Least-squares Fitting Analysis Research Articles

Direct Determination of the Relationship between the Intramolecular Oxygen-Hydrogen Bond Length and Its Stretching Vibrational Frequency of the Methanol Molecule in the Liquid State.

Time-of-flight (TOF) neutron diffraction measurements on pure liquid deuterated methanol and concentrated methanolic LiClO4 and LiTFSA solutions have been carried out to investigate the effect of intermolecular hydrogen bonds on the intramolecular O-D distance (rOD) of the methanol molecule in the liquid state. Intramolecular parameters for the methanol molecule are determined by the least-squares fitting analysis of the neutron total interference term observed in the high-Q region. Attenuated total reflection (ATR) IR spectra have been measured for methanolic solutions of natural abundance to determine the gravitational center frequency (νOH) of the stretching vibrational band of the methanol molecule. The relationship between rOD and νOH is approximated well by a linear function. The value dνOH/drOD = -17000 ± 3000 cm-1 Å-1 has been derived from the slope of the fitted function. It has been revealed that the O-D bond length of the methanol molecule is sensitively affected by the intermolecular hydrogen bonding interaction.

Compactness regularization in the analysis of dipolar EPR spectroscopy data

Dipolar electron paramagnetic resonance (EPR) experiments, such as double electron–electron resonance (DEER), measure distributions of nanometer-scale distances between paramagnetic centers, which are valuable for structural characterization of proteins and other macromolecular systems. One challenge in the least-squares fitting analysis of dipolar EPR data is the separation of the inter-molecular contribution (background) and the intra-molecular contribution. For noisy experimental traces of insufficient length, this separation is not unique, leading to identifiability problems for the background model parameters and the long-distance region of the intra-molecular distance distribution. Here, we introduce a regularization approach that mitigates this by including an additional penalty term in the objective function that is proportional to the variance of the distance distribution and thereby penalizes non-compact distributions. We examine the reliability of this approach statistically on a large set of synthetic data and illustrate it with an experimental example. The results show that the introduction of compactness can improve identifiability.

An anisotropic dressed pairwise potential model for the adsorption of noble gases on boron nitride sheets.

Development of empirical potentials with accurate parameterization is indispensable while modeling large-scale systems. Herein, we report accurate parameterization of an anisotropic dressed pairwise potential model (PPM) for probing the adsorption of noble gases, He, Ne, Ar and Kr on boron nitride sheets. For the noble gas binding on B48N48H24, we carried out a least-squares fit analysis of the dispersion and dispersionless contributions of the interaction potential separately. The transferability of the parameters for a range of molecular model systems of boron nitride is further established. The dressed PPM is then used in conjunction with a global optimization technique, namely particle swarm optimization (PSO) to assess the possibility of performing large-scale simulations with the PPM-PSO methodology. The results obtained for the adsorption of 2-5 noble gases on BN sheets establish the proof-of-concept, encouraging the pursuit of large-scale simulations using the PPM-PSO approach.

Occurrence of titanium dioxide nanoparticle in Taihu Lake (China) and its removal at a full-scale drinking water treatment plant.

The occurrence of titanium dioxide nanoparticle (TNP), an emerging contaminant, in Taihu Lake of China was investigated. Ti was present at a concentration of 224 ± 59 μg/L in the water samples collected from a water source in east Taihu Lake. Approximately 0.19% of the Ti-containing matter was at the nano-scale. Scanning Electron Microscope analysis verified the existence of Ti-containing components, such as TiOx and FeTiOx. Furthermore, Ti K-edge X-ray absorption near-edge structure spectroscopy was used to detect the phase composition of nano-scaled Ti-containing matter. The spectra showed the three characteristic peaks of TiO2 in the samples, suggesting the occurrence of TNP in Taihu Lake. A least-squares linear combination fitting analysis indicated that the TNP concentration in the water source was ~0.77 μg/L in water and ~0.85 μg/g-dry in sediment. The removal performance of the TNP at a full-scale conventional drinking water treatment plant indicated that ~61% of TNP was removed via coagulation/sediment, sand filtration, and disinfection/clear water reservoir. The coagulation/sediment process accounted for approximately 70% of the total removed TNP. The finished water contained ~ 0.30 μg/L TNP. This study is the first that reported the presence and transport of TNP in a full-scale drinking water treatment system.

