Conditions for equivalency of countercurrent vessel heat transfer formulations.

Previous models of countercurrent blood vessel heat transfer have used one of two, different, equally valid but previously unreconciled formulations, based either on: (1) the difference between the arterial and venous vessels' average wall temperatures, or (2) the difference between those vessels' blood bulk fluid temperatures. This paper shows that these two formulations are only equivalent when the four, previously undefined, "convective heat transfer coefficients" that are used in the bulk temperature difference formulation (two coefficients each for the artery and vein) have very specific, problem-dependent relationships to the standard convective heat transfer coefficients. (The average wall temperature formulation uses those standard coefficients correctly.) The correct values of these bulk temperature difference formulation "convective heat transfer coefficients" are shown to be either: (1) specific functions of (a) the tissue conduction resistances, (b) the standard convective heat transfer coefficients, and (c) the independently specified bulk arterial, bulk venous and tissue temperatures, or (2) arbitrary, user defined values. Thus, they are generally not equivalent to the standard convective heat transfer coefficients that are regularly used, and must change values depending on the blood and tissue temperatures. This dependence can significantly limit the convenience and usefulness of the bulk temperature difference formulations.     

Quality by Design: Scale-Up of Freeze-Drying Cycles in Pharmaceutical Industry

This paper shows the application of mathematical modeling to scale-up a cycle developed with lab-scale equipment on two different production units. The above method is based on a simplified model of the process parameterized with experimentally determined heat and mass transfer coefficients. In this study, the overall heat transfer coefficient between product and shelf was determined by using the gravimetric procedure, while the dried product resistance to vapor flow was determined through the pressure rise test technique. Once model parameters were determined, the freeze-drying cycle of a parenteral product was developed via dynamic design space for a lab-scale unit. Then, mathematical modeling was used to scale-up the above cycle in the production equipment. In this way, appropriate values were determined for processing conditions, which allow the replication, in the industrial unit, of the product dynamics observed in the small scale freeze-dryer. This study also showed how inter-vial variability, as well as model parameter uncertainty, can be taken into account during scale-up calculations.     

A body temperature model for lizards as estimated from the thermal environment

A physically based model was built to predict the transient body temperature of lizards in a thermally heterogeneous environment. Six heat transfer terms were taken into account in this model: solar radiation, convective heat flow, longwave radiation, conductive heat flow, metabolic heat gain and respiratory energy loss. In order to enhance the model predictive power, a Monte Carlo simulation was employed to calibrate the bio-physical parameters of the target animal. Animal experiments were conducted to evaluate the calibrated body temperature model in a terrarium under a controlled thermal environment. To avoid disturbances of the animal, thermal infrared imagers were used to measure the land surface temperature and the body temperature. The results showed that the prediction accuracy of lizard's transient temperature was substantially increased by the use of Monte Carlo techniques (RMSE=0.59 °C) compared to standard model parameterization (RMSE=1.35 °C). Because the model calibration technique presented here is based on physical principles, it should be also useful in more complex, field situations.     

A physiological systems approach to modeling and resetting of mouse thermoregulation under heat stress

Heat stroke (HS) is a serious civilian and military health issue. Due to the limited amount of experimental data available in humans, this study was conducted on a mouse mathematical model fitted on experimental data collected from mice under HS conditions, with the assumption there is good agreement among mammals. Core temperature (T(c)) recovery responses in a mouse model consist of hypothermia and delayed fever during 24 h of recovery that represent potential biomarkers of HS severity. The objective of this study was to develop a simulation model of mouse T(c) responses and identify optimal treatment windows for HS recovery using a three-dimensional predictive heat transfer simulation model. Several bioenergetic simulation variables, including nonlinear metabolic heat production (W/m3), temperature-dependent convective heat transfer through blood mass perfusion (W/m3), and activity-related changes in circadian T(c) were used for model simulation. The simulation results predicted the experimental data with few disparities. Using this simulation model, we tested a series of ambient temperature treatment strategies to minimize hypothermia and delayed fever to accelerate HS recovery. Using a genetic algorithm, we identified eight time segments (ambient temperature = 27, 30, 31, 29, 28, 28, 27, 26°C) of 110 min total duration that optimized HS recovery in our model simulation.     

