Experimental Temperature Profiles Research Articles

Original article: Apparent thermal diffusivity estimation for the heat transfer modelling of pork loin under air/steam cooking treatments

SummaryApparent thermal diffusivity linear functions vs. product temperature were estimated for pork cooked under two different treatments (forced convection, FC and forced convection/steam combined, FC/S) at 100, 110, 120 and 140 °C by means of experimental time–temperature data and a developed finite‐difference algorithm. Slope and intercept of each function were employed to calculate apparent thermal diffusivity at 40, 55 and 70 °C. Generally, FC/S treatments gave significantly higher apparent thermal diffusivities in comparison with FC conditions. Apparent thermal diffusivities were used to develop a model for cooking time and final core temperature prediction on the basis of oven setting. The model was validated by means of additional cooking tests performed at different temperatures of those employed for model development. Root mean square error values lower than 3.8 °C were obtained comparing predicted and experimental temperature profiles. Percentage errors lower than 3.1% and 3.5% were, respectively, obtained for cooking times and final core temperatures.

The dual-mode heat flow meter technique: A versatile method for characterizing thermal conductivity

The dual-mode heat flow meter technique was developed for steady-state thermal characterization by optimizing the curve fit between the experimental temperature profile and the prediction from a simple analytical solution taking into account conductive as well as radiative heat transfer. The validation results were seen to be in good agreement with published literature values and demonstrated the versatility of the method. Moreover, the technique is ideally suited for characterization of anisotropic materials without necessitating any additional information about the nature of anisotropy and lends itself as an attractive alternative for characterization of novel materials with engineered transport properties.

A Theoretical and Experimental Study of Combustion Tubes

When the air injection technique is used in a reservoir, the usual way to determine the fuel that would be burned and the temperature profiles, among other parameters, is by experimentation in a combustion tube. In this work, using medium oil (27 API) from the Gulf of Mexico, combustion tube experiments were carried out. A mathematical model, which takes into account the heat transfer ahead and behind from the combustion front, the combustion zone thickness, and the heat generated and loss in the combustion front, was solved numerically and used to predict the experimental temperature profiles. After validation of the mathematical model, further investigations of the effect of heat losses (along, at the top, and at the bottom of the combustion tube) on temperature profiles were done. The calculated combustion zone temperature and temperature profiles are in good agreement with our experimental data. It was found that not considering an isolated boundary in the mathematical model allows obtaining better predictions for the temperature profiles behind and ahead from the combustion front. On the other hand, the combustion front temperature increases as the heat losses decrease and the combustion front temperature attains its maximum value when there is no heat loss.

Computational fluid dynamics simulation of a transpiring wall reactor for supercritical water oxidation

A computational fluid dynamic (CFD) model of a transpiring wall reactor for supercritical water oxidation has been implemented and solved using the commercial software Fluent 6.3. Model results have been validated by comparison with experimental temperature profiles, and the influence of model simplifications on the accuracy of the results has been discussed. It has been found that the model presents some inaccuracies in the calculation of the maximum reaction temperature, which have been attributed to the simplifications in the calculation of thermal properties of the fluids imposed by limitations of the software. The effect of different process parameters has been studied, including transpiring water flow ratio, transpiring water temperature, flow rate and composition of the oxidant (pure oxygen or air) on different indicators of reactor performance such as temperature and composition contours, flow path lines and effluent compositions. The behaviour of three different transpiring wall designs comprising different sections of porous and non-porous materials has also been investigated. It has been found that making the upper cup of the reactor of a porous material has a very little influence on reactor performance, and therefore it is preferable to build this part of the reaction chamber using a non-porous, more durable material. On the other hand, the maximum reaction temperature in the reaction chamber can be increased if the upper part of the reaction chamber is made with a non-porous material, which is favourable for treating diluted feeds. Model results complement previous information obtained by experiments and by simplified models.