Experimental Determination of Relationship between Intramolecular O–D Bond Length and Its Stretching Vibrational Frequency of D2O Molecule in the Liquid State

Experimental evidence has been obtained for the structure-spectra relationship of hydrogen bonds in aqueous solutions. Intramolecular O-D distance, rOD, has been determined by the least-squares fitting analysis of the neutron interference term in the high-Q region observed for pure D2O and concentrated aqueous solutions. The average O-D stretching frequency, νOD, has been obtained from the position of the center of gravity of the observed ATR-IR O-D stretching band. The linear relationship between rOD and νOD has been confirmed in the liquid state. The slope of dνOD/drOD is evaluated to be -21 000 ± 1000 cm-1 Å-1.

Individual-Level Heterogeneity in Mask Wearing during the COVID-19 Pandemic in Malaysia.

ABSTRACT.Wearing a face mask has been a key approach to contain or slow down the spread of COVID-19 in the ongoing pandemic. However, there is huge heterogeneity among individuals in their willingness to wear face masks during an epidemic. This research aims to investigate the individual heterogeneity to wear face masks and its associated predictors during the COVID-19 pandemic when mask-wearing was not mandatory. Based on a survey of 708 Malaysian adults and a multivariate least-squares fitting analysis, the results reveal a significant variance among individuals in wearing masks, as 34% of the individual adults did not always wear masks in public places. Female individuals, individuals who wash their hands more frequently, and those who reported more availability of personal protective equipment were more likely to practice mask-wearing. The identification of less-compliant groups of mask wearing has critical implications by enabling more specific health communication campaigns.

On the Structure and Kinematics of an Algerian Eddy in the Southwestern Mediterranean Sea

An Algerian Eddy, anticyclonic vortex generated by the instability of the Algerian Current in the southwestern Mediterranean Sea, is studied using data provided by drifters (surface currents), Argo floats (temperature and salinity profiles), environmental satellites (absolute dynamic topography maps and ocean color images) and operational oceanography products. The eddy was generated in May 2018 and lasted as an isolated vortex until November 2018. Its morphology and kinematics are described in June–July 2018 when drifters were trapped in its core. During that period, the eddy was slowly moving to the NE (~2 km/day), with an overall diameter of about 200 km (slowly growing with time) and maximal surface swirl velocity of ~50 cm/s at a radius of ~50 km. Geostrophic currents derived from satellite altimetry data compare well with low-pass filtered drifter velocities, with only a slight overestimation, which is expected as its maximum vorticity corresponds to a small Rossby number of ~0.6. Satellite ocean color images and some drifters show that the eddy has an elliptical spiral structure. The looping tracks of the drifters trapped in the eddy were analyzed using two statistical methods: least-squares ellipse fitting and wavelet ridge analysis, revealing a typical eccentricity of about 0.5, a wide range of inclination and a rotation period between 3 and 10 days. Clusters of drifters on the northeastern limb of the eddy were also considered to estimate divergence and vorticity. The results indicate convergence (divergence) and downwelling (upwelling) at scales of 20–50 km near the northeastern (northwestern) edge of the eddy, in agreement with the quasi-geostrophic theory. Vertically, the eddy extends mostly down to 250 m depth, with a warm, low-salinity and low-density signature and with geostrophic currents near 50 cm/s in the top layer (down to ~80 m) reducing to less than 10 cm/s near 250 m. Near the surface, colder water is advected into it.

Analysis and Comparison of Quasi-Elastic Neutron Scattering (QENS) Spectra Model

The Quasi-Elastic Neutron Scattering (QENS) experiment is a novel method to study confined water dynamics by measuring the neutron energy transfer ( E )and scattering vector (Q) after the neutron interacts with the sample target. By adopting a suitable theoretical model and performing nonlinear least-squares fitting analysis on the Quasi- Elastic Neutron scattering spectra, the relevant physical parameters describing the water dynamics can be obtained, and then the constrained water dynamics in the sample can be detected. There are many types of Quasi-Elastic Neutron Scattering spectra fitting analysis models, and the fitting effects of different models and the relevant physical parameters obtained to characterize water dynamic information are not the same. This paper uses the Jump-diffusion and Rotating-diffusion Model (JRM) and the revised Jump-diffusion and Rotating-diffusion Model (rJRM) to fit the QENS spectra of pure magnesium silicate (M-S-H) and pure calcium silicate (C-S-H) samples, respectively. The measurement temperatures of QENS spectra from M-S-H and C-S-H samples are 210K up to 280K and 230K up to 280K, respectively, the E ranges from -120 to 120μev and the Q value 0.3 A^(-1)~1.9 A^(-1). Different physical parameters describing the dynamic information of confined water can be obtained by using the two models for QENS spectra fitting analysis. Compared with the JRM model, the physical parameters obtained by using the rJRM model are more comprehensive, and it is suitable for all neutron energy transfer and scattering vector measurements. From the qualitative point of view, the QENS spectra fitting curve of rJRM model is more consistent with the original data points. From the quantitative point of view, the chi-square value fitted by the rJRM model is more consistent with the mathematical statistics law than the JRM model, and the time required for nonlinear fitting is shorter.