Heat transfer modeling of the tongue

The heat transfer mechanism of tongue was investigated on the basis of experimental and theoretical research. Firstly, the relationship between tongue temperature and blood perfusion was obtained from animal experiment that mainly carried out on porcine tongue, subordinate on human tongue. Secondly, a one-dimensional variable coefficients second-order inhomogeneous heat transfer equation is developed by simplifying tongue as fin cube and the analytical solution is got. The results show that the change regulations of temperature by blood perfusion rate are the same in human and porcine tongue, and also, there is a good agreement between calculation and experimental results. When checking the model with corresponding properties of human tongue, the result is also satisfied. In conclusion, predicting temperature distribution of tongue is feasible with the fin cube model.     

Modeling enzyme production with Aspergillus oryzae in pilot scale vessels with different agitation, aeration, and agitator types

The purpose of this article is to demonstrate how a model can be constructed such that the progress of a submerged fed-batch fermentation of a filamentous fungus can be predicted with acceptable accuracy. The studied process was enzyme production with Aspergillus oryzae in 550 L pilot plant stirred tank reactors. Different conditions of agitation and aeration were employed as well as two different impeller geometries. The limiting factor for the productivity was oxygen supply to the fermentation broth, and the carbon substrate feed flow rate was controlled by the dissolved oxygen tension. In order to predict the available oxygen transfer in the system, the stoichiometry of the reaction equation including maintenance substrate consumption was first determined. Mainly based on the biomass concentration a viscosity prediction model was constructed, because rising viscosity of the fermentation broth due to hyphal growth of the fungus leads to significant lower mass transfer towards the end of the fermentation process. Each compartment of the model was shown to predict the experimental results well. The overall model can be used to predict key process parameters at varying fermentation conditions.     

Evaluation of manometric temperature measurement (MTM), a process analytical technology tool in freeze drying, part III: Heat and mass transfer measurement

This article evaluates the procedures for determining the vial heat transfer coefficient and the extent of primary drying through manometric temperature measurement (MTM). The vial heat transfer coefficients (K_v) were calculated from the MTM-determined temperature and resistance and compared with K_v values determined by a gravimetric method. The differences between the MTM vial heat transfer coefficients and the gravimetric values are large at low shelf temperature but smaller when higher shelf temperatures were used. The differences also became smaller at higher chamber pressure and smaller when higher resistance materials were being freeze-dried. In all cases, using thermal shields greatly improved the accuracy of the MTM K_v measurement. With use of thermal shields, the thickness of the frozen layer calculated from MTM is in good agreement with values obtained gravimetrically. The heat transfer coefficient “error” is largely a direct result of the error in the dry layer resistance (ie, MTM-determined resistance is too low). This problem can be minimized if thermal shields are used for freeze-drying. With suitable use of thermal shields, accurate K_v values are obtained by MTM; thus allowing accurate calculations of heat and mass flow rates. The extent of primary drying can be monitored by real-time calculation of the amount of remaining ice using MTM data, thus providing a process analytical tool that greatly improves the freeze-drying process design and control.     

Comparison of heat transfer in liquid and slush nitrogen by numerical simulation of cooling rates for French straws used for sperm cryopreservation

Slush nitrogen (SN₂) is a mixture of solid nitrogen and liquid nitrogen, with an average temperature of −207 °C. To investigate whether plunging a French plastic straw (commonly used for sperm cryopreservation) in SN₂ substantially increases cooling rates with respect to liquid nitrogen (LN₂), a numerical simulation of the heat conduction equation with convective boundary condition was used to predict cooling rates. Calculations performed using heat transfer coefficients in the range of film boiling confirmed the main benefit of plunging a straw in slush over LN₂ did not arise from their temperature difference (−207 vs. −196 °C), but rather from an increase in the external heat transfer coefficient. Numerical simulations using high heat transfer (h) coefficients (assumed to prevail in SN₂) suggested that plunging in SN₂ would increase cooling rates of French straw. This increase of cooling rates was attributed to a less or null film boiling responsible for low heat transfer coefficients in liquid nitrogen when the straw is placed in the solid-liquid mixture or slush. In addition, predicted cooling rates of French straws in SN₂ tended to level-off for high h values, suggesting heat transfer was dictated by heat conduction within the liquid filled plastic straw.     