Analytical and Experimental Analysis of a High Temperature Mercury Thermosyphon

High temperature thermosyphons are devices designed to operate at temperatures above 400°C. They can be applied in many industrial applications, including heat recovery from high temperature air fluxes. After a short literature review, which shows a deficiency of models for liquid metal thermosyphons, an analytical model, developed to predict the temperature distribution and the overall thermal resistance, is shown. In this model, the thermosyphon is divided into seven regions: three regions for the condensed liquid, including the condenser, adiabatic region, and evaporator; one region for vapor; one for the liquid pool; one for the noncondensable gases; and another for the tube wall. The condensation phenomenon is modeled according to the Nusselt theory for condensation in vertical walls. Numerical methods are used to solve the resulting equations and to determine the temperature distribution in the tube wall. Ideal gas law is applied for the noncondensable gases inside the thermosyphon, while the evaporator and condenser heat transfer coefficients are obtained from literature correlations. Experimental tests are conducted for thermosyphon with mercury as working fluid, designed and constructed in the laboratory. The results for two thermosyphons with different geometry configurations are tested: one made of a finned tube in the condenser region and another of a smooth tube. The finned tube presents lower wall temperature levels when compared with the smooth tube. The experimental data are compared with the proposed model for two different liquid pool heat transfer coefficients. It is observed that the comparison between the experimental data and theoretical temperature profiles is good for the condenser region. For the evaporator, where two distinct regions are observed (liquid film and pool), the comparison is not so good, independent of the heat transfer coefficient used. In a general sense, the model has proved to be a useful tool for the design of liquid metal thermosyphons.

Modeling temperature in chocolate mass to predict tempering quality

AbstractA computational model is developed to predict the temperature in chocolate as a function of space and time during a new tempering process where pellets of seed crystals of form V are added to the melted chocolate. The model, a refined version of a previous one (Debaste et al., J Food Eng. 2008, 88, 568–575) including a new expression for the heat sink, is based on the energy equation, simplified by the use of an effective thermal conductivity. A shrinking core model is used to express the heat sink term associated with the melting of pellets. The width of the limit layer around the pellets is the fitting parameter. The model is validated on experimental temperature profiles in bowls and compared to a previous kinetic model. The quality of tempering is then assessed by differential scanning calorimetry. Combining this information with the model, the quality of tempering based on the initial experimental conditions is predicted.

“Enzyme Test Bench,” a high‐throughput enzyme characterization technique including the long‐term stability

A new high throughput technique for enzyme characterization with specific attention to the long term stability, called "Enzyme Test Bench," is presented. The concept of the Enzyme Test Bench consists of short term enzyme tests in 96-well microtiter plates under partly extreme conditions to predict the enzyme long term stability under moderate conditions. The technique is based on the mathematical modeling of temperature dependent enzyme activation and deactivation. Adapting the temperature profiles in sequential experiments by optimal non-linear experimental design, the long term deactivation effects can be purposefully accelerated and detected within hours. During the experiment the enzyme activity is measured online to estimate the model parameters from the obtained data. Thus, the enzyme activity and long term stability can be calculated as a function of temperature. The engineered instrumentation provides for simultaneous automated assaying by fluorescent measurements, mixing and homogenous temperature control in the range of 10-85 +/- 0.5 degrees C. A universal fluorescent assay for online acquisition of ester hydrolysis reactions by pH-shift is developed and established. The developed instrumentation and assay are applied to characterize two esterases. The results of the characterization, carried out in microtiter plates applying short term experiments of hours, are in good agreement with the results of long term experiments at different temperatures in 1 L stirred tank reactors of a week. Thus, the new technique allows for both: the enzyme screening with regard to the long term stability and the choice of the optimal process temperature regarding such process parameters as turn over number, space time yield or optimal process duration. The comparison of the temperature dependent behavior of both characterized enzymes clearly demonstrates that the frequently applied estimation of long term stability at moderate temperatures by simple activity measurements after exposing the enzymes to elevated temperatures may lead to suboptimal enzyme selection. Thus, temperature dependent enzyme characterization is essential in primary screening to predict its long term behavior.

Laminar flame propagation on a horizontal fuel surface: Verification of classical Emmons solution

This work analyses the classical Emmons (1956) solution of flat plate laminar flame combustion on a film of liquid fuel. A two-dimensional (2D) numerical model developed for this purpose has been benchmarked with experimental results available in the literature for methanol. In the parametric study, numerical predictions have been compared with Emmons classical solution. The study shows that the Emmons solution is valid in a range of Reynolds numbers where flame anchors near the leading edge of the methanol pool and the combustion zone is confined around the hydrodynamic and thermal boundary layers. However, in cases of low free stream velocities the combustion zone is beyond the boundary layer zone and the Emmons solution deviates. In cases of very high free stream velocities, the flame moves away from the leading edge and anchors at a location downstream. The Emmons solution is not applicable in this case as well. For the fuel considered in this study (methanol), accounting for thermal radiation, employing an optically thin radiation model, allows better agreement between experimental and numerical temperature profiles but does not affect the mass burning rates.