The AME 2020 atomic mass evaluation (I). Evaluation of input data, and adjustment procedures* *This work has been undertaken with the endorsement of the IUPAP Commission on Symbols, Units, Nomenclature, Atomic Masses and Fundamental Constants (C2)

This is the first of two articles (Part I and Part II) that presents the results of the new atomic mass evaluation, AME2020. It includes complete information on the experimental input data that were used to derive the tables of recommended values which are given in Part II. This article describes the evaluation philosophy and procedures that were implemented in the selection of specific nuclear reaction, decay and mass-spectrometric data which were used in a least-squares fit adjustment in order to determine the recommended mass values and their uncertainties. All input data, including both the accepted and rejected ones, are tabulated and compared with the adjusted values obtained from the least-squares fit analysis. Differences with the previous AME2016 evaluation are discussed and specific examples are presented for several nuclides that may be of interest to AME users.

A fixed multi-site interaction charge model for an accurate prediction of the QM/MM interactions.

A fixed multi-site interaction charge (FMIC) model was proposed for the accurate prediction of intermolecular electrostatic interactions based on the quantum mechanical linear response of a molecule to an external electric field. In such a model, some additional off-center interaction sites were added for capturing multipole interactions for a given molecule. By multivariate least-square fitting analysis of the calculated QM/MM interactions of a given molecule with the electrostatic environment and the electrostatic potentials of the environment at the pre-defined distributed interaction sites, the FMIC of the molecule was obtained. The model system of CO in myoglobin (Mb) was utilized to demonstrate the derivation of the FMIC. The accuracy of FMIC in predicting the electrostatic interactions between CO and the Mb environment was investigated using 10 000 different Mb-CO configurations generated from the 400 ps QM/MM MD simulation. In comparison to the QM/MM calculations at the B3LYP/aug-cc-pVTZ/ff99SB level, the mean unsigned error (MUE) of the results based on the FMIC model was merely 0.10 kcal mol-1, and the root mean square error (RMSE) was only 0.13 kcal mol-1, which are significantly lower than the results predicted by the ESP charge model (MUE = 1.45 kcal mol-1, and RMSE = 1.7 kcal mol-1, respectively). The transferability of FMIC was tested by applying the obtained FMIC in the wild type Mb-CO system to the mutants of V68F and H64L Mb-CO systems. The MUEs of the obtained results for 10 000 different configurations are both smaller than 0.2 kcal mol-1 for the V68F and H64L Mb-CO systems in comparison to the B3LYP/aug-cc-pVTZ/ff99SB calculations, and the RMSEs are also lower than 0.2 kcal mol-1 for both mutants. The applications of FMIC were extended to model the electrostatic interactions between a hydrogen fluoride molecule and 492 waters in a truncated octahedron box; our study showed that the FMIC could give satisfactory results with a MUE of 0.12 kcal mol-1 and a RMSE of 0.16 kcal mol-1 in comparison to the B3LYP/aug-cc-pVDZ/TIP3P calculations for 10 000 different configurations generated using the 10 ns classical MD simulation. Therefore, the FMIC method provides an accurate and efficient tool for predicting intermolecular electrostatic interactions, which can be utilized in the future development of molecular force fields.

