Electrochemical reaction with RedOx electrolyte in toroidal conduits in the presence of natural convection

Transport processes in an upright, concentric, annular, electrochemical reactor filled with RedOx electrolyte solution are studied experimentally and theoretically. The electrodes form the two vertical surfaces of the reactor. The theoretical calculations consist of the solution of the Navier–Stokes and the Nernst–Planck equations accounting for species’ diffusion, migration, convection, and electrochemical reactions on the electrodes’ surfaces as a function of the difference in electrodes’ potentials and the average concentration of the electrolyte. Since the convection is driven by density gradients, the momentum and mass transport equations are coupled. The current transmitted through the electrolyte is significantly enhanced by natural convection. The current is measured as a function of the difference in the electrodes’ potentials. To obtain the reaction rate constants, an inverse problem is solved and the reaction rate constants are determined by minimizing the discrepancy between theoretical predictions and experimental observations. As an example, we study the reversible electrochemical reaction Fe⁺⁺⁺ + e⁻ = Fe⁺⁺ on platinum electrodes.     

An iterative regularization method in simultaneously estimating the inlet temperature and heat-transfer rate in a forced-convection pipe

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown space- and time-dependent inlet temperature and heat-transfer rate on the external wall of a pipe system using temperature measurements at two different locations. It is assumed that no prior information is available on the functional form of the unknown inlet temperature and heat-transfer rate; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The accuracy of the inverse analysis is examined by using simulated exact and inexact temperature measurements. Results show that an excellent estimation on the space- and time-dependent inlet temperature and heat-transfer rate can be obtained for the test case considered in this study.     

A benchmark solidification experiment on an Sn–10%wtBi alloy

The solidification of a 90/10%wt tin–bismuth alloy has been analyzed experimentally for a 50 × 60 × 10 mm ingot. The heat flux was extracted from one vertical side of the ingot. Instantaneous temperature measurements were performed using a lattice of 25 thermocouples located on one of the large sides of the sample. The temperature versus time curve exhibits the classical pseudo-plateau as well the eutectic step. A post-mortem analysis of the samples was carried out. Solidification is almost columnar over the range of solidification rates considered. Two types of segregations are observed. X-ray analysis reveals the development of segregated channels near the cold wall. Analysis of the solute composition shows the existence of significant macro-segregations. The locations of the segregations are confirmed by the measurements of the eutectic fraction.     

An iterative regularization method in estimating the transient heat-transfer rate on the surface of the insulation layer of a double circular pipe

In this study, a conjugate gradient method based inverse algorithm is applied to estimate the unknown space- and time-dependent heat-transfer rate on the surface of the insulation layer of a double circular pipe heat exchanger using temperature measurements. It is assumed that no prior information is available on the functional form of the unknown heat-transfer rate; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The accuracy of the inverse analysis is examined by using simulated exact and inexact temperature measurements. Results show that an excellent estimation on the space- and time-dependent heat-transfer rate can be obtained for the test case considered in this study.     

Nanostructured PbO materials obtained in situ by spray solution technique for Li-ion batteries

This paper describes a systematic study of the effect of various spray pyrolysis parameters, such as temperature, solution concentration and solution flow rate on the morphology, crystallization process, crystal size, specific surface area and electrochemical performance of in situ prepared α-PbO spherically agglomerated nano-structured powders. Different analytical methods such as XRD, SEM, TEM, BET gas sorption specific surface area measurements and electrochemical tests were performed. Crystallites in the range of 20–120 nm and easily dispersed powders were reproducibly prepared by optimization of the spray conditions. An increase of the temperature from 600 to 800 °C was found to lead to a three times increase in the average crystal size, from 31 to 102 nm. An increase of concentration from 0.15 to 0.5 M dramatically suppresses the crystal size from 127 to 25 nm. The BET surface area of sprayed PbO powders is increased up to 6.6 m² g⁻¹. For such PbO powders applied as anode materials in Li-ion batteries, we have managed to retain a reversible capacity above 60 mAh g⁻¹ beyond 50 cycles.     

