Shape Of Probability Density Function Research Articles

Micro-constructive Damage Model of Dry-Wet Cyclic Red Clay Based on Weibull Distribution

Abstract To address the strength damage of red clay under dry-wet cycles, systematic conventional triaxial tests under specific circumferential pressure and scanning electron microscope observation were carried out to describe the damage evolution of soil units under load conditions of dry-wet cycle red clay microunits based on the Weibull distribution. Damage variable expressions obeying the Weibull distribution were established and the micro-parameter pore area ratio and the macro-parameter dry-wet cycle number were introduced. The cross-scale characterization of macroscopic and microscopic parameters was realized by combining the damage mechanics equation of red clay under loading. The microscopic damage intrinsic model of red clay considering the number of dry-wet cycles was constructed. The model was verified to be reasonable and effective based on triaxial tests, in which the calculation errors of the secant modulus damage threshold, probability density function shape parameter, and dry-wet cycle red clay damage stress were within 10 %, 5 %, and 5 %, respectively.

Application of maximum statistical entropy in formulating a non-gaussian probability density function in flow uncertainty analysis with prior measurement knowledge

In mechanical, civil and chemical engineering systems the accuracies of flow measurement instruments is conventionally specified by certified measurement capabilities (CMCs) that are symmetric, however it is physically possible for some flow instruments and equipment to exhibit asymmetric non-Gaussian behaviour. In this paper the influence of non-Gaussian uncertainties is investigated using direct Monte Carlo simulations to construct a probability density function (PDF) using representative non-Gaussian surface roughness data for a commercial steel pipe friction factor. Actual PDF results are compared and contrasted with a symmetric Gaussian PDF, and reveal inconsistencies in the statistical distributions that cannot be neglected in high accuracy flow measurements. The non-Gaussian PDF is visualized with a kernel density estimate (KDE) scheme to infer an initial qualitative shape of the actual PDF using the approximate locations of the normalized peaks as a initial metrologist estimate of the measurement density. This is then utilized as inputs in a maximum statistical entropy functional to optimize the actual non-Gaussian PDF using a nonlinear optimization of Lagrange multipliers for a mathematically unique PDE. Novelties in the present study is that a new methodology has been developed for statistical sampling from non-monotonic non-Gaussian distributions with accompanying Python and Matlab/GNU Octave computer codes, and a new methodology for utilizing metrologist's expert prior knowledge of PDF peaks and locations for constructing an a priori estimate of the shape of unknown density have been incorporated into the maximum statistical entropy nonlinear optimization problem for a faster and more efficient approach for generating statistical information and insights in constructing high accuracy non-Gaussian PDFs of real world messy engineering measurements.

A DPIM-based probability analysis framework to obtain railway vehicle vibration characteristics considering the randomness of OOR wheel

The OOR (out-of-roundness) wheel is one of the main excitation sources causing vehicle vibration. However, the OOR wheel occurs randomly, indicating that the vibration behavior of a vehicle cannot be comprehensively evaluated using a deterministic approach. Thus, a probability analysis framework is proposed to obtain vehicle vibration characteristics while considering the randomness of the OOR wheel. The probability model of the random OOR wheel is derived by reducing the high-dimensional variables into a few independent variables of the radius, amplitude, and phase. Then, the vertical vehicle-track coupled system with OOR wheels is modelled. A DPIM (direct probability integral method) is further developed to analyze the evolution of excitation to response probabilities. Finally, the statistics of the random vibration of the vehicle are calculated. The proposed framework is verified using a numerical case. Results show that the PDF (probability density function) shape of the vehicle random vibration, induced by the Gaussian-distributed OOR wheel, deviates from the Gaussian distribution due to the nonlinear wheel/rail contact force. Instead, it exhibits a right-skewed shape, significantly impacting the dynamic performance. As the mean or coefficient of variation of the OOR wheel amplitude increases linearly, the reliability of the vehicle Sperling index experiences a quadratic or double-sloping decrease. Consequently, a maintenance threshold for OOR wheel amplitudes is given based on reliability considerations. Compared to Monte Carlo simulation, the proposed framework offers a computational efficiency improvement of at least one order of magnitude.