Thermal radiation of di-tert-butyl peroxide pool fires—Experimental investigation and CFD simulation

Instantaneous and time averaged flame temperatures T ¯ , surface emissive power S E P ¯ and time averaged irradiances E ¯ of di-tert-butyl peroxide (DTBP) pool fires with d = 1.12 and 3.4 m are investigated experimentally and by CFD simulation. Predicted centerline temperature profiles for d = 1.12 m are in good agreement with the experimental emission temperature profiles for x/ d > 0.9. For d = 3.4 m the CFD predicted maximum centerline temperature at x/ d = 1.4 is 1440 K whereas the emission temperature experimentally determined from thermograms at x/ d ≈ 1.3 is 1560 K. The predicted surface emissive power for d = 1.12 m is 115 kW/m 2 in comparison to the measured surface emissive power of 130 kW/m 2 whereas for d = 3.4 m these values are 180 and 250 kW/m 2. The predicted distance dependent irradiances agree well with the measured irradiances.

Inverse segregation during transient directional solidification of an Al–Sn alloy: Numerical and experimental analysis

In this article macrosegregation phenomenon is investigated by a finite volume numerical modeling technique and by upward unidirectional solidification of an Al–23 wt%Sn alloy casting. The numerical model consists of an explicit/implicit time integration scheme to couple thermal and solutal fields. The experimental solidification set-up allows a vertically aligned macrostructure to be obtained. The concentration profile was obtained by an X-ray fluorescence spectrometry technique carried out in cylindrical slices representing certain position inside the casting from the casting/chill interface. The simulated and experimental temperature and concentration profiles are compared and very good agreement has been observed.

‘Enzyme Test Bench’: A biochemical application of the multi-rate modeling

In the expanding field of ‘white biotechnology’ enzymes are frequently applied to catalyze the biochemical reaction from a resource material to a valuable product. Evolutionary designed to catalyze the metabolism in any life form, they selectively accelerate complex reactions under physiological conditions. Modern techniques, such as directed evolution, have been developed to satisfy the increasing demand on enzymes. Applying these techniques together with rational protein design, we aim at improving of enzymes' activity, selectivity and stability. To tap the full potential of these techniques, it is essential to combine them with adequate screening methods. Nowadays a great number of high throughput colorimetric and fluorescent enzyme assays are applied to measure the initial enzyme activity with high throughput. However, the prediction of enzyme long term stability within short experiments is still a challenge. A new high throughput technique for enzyme characterization with specific attention to the long term stability, called ‘Enzyme Test Bench’, is presented. The concept of the Enzyme Test Bench consists of short term enzyme tests conducted under partly extreme conditions to predict the enzyme long term stability under moderate conditions. The technique is based on the mathematical modeling of temperature dependent enzyme activation and deactivation. Adapting the temperature profiles in sequential experiments by optimum non-linear experimental design, the long term deactivation effects can be purposefully accelerated and detected within hours. During the experiment the enzyme activity is measured online to estimate the model parameters from the obtained data. Thus, the enzyme activity and long term stability can be calculated as a function of temperature. The results of the characterization, based on micro liter format experiments of hours, are in good agreement with the results of long term experiments in 1L format. Thus, the new technique allows for both: the enzyme screening with regard to the long term stability and the choice of the optimal process temperature. The presented article gives a successful example for the application of multi-rate modeling, experimental design and parameter estimation within biochemical engineering. At the same time, it shows the limitations of the methods at the state of the art and addresses the current problems to the applied mathematics community.