A new approach using artificial neural networks for determination of the thermodynamic properties of fluid couples

This paper presents a new approach using artificial neural networks (ANN) to determine the thermodynamic properties of two alternative refrigerant/absorbent couples (LiCl–H₂O and LiBr + LiNO₃ + LiI + LiCl–H₂O). These pairs can be used in absorption heat pump systems, and their main advantage is that they do not cause ozone depletion. In order to train the network, limited experimental measurements were used as training and test data. Two feedforward ANNs were trained, one for each pair, using the Levenberg–Marquardt algorithm. The training and validation were performed with good accuracy. The correlation coefficient obtained when unknown data were applied to the networks was 0.9997 and 0.9987 for the two pairs, respectively, which is very satisfactory. The present methodology proved to be much better than linear multiple regression analysis. Using the weights obtained from the trained network, a new formulation is presented for determination of the vapor pressures of the two refrigerant/absorbent couples. The use of this new formulation, which can be employed with any programming language or spreadsheet program for estimation of the vapor pressures of fluid couples, as described in this paper, may make the use of dedicated ANN software unnecessary.     

Simultaneous estimation of heat-transfer rate and coolant fluid velocity in a transpiration cooling process

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat-transfer rate on the heated surface and coolant fluid velocity in a transpiration cooling process using temperature measurements of the porous medium and coolant fluid. It is assumed that no prior information is available on the functional forms of the unknown heat-transfer rate and coolant fluid velocity; hence the procedure is classified as the function estimation inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The accuracy of the inverse analysis is examined by using simulated exact and inexact temperature measurements. Results show that an excellent estimation on the time-dependent heat-transfer rate and coolant fluid velocity can be obtained for the test case considered in this study.     

INVERSE FORCED CONVECTION PROBLEM OF SIMULTANEOUS ESTIMATION OF TWO BOUNDARY HEAT FLUXES IN IRREGULARLY SHAPED CHANNELS

This article deals with the use of the conjugate gradient method of function estimation for the simultaneous identification of two unknown boundary heat fluxes in channels with laminar flows. The irregularly shaped channel in the physical domain is transformed into a parallel plate channel in the computational domain by using an elliptic scheme of numerical grid generation. The direct problem, as well as the auxiliary problems and the gradient equations, required for the solution of the inverse problem with the conjugate gradient method are formulated in terms of generalized boundary-fitted coordinates. Therefore, the solution approach presented here can be readily applied to forced convection boundary inverse problems in channels of any shape. Direct and auxiliary problems are solved with finite volumes. The numerical solution for the direct problem is validated by comparing the results obtained here with benchmark solutions for smoothly expanding channels. Simulated temperature measurements containing random errors are used in the inverse analysis for strict cases involving functional forms with discontinuities and sharp corners for the unknown functions. The estimation of three different types of inverse problems are addressed in the paper: (i) time-dependent heat fluxes; (ii) spatially dependent heat fluxes; and (iii) time and spatially dependent heat fluxes.     

A Lie-group shooting method for reconstructing a past time-dependent heat source

We consider an inverse problem for the reconstruction of a past unknown time-dependent heat source H(t), t < t_f, in a heat conduction equation T_t(x,t) = T_xx(x,t) + H(t) with the aid of an extra measurement of temperature gradient on the left-boundary, where a final time condition is measured at the present terminal time t_f. This inverse problem is quite difficult to be solved numerically owing to a twofold ill-posedness, as a combination of the backward heat conduction problem and the inverse heat source identification problem, which is abbreviated as inverse heat source/backward heat conduction problem (IHSBHCP). The new method proposed here, namely the Lie-group shooting method (LGSM), is examined through the tests by several numerical examples. Although the recovery of an unknown heat source is carried out under a presently measured temperature at a final time and under a large measurement noise both imposed on the final time data and all boundary data, the LGSM still works effectively and accurately. The accuracy in the reconstruction of H(t) is almost uneffected by different levels of noise.     