Determination of measurement uncertainty by a Monte Carlo method for an RF power sensor calibration system using a VNA

This work proposes a systematic assessment of measuring type A uncertainty (caused by random errors) used in RF power sensor calibration. To reduce A type uncertainty, several successive measurements are repeated. The uncertainty arises from repeatability errors in connectors caused by changes in their electrical properties during repeated mating. The suitability of the METAS UncLib software was analysed and we concluded that software should be developed to take into account the shape of probability density function (PDF) using a Monte Carlo method (MCM), which was lacking in METAS UncLib. The self-developed software was then tested on an example taken from the literature and the superiority of the MCM over the analytical method (GUM) was confirmed. During the calibration of the RF sensor using a vector network analyzer (VNA), a series of repeated measurements were performed and, after applying our MCM software, it was found that the measurement uncertainties calculated by the MCM method were several times larger than those by the GUM. The reason for this was that the correlation between the measured input quantities was not taken into account. When this was done using a covariance matrix and assuming a normal PDF of the input quantities, the results obtained with the GUM and the MCM converged. Our main objective was to investigate the influence of the PDF shape of the input measurement samples on the measurement uncertainty. Taking more than a dozen measurements is too costly, on the other hand, the small sample size prevents a reliable determination of the PDF shape. Finally, to overcome this inconvenience, we have developed a special method that uses the histograms of standardized input data taken at all measurement frequencies under fixed conditions without disconnecting the connectors, to increasing the total number of results which were needed to create the PDF histograms of input quantities.

Cosmic birefringence from the Axiverse

We revisit the evidence for CMB birefringence in the context of a rich Axiverse. Using probability density functions (PDFs) for various axion parameters,such as the mass and axion decay constant, we construct the PDF for thecosmic birefringence angle and investigate its properties.By relating the observed value of the birefringence angle to the mean or standard deviationof the constructed PDF, we constrain the shape of the input PDFs, providing insightsinto the statistical distribution of the Axiverse. We focus on three different types of axionpotentials: cosine, quadratic, and asymptotically linear axion monodromy.Ouranalysis showcases the potential of cosmic birefringence in constraining the distributionof axion parameters and uncovering possible correlations among them.We additionally offerpredictions for “birefringence tomography”, anticipating future measurements of birefringence fromlower multipoles, and show how it can be used to rule out simpler versions of the Axiverse. Our findings contribute to theongoing exploration of the Axiverse and its implications for cosmic birefringence.

The Lévy walk with rests under stochastic resetting

The Lévy walk with rests (LWR) model is a typical two-state stochastic process that has been widely and successfully adopted in the study of intermittent stochastic phenomena in physical and biological systems. Stochastic processes under resetting provide treatable and interesting schemes to study foraging and search strategies. In this manuscript, we focus on the anomalous diffusive behavior of the LWR under stochastic resetting. We consider both the case of instantaneous resetting, in which the particle stochastically returns to a given position immediately, and the case of noninstantaneous resetting, in which the particle returns to a given position with a finite velocity. The anomalous diffusive behaviors are analyzed and discussed by calculating the mean squared displacement analytically and numerically. Results reveal that the stochastic resetting can not only hinder the diffusion, where the diffusion evolves toward a saturation state, but also enhances it, where as compared with the LWR without resetting, the diffusion exponent surprisingly increases. As far as we know, the enhancement effect caused by stochastic resetting has not yet been reported. In addition, the resetting time probability density function (PDF) of the instantaneous resetting and the return time PDF of the noninstantaneous resetting are studied. Results reveal that the resetting time PDF could follow a power law provided that the sojourn time PDF is power-law distributed and the sojourn time with a heavier tail plays a decisive role in determining the resetting time PDF, whereas the shape of the return time PDF is determined by not only by the sojourn time PDF, but also by the return manner.

Structural strengthening of a constructed timber bridge: Field application and numerical modeling

This paper presents the behavior of a timber bridge strengthened with lag bolts, carbon fiber reinforced polymer (CFRP) sheets, and hollow structural sections (HSS). The 83-old bridge is composed of three spans, supported by 14 Douglas Fir girders, and is tested employing truck loadings of 120 kN and 267 kN. Three-dimensional finite element models are formulated to study the flexural response of the bridge with and without the retrofit options. The magnitude of the truck load dominates the degree of dispersion in girder deflections and alters the shape of probability density functions, which are associated with behavioral uncertainty. The effectiveness of strengthening is apparent in terms of reducing the exceedance probability of deflection limits and increasing reliability indices above the design threshold of β = 3.5, stipulated in bridge specifications. Among the three methods, the stiffening efficiency of the HSS option is higher at the system level; however, the use of CFRP is most efficient at the member level. Live load distribution factors are examined and implementable recommendations are provided for practice. Parametric investigations clarify the efficacy of variable HSS sizes and the ramifications of a permit truck weighing 445 kN.