Numerical and experimental analysis of creep deformation and stress-relaxation in Sn-5Sb lead-free alloy

In-service performance of solder alloys is highly dependent on its high temperature behaviors like creep and stress relaxation. In this investigation, creep behavior of Sn-5Sb alloy is studied using three integrated creep equations, i.e., combination of power-law and omega model (PO), exponential and omega model (EO), and logarithmic and omega model (LO). In addition, stress relaxation (SR) curves are derived using two approaches of spring-dashpot (SD) and Peleg (P) model to establish the best fit to experimental data. Required creep data were attained using creep tests at several stresses at 500 K while relaxation ones were carried out under a constant strain of 0.5% at 300, 330, 360 and 400 K. Nonlinear least-square fitting (NLSF) analysis was carried out to deliver the best fit of the experimental data and recognition of constants for each equation. Results showed that in the lower stress level of 160 MPa, the CEO model presents a better fitting of experimental creep data with respect to CPO and CLO, whereas, CPO is with superior accuracy in the higher stress regions. In SR mode, SD model did not indicate good performance at 500 and 550 °C while showing good accordance with the experimental data at 600 and 650 °C. P model on the other hand, was superior to SD model in overall temperature range as obtained parameter values followed temperature dependence quite well. It is concluded that the EO and P models can accurately predict the creep and relaxation behavior of Sn-5Sb solder alloy, respectively.

Solvation Structure of Li+ in Methanol and 2-Propanol Solutions Studied by ATR-IR and Neutron Diffraction with 6Li/7Li Isotopic Substitution Methods.

Neutron diffraction measurements have been carried out on 10 mol % LiTFSA (TFSA: bis(trifluoromethylsulfonil)amide) solutions in methanol- d4 and 2-propanol- d8 to obtain information on the solvation structure of Li+. The detailed coordination structure of solvent molecules within the first solvation shell of Li+ was determined through the least-squares fitting analysis of the difference function between normalized scattering cross sections observed for 6Li/7Li isotopically substituted sample solutions. The nearest-neighbor Li+···O distance and coordination number determined for the 10 mol % LiTFSA-methanol- d4 solution are rLiO = 1.98 ± 0.02 Å and nLiO = 3.8 ± 0.6, respectively. In the 2-propanol- d8 solution, it has been revealed that 2-propanol- d8 molecules within the first solvation shell of Li+ take at least two different coordination geometries with the intermolecular nearest-neighbor Li+···O distance of rLiO = 1.93 ± 0.04 Å. The Li+···O coordination number, nLiO = 3.3 ± 0.3, is determined. Ion-pair formation in the LiTFSA-methanol and LiTFSA-2-propanol solutions has been investigated by the attenuated total reflection infrared spectroscopic method. Mole fractions of free, Li+-bound, and aggregated TFSA- are derived from the peak deconvolution analysis of vibrational bands observed for TFSA-.

Determination of gravity wave parameters in the airglow combining photometer and imager data

Abstract. Mesospheric airglow measurements of two or three layers were used to characterize both vertical and horizontal parameters of gravity waves. The data set was acquired coincidentally from a multi-channel filter (Multi-3) photometer and an all-sky imager located at São João do Cariri (7.4∘ S, 36.5∘ W) in the equatorial region from 2001 to 2007. Using a least-square fitting and wavelet analysis technique, the phase and amplitude of each observed wave were determined, as well as the amplitude growth. Using the dispersion relation of gravity waves, the vertical and horizontal wavelengths were estimated and compared to the horizontal wavelength obtained from the keogram analysis of the images observed by an all-sky imager. The results show that both horizontal and vertical wavelengths, obtained from the dispersion relation and keogram analysis, agree very well for the waves observed on the nights of 14 October and 18 December 2006. The determined parameters showed that the observed wave on the night of 18 December 2006 had a period of ∼43.8±2.19 min, with the horizontal wavelength of 235.66 ± 11.78 km having a downward phase propagation, whereas that of 14 October 2006 propagated with a period of ∼36.00±1.80 min with a horizontal wavelength of ∼195±9.80 km, and with an upward phase propagation. The observation of a wave taken by a photometer and an all-sky imager allowed us to conclude that the same wave could be observed by both instruments, permitting the investigation of the two-dimensional wave parameter. Keywords. Atmospheric composition and structure (airglow and aurora) – electromagnetics (wave propagation) – history of geophysics (atmospheric sciences)

Local Structure of Li+ in Concentrated Ethylene Carbonate Solutions Studied by Low-Frequency Raman Scattering and Neutron Diffraction with 6Li/7Li Isotopic Substitution Methods.

