically investigate the influence of different process paramaters. The mean difference between the predicted, and measured product temperatures in the steady state is ≈2 up to 3 K using the determined parameter set for the limit moisture, the critical moisture, and the exchange rate constant. The model is useful for the prediction of the air and product temperatures, the product moisture, and air humidity during a coating process in the Bohle Lab-Coater using round, biconvex tablets.     

Effect of operating conditions on solid substrate fermentation

In this work the effects of environmental parameters on the performance of solid substrate fermentation (SSF) for protein production are studied. These parameters are (i) air flow rate, (ii) inlet air relative humidity, (iii) inlet air temperature, and (iv) the heat transfer coefficient between the outer wall of the fermentor and the air in the incubator. The air flow is supplied to effect cooling of the fermented mass by evaporation of water. A dynamic model is developed, which permits estimation of biomass content, total dry matter, moisture content, and temperature of the fermented matter. The model includes the effects of temperature and moisture content on both the maximum specific growth rate and the maximum attainable biomass content. The results of the simulation are compared with actual experimental data and show good agreement with them. The most important conclusions are that (i) the evaporative cooling of the biomass is very effective for temperature control and (ii) the air flow rate and the heat transfer coefficient have strong effects but they affect the biomass morphology and are not controllable easily. Also, a simple technique for the determination of the optimum temperature and moisture content profile for cell protein production is applied. The simulated biomass production increases considerably employing the optimum temperature and moisture content profiles. The ultimate goal is to implement the determined effects of the environmental parameters on the SSF biomass production and the temperature and moisture variation profiles to effectively control the SSF and optimize the biomass production. (c) 1993 John Wiley & Sons, Inc.     

Simulation of sensible and latent heat losses from wet-skin surface and fur layer

A simulation model that simultaneously calculates heat and mass transfer from a wetted skin surface and fur layer of a cow is presented. The model predicts evaporative, convective and radiant heat losses for different levels of skin and fur wetness, air velocity, air temperature and relative humidity. In the model, fur layer (hair coat) properties such as fur thickness and hair density assumed are that of summer conditions. Evaporative cooling from wet-skin surface and hair coat is the dominant mode of heat mitigation mechanism in stressful hot environments and is further enhanced by increased air velocity. Evaporative cooling is, however, depressed by increased relative humidity because of deficit of water-vapor concentration between the skin surface and ambient air.     

基于冠层温湿度模型的日光温室黄瓜霜霉病预警方法

利用温室环境参数构建室内微环境模拟模型,并结合温室病害模型进行预警,便于开展病害生态防治,以减少农药使用,从而保护温室生态环境和保证农产品质量安全.本文利用温室内能量守恒原理和水分平衡原理,构建了日光温室冠层叶片温度和空气相对湿度模拟模型.叶片温度模拟模型考虑了温室内植物与墙体、土壤、覆盖物之间的辐射热交换,以及室内净辐射、叶片蒸腾作用引起的能量变化;相对湿度模拟模型综合了温室内叶片蒸腾、土壤蒸发、覆盖物与叶面的水汽凝结引起的水分变化.将温湿度估计模型输出值作为参数,输入黄瓜霜霉病初侵染和潜育期预警模型中,估计黄瓜霜霉病发病日期,并与田间观测的实际发病日期比较.试验选取2014年9月和10月的温湿度监测数据进行模型验证,冠层叶片温度实际值与模拟值的均方根偏差（RMSD)分别为0.016和0.024 ℃,空气相对湿度实际值与模拟值的RMSD分别为0.15%和0.13%.结合温湿度估计模型结果表明,黄瓜病害预警系统预测黄瓜霜霉病发病日期与田间调查发病日期相吻合.本研究可为黄瓜日光温室病害预警模型及系统构建提供微环境数据支持.     

A model of evaporative cooling of wet skin surface and fur layer

(1) A theoretical model that simultaneously solves heat and mass transfer in a wet skin surface and fur layer that occurs when an animal is cooled by blowing air over its wetted skin surface and hair coat is presented. (2) The model predicts evaporative and convective heat losses for different levels of wetness, air velocity, ambient temperature, relative humidity and fur properties. (3) Model predictions provide insight about evaporative and convective cooling processes of cows in stressful hot environments.     