Evolution of the velocity gradient invariants in homogeneous isotropic turbulence with an inverse energy cascade

An investigation of topological features of homogeneous isotropic turbulence with an inverse energy cascade is performed by using a direct numerical simulation. The inverse energy cascade is induced by reversing the velocity field (i.e., under the transformation from ui to −ui) of a freely decaying isotropic turbulence. In the backward energy transfer process, the joint probability density function (PDF) of Q and R exhibits a novel shape, which seems to be symmetric with the well-known teardrop shape about the Q-axis (Q and R are the second and third invariants of the velocity gradients tensor, respectively). The predominance of the top-right (R > 0 and Q > 0) and the bottom-left (R < 0 and Q < 0) quadrants is observed in the backward energy transfer process. This observation is different from that of the forward energy cascade, in which the top-left (R < 0 and Q > 0) and the bottom-right (R > 0 and Q < 0) quadrants are dominant. The unexpected shape of the joint PDF of Q and R indicates that the turbulence with an inverse energy cascade is dominated by vortex compression and tube-like structures. The PDF of the intermediate eigenvalue of the strain-rate tensor in the inverse energy cascade is negatively skewed, which is opposite to the universal feature of the forward energy cascade. Nevertheless, the preferential alignment of vorticity with the intermediate eigenvector is rather robust, no matter whether the direction of the energy transfer is forward or backward. In addition, it is universal that the vorticity is mostly perpendicular to the eigenvector, which corresponds to a strain-rate eigenvalue with the maximum absolute value among the three eigenvalues. Since the velocity gradient invariants are closely related to the local flow topology, the numerical results reported in this work are expected to shed light on the intrinsic dynamics and mechanisms of inverse energy cascade.

Accessing power-law statistics under experimental constraints

Power-law distributions appear in a large variety of situations and influence our understanding of various physical phenomena. Their identification and characterization are notoriously difficult because of the large fluctuations inherent to empirical data and also because of the unknown range over which the power-law behavior holds. Furthermore, the data on which one is trying to detect power laws are affected by technical constraints and experimental limitations. Here, we show how a power-law distribution is modified by two fundamental limitations: the spatiotemporal resolution and the time window. We consider a time series of events or states and investigate the interevent time probability density function (PDF) or the PDF of the duration of a state. We present in detail how each limitation affects the PDF and derive mathematical expressions that relate the observed distribution to the true one: the resolution globally affects the shape of PDF while preserving the asymptotic exponent and the time window introduces a nonexponential cutoff. We demonstrate that, instead of looking for a simple power law in experimental data, one should fit the data with the modified PDF that we derived for given experimental constraints. We apply our theory to data from an experimental study of the transport of mRNA-protein complexes along dendrites. The presented mathematical theory widens our understanding of the identification and characterization of power-law distributions in experimental data and can be used in a broad spectrum of science fields.

Age-sensitive high density surface electromyogram indices for detecting muscle fatigue using core shape modelling

The purpose of this preliminary study was to examine age-sensitive High Density surface Electromyogram (HD-sEMG) features by Core Shape Modelling (CSM) method. Fatiguing low force isometric contractions of the biceps brachii was performed by eight young (age, 24.40 ± 2.42 years) and five elderly (72.90 ± 2.21 years) males, while HD-sEMG recorded signals from the biceps brachii. The task was performed at 20 % maximal voluntary contraction (MVC). From the recorded HD-sEMG signals, three Probability Density Function (PDF) shape distances (SD) measures the departure from Gaussianity, i.e. Left (LSD), Right (RSD), and Central (CSD), were derived by the CSM method from non-overlapping five-second windows until task failure. A linear regression analysis was then used to quantify the change of these shape parameters throughout the contraction. The resultant slopes revealed that the elderly group showed a decreasing trend in PDF shape parameters as the contraction approached task failure. In contrast, the young showed an increasing trend. Statistical differences between the two groups were found for LSD (p = 0.006) and RSD (p = 0.001). No such age-sensitivity was detected using conventional sEMG fatigue features. These results suggest that the proposed CSM method can be used to obtain fatigue-related features from HD-sEMG that are age-sensitive and possibly related to different motor unit recruitment and synchronization schemes.