Physical constraints on temperature difference in some thermogenic aroid inflorescences

* BACKGROUNDS AND AIMS: Thermogenesis in reproductive organs is known from several plant families, including the Araceae. A study was made of the relationship between temperature increase and spadix size in the subfamily Aroideae in order to determine whether the quantitative variation of heat production among species and inflorescences of different sizes follows a physical law of heat transfer. * METHODS: Spadix temperature was measured in 18 species from eight genera of tropical Araceae from the basal clade of Aroideae, both in French Guiana and in the glasshouses of the Montreal Botanical Garden. * KEY RESULTS: A significant logarithmic relationship was found between the volume of the thermogenic spadix zone and the maximum temperature difference between the spadix and ambient air. Four heat transfer models were applied to the data (conductive heat transfer alone, convective heat transfer alone, radiative heat transfer alone, and convective and radiative heat transfers) to test if physical (geometric and thermic) constraints apply. Which heat transfer model was the most probable was determined by using the criterion of a classical minimization process represented by the least-squares method. Two heat transfer models appeared to fit the data well and were equivalent: conductive heat transfer alone, and convective plus radiative heat transfers. * CONCLUSIONS: The increase in the temperature difference between the spadix and ambient air appears to be physically constrained and corresponds to the value of a thermal model of heat conduction in an insulated cylinder with an internal heat source. In the models, a heat metabolic rate of 29.5 mW g(-1) was used, which was an acceptable value for an overall metabolic heat rate in aroid inflorescences.     

Biofilm development in a membrane-aerated biofilm reactor: effect of flow velocity on performance

The effect of liquid flow velocity on biofilm development in a membrane-aerated biofilm reactor was investigated both by mathematical modeling and by experiment, using Vibrio natriegens as a test organism and acetate as carbon substrate. It was shown that velocity influenced mass transfer in the diffusion boundary layer, the biomass detachment rate from the biofilm, and the maximum biofilm thickness attained. Values of the overall mass transfer coefficient of a tracer through the diffusion boundary layer, the biofilm, and the membrane were shown to be identical during different experiments at the maximum biofilm thickness. Comparison of the results with published values of this parameter in membrane attached biofilms showed a similar trend. Therefore, it was postulated that this result might indicate the mechanism that determines the maximum biofilm thickness in membrane attached biofilms. In a series of experiments, where conditions were set so that the active layer of the membrane attached biofilm was located close to the membrane biofilm interface, it was shown that the most critical effect on process performance was the effect of velocity on biofilm structure. Biofilm thickness and effective diffusivity influenced reaction and diffusion in a complex manner such that the yield of biomass on acetate was highly variable. Consideration of endogenous respiration in the mathematical model was validated by direct experimental measurements of yield coefficients. Good agreement between experimental measurements of acetate and oxygen uptake rates and their prediction by the mathematical model was achieved.     

Reactive extraction of penicillin G in a pilot plant Karr-column III. Modelling and simulation of the extraction process

Summary The longitudinal concentration profiles of penicillin the continuous aqueous phase of a pilot plant Karr-column of 7.6 m height was calculated by a mathematic model consisting of reaction rate and cascase models. Satisfactory agreements between calculated and measured profiles were found. The identified mass transfer coefficients are identical in the bench-scale and pilot plant columns, in the model medium and fermentation medium as well as at different stroke frequencies. The specific interfacial area are strongly influenced by these parameters. The model can be used for calculation of penicillin extraction columns of different sizes. For the layout of the columns, hydrodynamic data are needed, which, however, cannot yet be calculated on a theoretical basis.     

基于区域剖分算法的土壤碳通量空间采样策略

由于土壤碳通量在空间分布上具有很强的异质性,传统的采样方法难以对区域土壤碳通量进行精确估算,因此确定适当的采样策略对区域土壤碳通量的估算具有重要意义.本文提出一种逐点递增式采样的区域剖分部署策略(RDPG):设定初始采样点,使用改进的凸包插值算法构造Delaunay三角网,根据邻近已知采样点插值计算三角形各边垂直平分线的交点的离散度,选择离散度最大的点作为新增采样点.采用该方法对变异系数为0.42～0.59的仿真试验区域进行多次试验,结果表明:在相同试验条件下,RDPG布局策略能够获得比随机采样和均匀采样策略更高的区域土壤碳通量估算准确度.RDPG方法考虑了区域土壤碳通量的空间异质性,提高了区域土壤碳通量拟合精度.     

Comparison of two methods for designing calorimeters using stirred tank reactors

Calorimetry is a robust method for online monitoring and controlling bioprocesses in stirred tank reactors. Up to now, reactor calorimeters have not been optimally constructed for pilot scale applications. Thus, the objective of this paper is to compare two different ways for designing reactor calorimeters and validate them. The “heat capacity” method based on the mass flow of the cooling liquid in the jacket was compared with the “heat transfer” method based on the heat transfer coefficient continuously measured in the cultivation of Escherichia coli VH33 in a 50 L stirred tank reactor. It was found that the values of the “heat transfer” method agreed very well with the calculated values from the oxygen consumption. By contrast, the curve of the “heat capacity” method deviated from that of the oxygen consumption calculated with the oxycaloric equivalent. In conclusion, the “heat transfer” method has been proven to have a higher degree of validity than the “heat capacity” method. Thus, it is a better and more robust means to measure heat generation of fermentations in stirred tank bioreactors on a pilot scale. Biotechnol. Bioeng. 2013; 110: 180–190. © 2012 Wiley Periodicals, Inc.     