合肥市不同生态功能区空气负离子浓度分布特征及其与气象因子的关系

空气负离子浓度与空气环境质量密切相关.以合肥市为研究对象,按照4个生态功能区(公园游览区、生活居住区、商业交通繁华区和工业区),同步进行了空气负离子浓度、主要气象要素(光照强度、气温、空气相对湿度等)观测.不同功能区空气负离子浓度的日变化特点是: 公园游览区和生活居住区日变化呈单峰形式,工业区呈双峰形式,而商业交通繁华区则比较复杂;极值出现的时间也有差异;4个功能区空气负离子浓度日变化的波动性从大到小依次为商业交通繁华区＞工业区＞生活居住区＞公园游览区.4个功能区空气负离子浓度年变化趋势基本一致,夏季最高,冬季最低.公园游览区、生活居住区、商业交通繁华区和工业区空气负离子浓度年平均值分别是819、340、149和126 个·cm^-3.影响合肥市空气负离子浓度的最主要气象因子是空气相对湿度,其次是光照强度,最小为气温.空气负离子浓度与空气相对湿度呈指数递增关系.     

Study of SARS transmission via liquid droplets in air

Microscale liquid droplets could act as the SARS carriers in air when released from an infected person through breathing, coughing, or sneezing. In this study, a dynamic model has been built to quantitatively investigate the effect of the relative humidity on the transport of liquid-droplets in air using coupled mass transfer and momentum equations. Under higher relative humidity, the exhaled liquid droplets evaporate slowly. Larger droplets fall faster, which could reduce the probability of the droplets inhalation. This may be one of the most important factors that influence the SARS transmission in air.     

Modeling conductive cooling for thermally stressed dairy cows

Conductive cooling, which is based on direct contact between a cow lying down and a cooled surface (water mattress, or any other heat exchanger embedded under the bedding), allows heat transfer from the cow to the cooled surface, and thus alleviate heat stress of the cow. Conductive cooling is a novel technology that has the potential to reduce the consumption of energy and water in cooling dairy cows compared to some current practices. A three-dimensional conduction model that simulates cooling thermally-stressed dairy cows was developed. The model used a computational fluid dynamics (CFD) method to characterize the air-flow field surrounding the animal model. The flow field was obtained by solving the continuity and the momentum equations. The heat exchange between the animal and the cooled water mattress as well as between the animal and ambient air was determined by solving the energy equation. The relative humidity was characterized using the species transport equation. The conduction 3-D model was validated against experimental temperature data and the agreement was very good (average error is 4.4% and the range is 1.9–8.3%) for a mesh size of 1117202. Sensitivity analyses were conducted between heat losses (sensible and latent) with respect to air temperature, relative humidity, air velocity, and level of wetness of skin surface to determine which of the parameters affect heat flux more than others. Heat flux was more sensitive to air temperature and level of wetness of the skin surface and less sensitive to relative humidity.     

Variational finite element approach to study heat transfer in the biological tissues of premature infants

The body temperature of newborn preterm infants depends on the heat transfer between the infant and the external environment. Factors that influence the heat exchange include the temperature and humidity of the air and the temperature of surfaces in contact with and around the infant. Neonatal thermoregulation has a different pattern as they have an immature thermoregulatory system. For this purpose, mathematical models can provide detailed insights for the heat transfer processes and its applications for clinical purposes. A new multi-compartment mathematical model of the neonatal thermoregulatory system is presented. The formulation of the model is based on the Pennes’ bio-heat equation with suitable boundary and initial conditions. The variational finite element method has been employed to determine heat transfer and exchange in the biological tissues of premature infants. The results obtained in this paper have shown that premature infants are unable to maintain a constant core temperature and resemble the empirically obtained results, proving the validity and feasibility of our model.AMS (2010): Subject classification92BXX, 92CXX, 92C35, 92C50, 46N60.     