Estimation of heat flux and temperature distributions in a composite strip and homogeneous foundation

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat flux and temperature distributions for the system composed of a multi-layer composite strip and semi-infinite foundation, from the knowledge of temperature measurements taken within the strip. It is assumed that no prior information is available on the functional form of the unknown heat flux; hence the procedure is classified as the function estimation in inverse calculation. Results show that an excellent estimation on the time-dependent heat flux can be obtained for the test case considered in this study.     

Ion-implantation modification of lithium–phosphorus oxynitride thin-films

Among various solid electrolytes, the lithium–phosphorus oxynitride (Lipon) electrolyte synthesized by sputtering of Li₃PO₄ in pure N₂ has a good ionic conductivity of 2(±1)×10⁻⁶ S cm⁻¹ at 25° C. As the nitrogen concentration increases in the Lipon electrolyte, the ionic conductivity is reported to increase as a result of a higher degree of cross-links. When Lipon films are deposited by sputtering, however, it is reported that the maximum nitrogen concentration saturates approximately at 6 at.%. By non-equilibrium processes, such as ion-implantation, nitrogen concentration can be controlled over 6 at.%. This study investigates the effect of nitrogen concentration on the ionic conductivity in Lipon films by using ion-implantation. Impedance measurements at 25° C show that the nitrogen-implanted Lipon films enhance or retard the ionic conductivity over a wide range after nitrogen-implantation, when compared with as-deposited thin-films.     

Optimization of ethanol production from sweet sorghum (Sorghum bicolor) juice using response surface methodology

Sweet sorghum juice was fermented into ethanol using Saccharomyces cerevisiae (ATCC 24858). Factorial experimental design, regression analysis and response surface method were used to analyze the effects of the process parameters including juice solid concentration from 6.5 to 26% (by mass), yeast load from 0.5 g L⁻¹ to 2 g L⁻¹ and fermentation temperature from 30 °C to 40 °C on the ethanol yield, final ethanol concentration and fermentation kinetics. The fermentation temperature, which had no significant effect on the ethanol yield and final ethanol concentration, could be set at 35 °C to achieve the maximum fermentation rate. The yeast load, which had no significant effect on the final ethanol concentration and fermentation rate, could be set at 1 g L⁻¹ to achieve the maximum ethanol yield. The juice solid concentration had significant inverse effects on the ethanol yield and final ethanol concentration but a slight effect on the fermentation rate. The raw juice at a solid concentration of 13% (by mass) could be directly used during fermentation. At the fermentation temperature of 35 °C, yeast solid concentration of 1 g L⁻¹ and juice solid concentration of 13%, the predicted ethanol yield was 101.1% and the predicted final ethanol concentration was 49.48 g L⁻¹ after 72 h fermentation. Under this fermentation condition, the modified Gompertz's equation could be used to predict the fermentation kinetics. The predicted maximum ethanol generation rate was 2.37 g L⁻¹ h⁻¹.     

Time evolution of double-diffusive convection in a vertical cylinder with radial temperature and axial solutal gradients

The characteristics of transient double-diffusive convection in a vertical cylinder are numerically simulated using a finite element method. Initially the fluid in the cavity is at uniform temperature and solute concentration, then constant temperature and solute concentration, which are lower than their initial values, are imposed along the sidewall and bottom wall, respectively. The time evolution of the double-diffusive convection is investigated for specific parameters, which are the Prandtl number, Pr = 7, the Lewis number, Le = 5, the thermal Grashof number, Gr_T = 10⁷, and the aspect ratio, A = 2, of the enclosure. The objective of the work is to identify the effect of the buoyancy ratio (the ratio of solutal Grashof to thermal Grashof numbers: N = Gr_S/Gr_T) on the evolution of the flow field, temperature and solute field in the cavity. It is found that initially the fluid near the bottom wall is squeezed by the cold flow from the sidewall, a crest of the solute field forms and then pushed to the symmetry line. In the case of N > 0, a domain with higher temperature and weak flow (dead region) forms on the bottom wall near the symmetry line, and the area of dead region increases when N varies from 0.5 to 1.5. More crests of the solute field are formed and the flow near the bottom wall fluctuates continuously for N < 0. The frequency of the fluctuation increases when N varies from −0.5 to −1.5. Corresponding to the variety of the thermal and solutal boundary layers, the average rates of heat transfer (Nu) at the sidewall remain almost unchanged while the average rates of mass transfer (Sh) at the bottom wall change much in the cases of N = 1, 0, −1.     