A Maximum Power Point Tracking Control Method Based on Rotor Speed PDF Shape for Wind Turbines

Maximum power point tracking (MPPT) is the key to improve the conversion efficiency of wind energy. Concerning the current research on the MPPT control, based on the accurate tracking of rotor speed probability density function (PDF) shape for wind turbines, a novel MPPT algorithm was introduced in detail to improve the power capture and reduce mechanical damage for wind turbines. Considering the influence of wind speed distribution on the wind power generation system performance, this paper expounds a PDF shape control method of a stochastic system based on the Fokker–Planck–Kolmogorov (FPK) equation. Combining the conventional optimal torque (OT) control algorithm with the FPK equation solved by linear least-square (LLS) method, the novel MPPT control law is designed to make the PDF shape of rotor speed track the desired PDF shape as accurately as possible. The simulation verification of the novel MPPT method is carried out in the 1.5 MW wind turbine system. The results reveal that the novel MPPT method can improve the conversion efficiency of wind energy, reduce the frequent fluctuations of system variables, and significantly optimize the performance of wind power generation system.

A Novel PDF Shape Control Approach for Nonlinear Stochastic Systems

In this work, a novel shape control approach of the probability density function (PDF) for nonlinear stochastic systems is presented. First, we provide the formula for the PDF shape controller without devising the control law of the controller. Then, based on the exact analytical solution of the Fokker-Planck-Kolmogorov (FPK) equation, the product function of the polynomial and the exponential polynomial is regarded as the stationary PDF of the state response. To validate the performance of the proposed control approach, we compared it with the exponential polynomial method and the multi-Gaussian closure method by implementing comparative simulation experiments. The results show that the novel PDF shape control approach is effective and feasible. Using an equal number of parameters, our method can achieve a similar or better control effect as the exponential polynomial method. By comparison with the multi-Gaussian closure method, our method has clear advantages in PDF shape control performance. For all cases, the integral of squared error and the errors of first four moments of our proposed method were very small, indicating superior performance and promising good overall control effects of our method. The approach presented in this study provides an alternative for PDF shape control in nonlinear stochastic systems.

Future Changes in Drought Frequency Due To Changes in the Mean and Shape of the PDSI Probability Density Function Under RCP4.5 Scenario

This study investigates the changes in the drought frequency in 2070–2099 relative to 1970–1999, due to the mean and shape changes of the probability density function (PDF) of the self-calibrated Palmer Drought Severity Index (PDSI), using CMIP5 multi-model historical simulations and projections under the RCP4.5 scenario. For severe droughts defined with PDSIs less than the 10th percentile, it is shown that over 41% of the global land, the increase in the severe drought frequency due to the shape change exacerbates the increase due to the mean change. Over 28% of the global land, the decrease in the drought frequency due to the shape change partially offsets the increase due to the mean change. Over 31% of the global land, the drought frequency increases due to the shape changes, but decreases due to the mean changes. The severe drought frequency due to both PDSI PDF mean and shape changes increases over almost the entire global land. We show that the PDSI standard deviation change is mainly determined by the mean precipitation change, while the PDSI mean change is determined by both mean precipitation and potential evapotranspiration changes. In particular, the PDSI standard deviation increases with the increase in mean precipitation which broadens the PDSI PDF, and thus enhances the severe drought frequency, and vice versa. On the other hand, the PDSI mean decreases with the decrease (increase) in mean precipitation (mean potential evapotranspiration). The difference in the attribution of drought frequency changes to the mean and shape changes over different regions can thus be largely explained by the mean precipitation and potential evapotranspiration changes. We also examine the moderate droughts defined with PDSIs between 10th and 20th percentiles in this study. For the moderate drought frequency, the spatial pattern of its changes due to the PDSI mean changes is similar to that of severe drought but with much smaller magnitudes, while its change in the spatial pattern due to the shape changes differs from severe drought with no significant changes. The moderate drought frequency due to both PDSI PDF mean and shape changes increases over 71% of the global land but decreases over 29% of the land.