A canine thermal model for simulating temperature responses of military working dogs

Military working dogs (MWDs) are often required to operate in dangerous or extreme environments, to include hot and humid climate conditions. These scenarios can put MWD at significant risk of heat injury. To address this concern, a two-compartment (core, skin) rational thermophysiological model was developed to predict the temperature of a MWD during rest, exercise, and recovery. The Canine Thermal Model (CTM) uses inputs of MWD mass and length to determine a basal metabolic rate and body surface area. These calculations are used along with time series inputs of environmental conditions (air temperature, relative humidity, solar radiation and wind velocity) and level of metabolic intensity (MET) to predict MWD thermoregulatory responses. Default initial values of core and skin temperatures are set at neutral values representative of an average MWD; however, these can be adjusted to match known or expected individual temperatures. The rational principles of the CTM describe the heat exchange from the metabolic energy of the core compartment to the skin compartment by passive conduction as well as the application of an active control for skin blood flow and to tongue and lingual tissues. The CTM also mathematically describes heat loss directly to the environment via respiration, including panting. Thermal insulation properties of MWD fur are also used to influence heat loss from skin and gain from the environment. This paper describes the CTM in detail, outlining the equations used to calculate avenues of heat transfer (convective, conductive, radiative and evaporative), overall heat storage, and predicted responses of the MWD. Additionally, this paper outlines examples of how the CTM can be used to predict recovery from exertional heat strain, plan work/rest cycles, and estimate work duration to avoid overheating.     

Efficient solution of ordinary differential equations modeling electrical activity in cardiac cells

The contraction of the heart is preceded and caused by a cellular electro-chemical reaction, causing an electrical field to be generated. Performing realistic computer simulations of this process involves solving a set of partial differential equations, as well as a large number of ordinary differential equations (ODEs) characterizing the reactive behavior of the cardiac tissue. Experiments have shown that the solution of the ODEs contribute significantly to the total work of a simulation, and there is thus a strong need to utilize efficient solution methods for this part of the problem. This paper presents how an efficient implicit Runge-Kutta method may be adapted to solve a complicated cardiac cell model consisting of 31 ODEs, and how this solver may be coupled to a set of PDE solvers to provide complete simulations of the electrical activity.     

A mathematical model of the dynamic heat transfer from the respiratory tract of a chicken

A mathematical model of the dynamic (periodic) heat exchange from the respiratory tract of a chicken is postulated and solved analytically. The model expresses the periodic respiratory heat loss as a function of respiration rate, respiratory air velocity, ambient temperature and humidity ratio, and body (trachea) temperature. It is unique in that previous models have been formulated for steady state heat transfer. The processes of sensible and latent heat exchange are considered as uncoupled processes.     

The potential for establishment of axial temperature profiles during solid-state fermentation in rotating drum bioreactors

The mixing and heat transfer phenomena within rotating drum bioreactors (RDBs) used for solid-state fermentation processes are poorly studied. The potential for the establishment of axial temperature gradients within the substrate bed was explored using a heat transfer model. For growth of Aspergillus oryzae on wheat bran within a 24 L RDB with air at a superficial velocity of 0.0023 m s(-1) and 15% relative humidity, the model predicts an axial gradient between the air inlet and outlet of 2 degrees C during rapid growth, compared to experimental axial temperature gradients of between 1 and 4 degrees C. Undesirably high temperatures occur throughout the bed under these operating conditions, but the model predicts that good temperature control can be achieved using humid air (90% relative humidity) at superficial velocities of 1 m s(-1) for a 204 L RDB. For a 2200 L RDB, good temperature control is predicted with superficial velocities as low as 0.4 m s(-1) with the airflow being switched from 90% to 15% relative humidity whenever the temperature at the outlet end of the drum exceeds the optimal temperature for growth. This work suggests that significant axial temperature gradients can arise in those RDBs that lack provision for axial mixing. It is therefore advisable to use angled lifters within RDBs to promote axial mixing.     

Intermittent drying of bioproducts--an overview

Unlike the conventional practice of supplying energy for batch drying processes at a constant rate, newly developed intermittent drying processes employ time-varying heat input tailored to match the drying kinetics of the material being dried. The energy required may be supplied by combining different modes of heat transfer (e.g. convection coupled with conduction or radiation or dielectric heating simultaneously or in a pre-selected sequence) in a time-varying fashion so as to provide optimal drying kinetics as well as quality of the bioproduct. This is especially important for drying of heat-sensitive materials (such as foods, pharmaceutical, neutraceutical substances, herbs, spices and herbal medicines). Intermittent heat supply is beneficial only for materials which dry primarily in the falling rate period where internal diffusion of heat and moisture controls the overall drying rate. Periods when little or no heat is supplied for drying allow the tempering period needed for the moisture and heat to diffuse within the material. As the moisture content increases at the surface of the biomaterial during the tempering period, the rate of drying is higher when heat input is resumed. It is possible to control the heat input such that the surface temperature of the product does not exceed a pre-determined value beyond which thermal damage of the material may occur. This process results in reduction in the use of thermal energy as well as the mass of air used in convective drying. Thus, the thermal efficiency of such a process is higher. The quality of the product, as such color and ascorbic acid content, is also typically superior to that obtained with a continuous supply of heat. However, in some cases, there will be a nominal increase in drying time. In the case of microwave-assisted and heat pump drying, for example, the capital cost of the drying system can also be reduced by drying in the intermittent mode.