Cultivation of a filamentous mold in a glass pilot-scale airlift fermentor

Results of pilot plant studies using a glass airlift fermentation device (55 liter fermentation volume) have proven the relative merits of such a system in the fermentation of a filamentous mold, Monascus purpureus, on 4% (w/w) starch media. The resultant overall yield of cell mass (Y_x/s) of 0.38 was an appreciable increase over the 0.32 obtained with a pilot scale stirred tank fermentor previously studied. Power requirements of the airlift fermentor were approximately 50% of those for the mechanically agitated system. The lack of mechanical shear in the airlift system provides a more gentle environment or the cultivation of organisms than does the high degree of shear prevalent in the mechanically agitated vessels. Mass transfer of oxygen to the aqueous phase of the fermentation volume is improved significantly through use of the airlift device. Mass transfer coefficients in the range of 200 reciprocal hr were obtained to approximately 80 reciprocal hr in the stirred tank fermentor.     

Development of a novel reactor for the oxidative degradation of straw

A pilot scale system and a computer model have been developed to evaluate the performances of a novel straw pyrolyzer based on direct (convective) heating. A horizontal cylindrical reactor is continuously fed from the end by straw, while hot gas enters through holes distributed along the lateral surface. The model includes the unsteady, two-dimensional conservation equations of heat and mass transfer for the solid and the gas phase, the generalized Darcy law and a multi-step devolatilization mechanism. Numerical simulations have been carried out to investigate the influences of gas temperature and gas to straw ratio. It was found that the key parameter for high conversion of straw to volatile products and char is the solid residence time. Predicted and measured conversion efficiencies compared well.     

Multi-spectral mapping of reef bathymetry and coral cover; Kailua Bay,Hawaii

We used high-resolution, airborne, digital, multi-spectral imagery to map bathymetry and the percent of living coral in the nearshore marine environment of Kailua Bay, Oahu, Hawai'i. Three spectral bands, with centers at 488, 551, and 577 nm (each with a full-width half maximum of 10 nm), were selected for good water transmission and good coral/sand/algae discrimination. However, the third band (577 nm) was not used in the depth and bottom-type solutions. The spatial resolution of 1 m per pixel was selected to balance resolution with the size of the total data set. A radiative transfer model accounting for the optical effects of the atmosphere, ocean surface, water, and reflection off the ocean bottom substrates was applied to the multi-spectral images, normalizing multiple images to one another for a mosaic that spans the bay. Atmospheric parameters in the radiative transfer model were estimated from published values measured for similar environments. Water-attenuation coefficients for the model were determined from the observed spectral data values over the sand bottom type in the bay. Relative depth and bottom-type coefficients were derived by a method most simply described as the "differencing" of two spectral bands. Accuracy exceeding 85% in predicted depth was achieved to a depth of 25 m. Depth prediction errors were assessed with comparison to hydrographic survey data. Classification of bottom-type coefficients into seven "percent living coral" categories results in 77% overall accuracy tested by diver-obtained line-intercept transect data (ground truth). Bottom-type coefficients derived by the model were corrected for atmospheric and ocean conditions on the date of collection, so spatial changes in bathymetry and "percent living coral" through time can be analyzed and related to environmental factors. The radiative transfer model and the "differencing" method used to solve for depth and "percent living coral" can be applied to any airborne, passive remote sensing digital data with appropriate spectral bands.     