Evaluation of Eleven Numerical Methods for Determining Weibull Parameters for Wind Energy Generation in the Caribbean Region of Colombia

The two-parameter Weibull probability density function (PDF) is widely utilized by different researchers and engineers to fit wind speed data for statistical analysis and modeling. The characterization of wind resources in the frequency and probability domain is necessary to estimate the power output potential of new wind energy projects. Considering that exist a variety of Weibull equations evidenced in the literature review, this article evaluates 11 different methods to calculate the shape and scale parameters of the Weibull PDF. In this sense, it was written an algorithm within a Matlab function that solves the 11 methods for calculating the Weibull PDF parameters. Wind speed data extracted from the ERA5 database was used as input data for applying the proposed algorithm, and statistical parameters such as the Root Mean Square Error (RMSE), the Relative Root Mean Square Error (RRMSE), and chi-square test (X2) we utilized for assessing the performance of each one of the 11 methods for modeling the wind distribution. The statistical results pointed that the numerical iteration methods (e.g. maximum likelihood method) showed better results than parameterized equations such as the Graphical Method, hence, this research recommends the implicit methods for determining Weibull PDF parameters of wind speed data.

Examination of probability distribution of mixture fraction in LES/FDF modelling of a turbulent partially premixed jet flame

An accurate prediction of the probability density function (PDF) of the mixture fraction is crucial to the prediction of combustion since mixing plays an important role in turbulent non-premixed and partially premixed flames. This work provides an assessment of the large-eddy simulation (LES)/filtered density function (FDF) method for the prediction of the PDF of the mixture fraction. The advantage of the LES/FDF method is that it provides the full predictions of the statistical distribution of scalars including the mixture fraction. The predictive accuracy of the method for the PDF is yet to be fully validated. Assessing the prediction of the PDF of the mixture fraction, a conserved scalar, is an important starting point. The Sydney/Sandia inhomogeneous inlet jet flame is used as a test case. A quick comparison shows that the LES/FDF predicted PDF shapes of the mixture fraction deviate significantly from the commonly presumed Beta-PDF as well as from the experimental data in the flame. To examine the source of the discrepancy, we clarify the different PDF definitions used in the comparison among the predictions, measurements, and presumed shape PDFs. The discrepancy observed from the comparison is largely reconciled by clarifying the difference between the PDFs that are examined. The PDF of the resolved mixture fraction is shown to be close to the Beta-PDF in both the measurements and predictions, while the PDF directly deduced from the LES/FDF particles deviates significantly from the Beta-PDF. A multimodal PDF analysis and a pseudo convergence analysis are conducted to provide plausible evidence to support the predicted multimodal PDF shapes. The sub-filter scale FDF is shown to be close to the Beta-PDF too through the construction of a synthesised PDF, which supports the common presumed Beta-PDF assumption used in the presumed PDF methods when combined with LES.

Corrigendum to: “Developing an innovative method to control the probability density function shape of the state response for nonlinear stochastic systems”

Corrigendum to: “Developing an innovative method to control the probability density function shape of the state response for nonlinear stochastic systems”

Statistical dependence analysis of Erbium doped fiber ring lasers (EDFRL) chaos

Utilizing ergodic nature of chaotic lasers, the probability density function (PDF) estimation is carried out for peak amplitudes of pulsed chaos in Erbium Doped Fiber Ring Laser (EDFRL) in relation to varying the four key cavity parameters i.e. cavity gain, pump power, modulation index and modulation frequency. Kernel based non-parametric probability distributions are found more suitable to fit the chaos peaks data instead of parametric Gaussian, Rayleigh or Poisson Probability Density Functions. The resulting non-parametric PDFs’ shape, modes, skew and variance is found controllable by changing cavity parameters which is beneficial for random number generation with desired properties. The non-parametric distribution changed its shape between uni-modal and bimodal Gaussian like PDFs alternately and the variance also changes. The PDF shape corresponds to density of points in chaotic data bifurcation plots. This statistical in depth analysis is important while employing the EDFRL for random number generation and in chaotic secure communication applications. EDFRL chaos is found here to be a non-Poisson doubly stochastic point process implying it does depend on history of the chaos generation process, which is hidden in the slowly varying population inversion density of the laser. The bimodality skew keeps altering between left and right while becoming uni-modal every time between switching with modulation index and pump power changes. At high gain the variance of PDF decreases and it approaches uni-modal Gaussian. At high modulation frequency the PDF is left skewed with higher number of shorter pulses bursting.