This paper provides an overview of the basic process, selected results from experiments and mathematical models for a variety of biomaterials dried in a wide assortment of dryers. It begins with a classification of intermittent drying processes that may be applied e.g. time-varying temperature, air flow rate, operating pressure as well as heat input by different modes and in different temporal variations. The beneficial effects of improving the quality of dried bioproducts by different intermittent processes are also included and discussed.     

Simulation of a steady-state mass-heat exchange in the respiratory tract

On the basis of Weibel respiratory tract model the mathematical model of mass and heat transfer in the lungs was solved for steady-state one-dimensional case. Coefficients of mass and heat transfer were taken from empirical expressions for canals. The model shows that independent water vapour or air heat saturation in the lungs occurs in 12-14 generations of the bronchial tree. The saturation site depends upon volume velocity of the air and functioning of the upper respiratory tract.     

Changing air mass frequencies in Canada: potential links and implications for human health

Many individual variables have been studied to understand climate change, yet an overall weather situation involves the consideration of many meteorological variables simultaneously at various times diurnally, seasonally, and yearly. The current study identifies a full weather situation as an air mass type using synoptic scale classification, in 30 population centres throughout Canada. Investigative analysis of long-term air mass frequency trends was completed, drawing comparisons between seasons and climate zones. We find that the changing air mass trends are highly dependent on the season and climate zone being studied, with an overall increase of moderate (‘warm’) air masses and decrease of polar (‘cold’) air masses. In the summertime, general increased moisture content is present throughout Canada, consistent with the warming air masses. The moist tropical air mass, containing the most hot and humid air, is found to increase in a statistically significant fashion in the summertime in 46 % of the areas studied, which encompass six of Canada’s ten largest population centres. This emphasises the need for heat adaptation and acclimatisation for a large proportion of the Canadian population. In addition, strong and significant decreases of transition/frontal passage days were found throughout Canada. This result is one of the most remarkable transition frequency results published to date due to its consistency in identifying declining trends, coinciding with research completed in the United States (US). We discuss relative results and implications to similar US air mass trend analyses, and draw upon research studies involving large-scale upper-level air flow and vortex connections to air mass changes, to small-scale meteorological and air pollution interactions. Further research is warranted to better understand such connections, and how these air masses relate to the overall and city-specific health of Canadians.     

MicroclimOz – A microclimate data set for Australia,with example applications

Many problems in pure and applied ecology require the quantification of above‐ and below‐ground microclimates. Here I describe a data set of hourly microclimates for the Australian continent, simulated from the years 1990 to 2017 across a grid of 1893 locations approx. 60 km apart. The data were generated with the NicheMapR microclimate model, driven by 0.05° gridded daily meteorological forcing data (air temperature, wind speed, humidity, cloud cover, rainfall), 0.025° elevation and 0.008° soil texture data. The above‐ground microclimate variables include horizontal plane solar radiation, solar zenith angle, sky temperature (from which down‐welling longwave radiation can be computed), air temperature, relative humidity and wind speed at 1 and 120 cm height, and snow depth. The below‐ground variables include soil temperature, pore humidity, soil moisture and soil water potential for 0, 2.5, 5, 10, 15, 20, 30, 50, 100 and 200 cm below‐ground. The computations are for four shade levels (0%, 50%, 70% and 90%). The data set can be used for a wide variety of applications, including the computation of heat and water budgets of organisms, the potential for vegetation growth, and the computation of stress and growth indices. The use of daily forcing data also allows assessments of the consequences of extreme events including heat waves. Example applications are provided for computing plant growth potential, grasshopper egg development, lizard body temperature and mammalian energy and water requirements.