Boundary Conditions for Heat Transfer and Evaporative Cooling in the Trachea and Air Sac System of the Domestic Fowl: A Two-Dimensional CFD Analysis

Various parts of the respiratory system play an important role in temperature control in birds. We create a simplified computational fluid dynamics (CFD) model of heat exchange in the trachea and air sacs of the domestic fowl (Gallus domesticus) in order to investigate the boundary conditions for the convective and evaporative cooling in these parts of the respiratory system. The model is based upon published values for respiratory times, pressures and volumes and upon anatomical data for this species, and the calculated heat exchange is compared with experimentally determined values for the domestic fowl and a closely related, wild species. In addition, we studied the trachea histologically to estimate the thickness of the heat transfer barrier and determine the structure and function of moisture-producing glands. In the transient CFD simulation, the airflow in the trachea of a 2-dimensional model is evoked by changing the volume of the simplified air sac. The heat exchange between the respiratory system and the environment is simulated for different ambient temperatures and humidities, and using two different models of evaporation: constant water vapour concentration model and the droplet injection model. According to the histological results, small mucous glands are numerous but discrete serous glands are lacking on the tracheal surface. The amount of water and heat loss in the simulation is comparable with measured respiratory values previously reported. Tracheal temperature control in the avian respiratory system may be used as a model for extinct or rare animals and could have high relevance for explaining how gigantic, long-necked dinosaurs such as sauropoda might have maintained a high metabolic rate.     

Systematic simulation of a tubular recycle reactor on the basis of pilot plant experiments

Systematic simulation may decisively help in development and optimization of bioprocesses. By applying simulation techniques, optimal use can be made of experimental data, decreasing development costs and increasing the accuracy in predicting the behavior of an industrial scale plant.The procedure of the dialogue between simulation and experimental efforts will be exemplified in a case study. Alcoholic fermentation of glucose by zymomonas mobilis bacteria in a gasified tubular recycle reactor was studied first by systematic simulation, using a computer model based solely on literature data. On the base of the results of this simulation, a 0.013 m³ pilot plant reactor was constructed. The pilot plant experiments, too, were based on the results of the systematic simulation.Simulated and experimental data were well in agreement. The pilot plant experiments reiterated the trends and limits of the process as shown by the simulation results. Data from the pilot plant runs were then used to improve the simulation model. This improved model was subsequently used to simulate the performances of an industrial scale plant. The results of this simulation are presented. They show that the alcohol fermentation in a tubular recycle reactor is potentially advantageous to other reactor configurations, especially to continuous stirred tanks.List of Symbols CPFR Continous plug flow reactor - CST R Continous stirred tank reactor - CTR Continous tubular reactor - FMC Fermentation micro computer - P kg/m³ Product concentration - S kg/m³ Glucose concentration - S _o kg/m³ Glucose concentration in the feed - X kg/m³ Biomass concentration - z Cell damage     

Temperature evolution in tissues embedded with large blood vessels during photo-thermal heating

During laser-assisted photo-thermal therapy, the temperature of the heated tissue region must rise to the therapeutic value (e.g., 43 °C) for complete ablation of the target cells. Large blood vessels (larger than 500 micron in diameter) at or near the irradiated tissues have a considerable impact on the transient temperature distribution in the tissue. In this study, the cooling effects of large blood vessels on temperature distribution in tissues during laser irradiation are predicted using finite element based simulation. A uniform flow is assumed at the entrance and three-dimensional conjugate heat transfer equations in the tissue region and the blood region are simultaneously solved for different vascular models. A volumetric heat source term based on Beer–Lambert law is introduced into the energy equation to account for laser heating. The heating pattern is taken to depend on the absorption and scattering coefficients of the tissue medium. Experiments are also conducted on tissue mimics in the presence and absence of simulated blood vessels to validate the numerical model. The coupled heat transfer between thermally significant blood vessels and their surrounding tissue for three different tissue-vascular networks are analyzed keeping the laser irradiation constant. A surface temperature map is obtained for different vascular models and for the bare tissue (without blood vessels). The transient temperature distribution is seen to differ according to the nature of the vascular network, blood vessel size, flow rate, laser spot size, laser power and tissue blood perfusion rate. The simulations suggest that the blood flow through large blood vessels in the vicinity of the photothermally heated tissue can lead to inefficient heating of the target.     

An evaluation of the wind chill factor: its development and applicability.

The wind chill factor has become a standard meteorologic term in cold climates. Meteorologic charts provide wind chill temperatures meant to represent the hypothetical air temperature that would, under conditions of no wind, effect the same heat loss from unclothed human skin as does the actual combination of air temperature and wind velocity. As this wind chill factor has social and economic significance, an investigation was conducted on the development of this factor and its applicability based on modern heat transfer principles. The currently used wind chill factor was found to be based on a primitive study conducted by the U.S. Antarctic Service over 50 years ago. The resultant equation for the wind chill temperature assumes an unrealistic constant skin temperature and utilizes heat transfer coefficients that differ markedly from those obtained from equations of modern convective heat transfer methods. The combined effect of these two factors is to overestimate the effect of a given wind velocity and to predict a wind chill temperature that is too low.