Analytical prediction of low-frequency fluctuations inside a one-dimensional shock

Linear instability of high-speed boundary layers is routinely examined assuming quiescent edge conditions, without reference to the internal structure of shocks or to instabilities potentially generated in them. Our recent work has shown that the kinetically modeled internal nonequilibrium zone of straight shocks away from solid boundaries exhibits low-frequency molecular fluctuations. The presence of the dominant low frequencies observed using the direct simulation Monte Carlo (DSMC) method has been explained as a consequence of the well-known bimodal probability density function (PDF) of the energy of particles inside a shock. Here, PDFs of particle energies are derived in the upstream and downstream equilibrium regions, as well as inside shocks, and it is shown for the first time that they have the form of the noncentral Chi-squared (NCCS) distributions. A linear correlation is proposed to relate the change in the shape of the analytical PDFs at a specified upstream number density and temperature as a function of Mach number, within the range \(3 \le M \le 10\), with the DSMC-derived average characteristic low-frequency of shocks, as computed in our earlier work. At a given Mach number \(M=7.2\) and upstream number density \(n_1=10^{22}\,\hbox {m}^{-3}\), it is shown that the variation in DSMC-derived low frequencies is correlated with the change in most-probable-speed inside shocks at the location of maximum bulk velocity gradient for upstream translational temperature in the range \(\sim 90 \le T_{tr,1}/(K) \le 1420\). Using the proposed linear functions, average low frequencies are estimated within the examined ranges of Mach number and input temperature and a semi-empirical relationship is derived to predict low-frequency oscillations in shocks. Our model can be used to provide realistic physics-based boundary conditions in receptivity and linear stability analysis studies of laminar-turbulent transition in high-speed flows.

Characteristics of wall-shear stress fluctuations in shock wave and turbulent boundary layer interaction

The wall-shear stress (WSS) fluctuations in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer are investigated by means of direct numerical simulation (DNS) at Mach 2.25. The numerical results agree very well with previous experiments and DNS data in terms of turbulence statistics, wall pressure, and skin friction. The fluctuating WSS characteristics, including probability density function (PDF), frequency spectrum, space–time correlation, and convection velocity, are analysed systematically. It is found that the positively skewed PDF shape of the streamwise WSS fluctuations is significantly changed due to the presence of a separation bubble, while the PDF shape of the spanwise component is slightly affected, exhibiting a symmetric behaviour across the interaction. The weighted power-spectrum density map indicates that the low-frequency unsteadiness associated with the separated shock - exhibits little influence on the spectrum for either component, and no enhancement of the low-frequency energy is observed. A significant reduction in the spatial extent of the two-point correlation is observed, causing spanwise elongated coherence for the streamwise WSS fluctuations in the separation region. Moreover, the elliptic behaviour of the space–time correlations is essentially preserved throughout the interaction, and this is accompanied by a sudden reduction of the convection velocity in the separation bubble.

Numerical Simulation of the Exit Temperature Pattern of an Aircraft Engine Using a Temperature-Dependent Turbulent Schmidt Number

Abstract This paper presents a numerical simulation for predicting the combustor exit temperature pattern of an aircraft engine, developed using the commercial fluid simulation software Ansys Fluent, which assumes a shape probability density function for the instantaneous chemistry in the conserved scalar combustion model and the standard k-ε model for turbulence. We found the compliance of the radial and circumferential non-uniformities of the exit temperature with the experimental data to be insufficient. To achieve much more accurate result, the mixing intensity was enhanced with respect to the initial calculation due to using the reduced value of the turbulent Schmidt number Sc. Numerical simulation was performed for values of the turbulent Schmidt number from Sc = 0.85 (default) up to Sc = 0.2, with results confirming the reduction of radial and circumferential non-uniformities of exit temperature. However, correlation between radial and circumferential non-uniformities is not admissible for these cases. Therefore, we propose to use a temperature-dependent formulation of the turbulent Schmidt number Sc, accounting for the increase in Sc number with increasing gas temperature. A user defined function (UDF) was used to implement the Sc number temperature dependence in Ansys Fluent. The numerical results for the proposed Schmidt number Sc temperature dependence were found to be in acceptable agreement with the experimental data both for radial and circumferential non-uniformities of the exit temperature pattern.