Auto-cyclic reactor: Design and evaluation for the removal of unburned methane from emissions of natural gas engines

A non-adiabatic fixed bed auto-cyclic reactor (ACR) consisting of two counter-current concentric compartments was designed and built for removing low concentrations of methane from exhaust gases from natural gas engines. The length was based on simulations by a simple heterogeneous one dimensional model using literature parameters and kinetic data, while the diameter was selected to assure a linear fluid velocity between 0.5 and 2 m/s. Its innovative design consists of a judicious combination of 14 longitudinal fins welded to the outlet part of inner reactor compartment to maximize the heat transfer to the inlet section and highly active pellet type catalyst filling the space between fins to lower the ignition temperature. The experimental ACR pilot unit was loaded by a combination of highly active laboratory prepared catalysts: palladium/alumina pellets and palladium/alumina coated cordierite monoliths. The efficiency of methane removal from air and from synthetic exhaust gas containing 7 vol% CO 2 and 14 vol% H 2O was evaluated under a wide range of operating conditions: temperature from 290 to 500 °C, methane concentration between 500 and 3800 ppm. The reactor performance was monitored in terms of axial temperature profiles and methane conversion both in transient and steady state conditions. Reproducible performance of the ACR was observed even after 1200 h of cumulative operation and complete methane removal was obtained at relatively low temperatures. To simulate the obtained experimental data, a heterogeneous one-dimensional model was developed to suit the final reactor configuration using actual laboratory determined kinetic data. The model described adequately the experimental temperature profiles and methane conversion when heat transfer between the reactor compartments and heat loss were taken into account.

Development of multichannel intermediate frequency system for electron cyclotron emission radiometer on KSTAR Tokamak

Plasma experiments on KSTAR are scheduled to start up this year (2008). We have developed an electron cyclotron emission (ECE) radiometer to measure the radial electron temperature profiles in KSTAR experiments. The radiometer system consists, briefly, of two downconversion stages, amplifiers, bandpass filter banks, and video detectors. These components are made commercially or developed in house. The system detects ECE power in the frequency range from 110 to 196 GHz, the detected signal being resolved by means of 48 frequency windows. Before installation of this system on KSTAR, we installed a part of this system on large helical device (LHD) to study the system under similar plasma conditions. In this experiment, the signal amplitude, considered to be proportional to the electron temperature, is measured. The time-dependent traces of the electron temperature measured by this radiometer are in good agreement with those provided by the LHD Michelson spectrometer. The system noise level which limits the minimum measurable temperature (converted to the electron temperature) is about 30 eV.

Gravity-driven inverse segregation during transient upward directional solidification of Sn–Pb hypoeutectic alloys

Upward unidirectional solidification experiments were performed with Sn–4.0 wt.%Pb and Sn–12.5 wt.%Pb alloys. Transitory conditions of heat flow extraction were sustained during these solidification experiments, which mean that all solidification variables (cooling rate, tip growth rate, thermal gradient, and metal/mold heat transfer coefficient) have varied freely along solidification. In this work, the macrosegregation phenomenon is experimentally and theoretically evaluated considering both solidification shrinkage and gravity induced flows. The numerical model is based on a one-dimensional solution consisting of an implicit/explicit time integration scheme to couple thermal and solutal fields, which is supported by a finite volume numerical modeling technique to be solved. The applied solidification system permitted columnar growth to prevail along the castings. Since the Pb-rich melt tends to flow downward (in favor of the gravity vector), the bottom of the castings exhibited positive Pb content, mainly induced by gravity. The numerically simulated and experimental temperature and concentration profiles were compared and a very good agreement has been observed.

Validation of a Rapid Thermal Processing model in steady-state

Rapid Thermal Processing (RTP) is widely used in advanced semiconductor manufacturing. The present work deals with the heat transfer from infrared lamps to the silicon wafer in a commercial RTP equipment. Both numerical and experimental approaches are considered. For numerical purposes, the RTP system is modelled in two (2D) and three dimensions (3D). Calculations are performed in steady-state. The computational fluid dynamics method (CFD) is used for solving the mass and heat conservation equations. The radiative heat transfer equation is solved with the Monte Carlo method. In order to validate these models, measurements of the wafer temperature are realized for five electric power values supplied to the infrared lamps. The experimental wafer temperature profiles are in good agreement with the numerically calculated ones. Moreover, a confrontation between the experimental temperature of the infrared lamp filaments evaluated from the Ohm law and the one used in the numerical calculations shows a good agreement with the 3D model. The slight difference observed with the 2D model is explained. So the numerical simulations are fully validated. Two relations are established in order to predict the power which has to be applied to infrared lamps to obtain the required wafer temperature.