Investigation of NCN and prompt-NO formation in low-pressure C1–C4 alkane flames

Temperature, CH, NCN, and NO profiles were measured for eight low-pressure hydrocarbon flames fueled by methane, ethane, propane, and butane using laser-induced fluorescence (LIF) diagnostics. These measurements were used (1) to assess NCN and prompt-NO formation chemistry across a series of fuels of increasing number of carbons at different equivalence ratios (? = 1.07 and 1.28); (2) to examine the predictive capabilities of current C1–C4 hydrocarbon and NCN formation/consumption combustion mechanisms on properly capturing prompt-NO formation and (3) to examine the postulation that additional prompt-NO precursors (other than CH) exist for fuels larger than methane. For a given equivalence ratio, the measured peak CH concentration is fairly constant across all four fuels, while both the peak NCN and post-flame NO concentrations steadily increase. Furthermore, it is found that as the fuels increase in number of carbons, i.e., methane to butane, the correlation between the peak NCN and post-flame NO remains high, while the correlation between peak CH and peak NCN and peak CH and post-flame NO becomes increasingly lower. This is especially evident for rich flame cases. The experimental profiles are compared to numerical calculations using two comprehensive kinetic mechanisms suitable for C4 chemistry, where the CH + N₂ → NCN + H reaction is assumed as the only prompt-NO initiation reaction. For the ? = 1.28 flame cases, CH is over-predicted using both mechanisms for all four fuels and by as much as 60%, while for the ? = 1.07 cases, CH is predicted to within 15% of the experimentally-derived results, although there is some discrepancy concerning the spatial locations of the CH profiles. For both NCN and NO, there is an increasing under-prediction for the ? = 1.28 cases as the fuel increases in number of carbons, while for the ? = 1.07 cases there is a systematic under-prediction of NCN and NO with a weaker (although evident) fuel dependence. From the experimental results and the comparison to modeling predictions, it is apparent that additional work concerning CH formation and consumption kinetics is necessary to accurately capture the CH concentration profiles across a broad range of conditions. Furthermore the comparisons to the modeling predictions using only a single prompt-NO precursor, CH, indicate a reasonable plausibility that (an) additional prompt-NO precursor (s) exist and become important when considering fuels larger than methane, especially under rich flame conditions. Possible precursors in addition to CH are discussed.     

An inverse problem in simultaneous estimating the Biot numbers of heat and moisture transfer for a porous material

A conjugate gradient method based inverse algorithm is applied in the present study in simultaneous determining the unknown time-dependent Biot numbers of heat and moisture transfer for a porous material based on interior measurements of temperature and moisture.It is assumed that no prior information is available on the functional form of the unknown Biot numbers in the present study, thus, it is classified as the function estimation in inverse calculation.The accuracy of this inverse heat and moisture transfer problem is examined by using the simulated exact and inexact temperature and moisture measurements in the numerical experiments. Results show that the estimation on the time-dependent Biot numbers can be obtained with any arbitrary initial guesses on a Pentium IV 1.4 GHz personal computer.     

A self-adaptive LGSM to recover initial condition or heat source of one-dimensional heat conduction equation by using only minimal boundary thermal data

The present study is concerned with the recovery of an unknown initial condition for a one-dimensional heat conduction equation by using only the usual two boundary conditions of the direct problem for heat equation. The algorithm assumes a function for the unknown initial condition and derives an inverse problem for estimating a spatially-dependent heat source F(x) in T_t(x, t) = T_xx(x, t) + F(x). A self-adaptive Lie-group shooting method, namely a Lie-group adaptive method (LGAM), is developed to find F(x), and then by integrations or by solving a linear system we can extract the information for unknown initial condition. The new method possesses twofold advantages in that no a priori information of unknown functions is required and no extra data are needed. The accuracy and efficiency of present method are confirmed by comparing the estimated results with some exact solutions.     