Thermal Modeling of Terahertz Quantum-Cascade Lasers: Comparison of Optical Waveguides

We compare a set of experimental lattice temperature profiles measured in a surface-emitting terahertz (THz) quantum-cascade laser (QCL) with the results of a 2-D anisotropic heat diffusion model. We evaluate the temperature dependence of the cross-plane thermal conductivity (kappaperp) of the active region which is known to be strongly anisotropic due to its superlattice-like nature. Knowledge of kappaperp and its temperature dependence is crucial in order to improve the temperature performance of THz QCLs and this has been used to investigate the longitudinal lattice temperature distribution of the active region and to compare the thermal properties of metal-metal and semi-insulating surface-plasmon THz optical waveguides using a 3-D anisotropic heat diffusion model.

Investigation of thermal resistive probe behaviour used in Scanning Thermal Microscope by infrared imaging system

A new approach to estimate heat fluxes lost by the thermal-resistive probe of SThM has been used. This approach is based on an experimental set-up with infrared thermography measurement system coupled with an infrared transparent material. The measurements allow us to obtain experimental temperature profiles along the probe but also, experimental temperature profiles of samples in contact with the thermal probe. A modeling combined with these experimental results allows to estimate heat fluxes participating in the thermal balance of the probe and to define the operating temperature range to use the SThM with a higher sensitivity.

Modeling the forced-air cooling process of fresh strawberry packages, Part III: Experimental validation of the energy model

The aim of this study was to validate a mathematical model previously developed for predicting the cooling rate of individual packages of strawberries (clamshells) during an industrial forced-air cooling application. The differences between the predicted and experimental profiles of the average-fruit temperature per clamshell were less than 0.7 °C (within the limits of the experimental uncertainty). The 7/8th cooling time of individual clamshells was predicted within less than 3% of the experimental value. In addition, the local performance of the model and its capability to predict the strawberry moisture loss were qualitatively analyzed. The moisture loss was predicted between 73% and 88% of the experimental value. The predicted temperature profile of individual fruits and airflow within clamshells followed the general trends experimentally determined. Finally, the results corroborated that the transport phenomena during force-air cooling applications can be modeled by decoupling the momentum transport from the transport of energy and mass.

The first transport code simulations using the trapped gyro-Landau-fluid model

The first transport code simulations using the newly developed trapped gyro-Landau-fluid (TGLF) theory-based transport model are presented. TGLF has comprehensive physics to approximate the turbulent transport due to drift-ballooning modes in tokamaks. The TGLF model is a next generation gyro-Landau-fluid model that improves the accuracy of the trapped particle response and the finite Larmor radius effects compared to its predecessor, GLF23. The model solves for the linear eigenmodes of trapped ion and electron modes, ion and electron temperature gradient modes, and electromagnetic kinetic ballooning modes in either shifted circle or shaped geometry. A database of over 400 nonlinear gyrokinetic simulations using the GYRO code has been created. A subset of 83 simulations with shaped geometry has been used to find a model for the saturation levels. Using a simple quasilinear (QL) saturation rule, remarkable agreement with the energy and particle fluxes from a wide variety of GYRO simulations is found for both shaped or circular geometry and also for low aspect ratio. Using this new QL saturation rule along with a new E×B shear quench rule for shaped geometry, the density and temperature profiles have been predicted in over 500 transport code runs and the results compared against experimental data from 96 tokamak discharges. Compared to GLF23, the TGLF model demonstrates better agreement between the predicted and experimental temperature profiles. Surprisingly, TGLF predicts that the high-k modes are found to play an important role in the central core region of low and high confinement plasmas lacking transport barriers.

Gas temperature in the cathode region of a dc glow discharge with a thermionic cathode

The gas temperature in the cathode region of a low pressure dc He–Xe glow discharge in spot mode is determined from the Doppler broadened line profile of the xenon 1s5–2p6 transition (823.16 nm), which is obtained by means of a laser atom absorption spectroscopy. The inhomogeneous temperature distribution in the radial direction has to be taken into consideration. In order to model the gas temperature distribution the heat balance equation is solved. The comparison of the experimental and theoretical temperature profiles shows good agreement.