Fluid flow and convective heat transfer in flat microchannels

This study investigates the design, construction and instrumentation of an experimental microchannel, with a rectangular cross-section and large aspect ratio, that allows characterization of the flow and convective heat transfer under well defined and precise conditions and makes it possible to vary the hydraulic diameter of the microchannel. The flow friction coefficient is estimated by direct pressure drop measurements inside the microchannel in a zone where the flow is fully developed. Since the wall thermal conditions inside the microchannel can not be measured directly, their estimation requires temperature measurements in the wall thickness and an inverse heat conduction method. The thermal and hydrodynamic results obtained by varying the hydraulic diameter between 1 mm and 100 μm do not deviate from the theory or empirical correlations for large-scale channels. These results let us confirm that for smooth walls the continuum mechanics laws for convection and fluid mechanics remain valid in microchannels of hydraulic diameter greater than or equal to 100 μm.     

Estimation of temperature dependent heat transfer coefficient in a vertical rectangular fin using liquid crystal thermography

This paper presents a methodology for the estimation of temperature dependent heat transfer coefficient for a vertical rectangular fin by using the inverse heat transfer method with Liquid crystal thermography (LCT) data. Steady state, laminar natural convection experiments have been done on a vertical rectangular fin of size 150 × 250 × 4, (L × w × t, all dimensions are in mm). The variation of heat transfer coefficient is considered as a power law function of temperature excess (h = a_oθ^b) and is derived from the basic Nusselt number equation used for laminar natural convection, Nu = aRa^b. With this functional form, the one dimensional fin equation in finite difference form is repeatedly solved using the Gauss–Seidel iterative method. Treating this as a one parameter estimation in ‘a’ the sum of the squares of the difference between the simulated and Thermochromic Liquid Crystal (TLC) measured temperatures is minimized with the Golden section search algorithm to retrieve ‘a’. Estimate of ‘a’ and the accompanying uncertainties are first reported for synthetically generated temperature distribution for assumed values of ‘a’. The effect of noise on the estimate of ‘a’ is discussed. This is followed by retrievals with experimentally obtained TLC temperature distribution for a range of heat inputs to the fin base. The required temperature distributions for accomplishing the retrievals over the surface are obtained using calibrated R40C5W Thermochromic Liquid Crystal (TLC) sheets. As an additional proof of the accuracy of the method, the retrieved value of ‘a’ is used to simulate the temperature distribution in the fin which is then compared with the actual TLC measured temperature distribution.     

Inverse problem of estimating time-dependent heat generation in a frictional heated strip and foundation

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent frictional heat generation for the tribosystem consisting of a semi-infinite foundation and a plane-parallel strip sliding over its surface, from the knowledge of temperature measurements taken within the foundation. It is assumed that no prior information is available on the functional form of the unknown heat generation; hence the procedure is classified as the function estimation in inverse calculation. Results show that an excellent estimation on the time-dependent heat generation can be obtained for the test case considered in this study. The current methodology can be applied to the prediction of heat generation in engineering problems involving sliding-contact elements.     

A two-stage Lie-group shooting method (TSLGSM) to identify time-dependent thermal diffusivity

We consider an inverse problem for identifying a time-dependent thermal diffusivity α(t) in a heat conduction equation T_t(x, t) = α(t)T_xx(x, t), with the aid of an extra measurement of temperature at an internal point of a rod. Because the data are acquired at an inner point we require to develop a two-stage Lie-group shooting method (TSLGSM) to solve this inverse problem. The present approach is novel and is examined through some numerical tests. By comparing the calculated results with exact ones we can assure that the TSLGSM is an accurate and efficient method, whose estimation error is small even for the identification of a discontinuous and oscillatory thermal diffusivity. Under noise, the identified solutions are also acceptable.