Isotropic Raman scattering and time-of-flight neutron diffraction measurements were carried out for concentrated LiTFSA-EC solutions to obtain structural insight on solvated Li+ as well as the structure of contact ion pair, Li+···TFSA-, formed in highly concentrated EC solutions. Symmetrical stretching vibrational mode of solvated Li+ and solvated Li+···TFSA- ion pair were observed at ν = 168-177 and 202-224 cm-1, respectively. Detailed structural properties of solvated Li+ and Li+···TFSA- contact ion pair were derived from the least-squares fitting analysis of first-order difference function, ΔLi(Q), between neutron scattering cross sections observed for 6Li/7Li isotopically substituted 10 and 25 mol % *LiTFSA-ECd4 solutions. It has been revealed that Li+ in the 10 mol % LiTFSA solution is fully solvated by ca. 4 EC molecules. The nearest neighbor Li+···O(EC) distance and Li+···O(EC)═C(EC) bond angle are determined to be 1.90 ± 0.01 Å and 141 ± 1°, respectively. In highly concentrated 25 mol % LiTFSA-EC solution, the average solvation number of Li+ decreases to ca. 3 and ca. 1.5. TFSA- are directly contacted to Li+. These results agree well with the results of band decomposition analyses of isotropic Raman spectra for intramolecular vibrational modes of both EC and TFSA-.

The AME2016 atomic mass evaluation (I). Evaluation of input data; and adjustment procedures

This paper is the first of two articles (Part I and Part II) that presents the results of the new atomic mass evaluation, AME2016. It includes complete information on the experimental input data (also including unused and rejected ones), as well as details on the evaluation procedures used to derive the tables of recommended values given in the second part. This article describes the evaluation philosophy and procedures that were implemented in the selection of specific nuclear reaction, decay and mass-spectrometric results. These input values were entered in the least-squares adjustment for determining the best values for the atomic masses and their uncertainties. Details of the calculation and particularities of the AME are then described. All accepted and rejected data, including outweighted ones, are presented in a tabular format and compared with the adjusted values obtained using the least-squares fit analysis. Differences with the previous AME2012 evaluation are discussed and specific information is presented forseveral cases that may be of interest to AME users. The second AME2016 article gives a table with the recommended values of atomic masses, as well as tables and graphs of derived quantities, along with the list of references used in both the AME2016 and the NUBASE2016 evaluations (the first paper in this issue).AMDC: http://amdc.impcas.ac.cn/Contents The AME2016 atomic mass evaluation (I). Evaluation of input data; and adjustment proceduresAcrobat PDF (1.2 MB) Table I. Input data compared with adjusted valuesAcrobat PDF (1.3 MB)

Thermodynamic model for Zr solubility in the presence of gluconic acid and isosaccharinic acid

ABSTRACTZr solubility in the presence of gluconic acid (GLU) and isosaccharinic acid (ISA) was investigated as a function of hydrogen ion concentration (pHc) and the total concentration of GLU or ISA. The dependence of the increase in Zr solubility on the pHc and GLU concentration suggested the existence of Zr(OH)4(GLU)22− in the neutral pH region and Zr(OH)4(GLU)(GLU-H)3− in the alkaline pH region above pHc 10 as the dominant species in the presence of 10−3–10−1 mol/dm3 (M) GLU. In the presence of ISA, the dominant species Zr(OH)4(ISA)22− and Zr(OH)4(ISA)(ISA-H)3− were proposed to occur in the neutral and alkaline pH regions, similar to those found in the presence of GLU. From X-ray diffraction analysis, the solubility-limiting solid phase in the presence of GLU and ISA was considered to be Zr(OH)4(am). The formation constants of the Zr gluconate and isosaccharinate complexes were determined by least-squares fitting analysis of the solubility data, and the obtained values were discussed in comparison with those of tetravalent actinides.

Microscopic Structure of Contact Ion Pairs in Concentrated LiCl- and LiClO4-Tetrahydrofuran Solutions Studied by Low-Frequency Isotropic Raman Scattering and Neutron Diffraction with (6)Li/(7)Li Isotopic Substitution Methods.

Low-frequency isotropic Raman scattering and time-of-flight neutron diffraction measurements were carried out for (6)Li/(7)Li and H/D isotopically substituted *LiCl- and *LiClO4-tetrahydrofuran (*THF) solutions in order to obtain microscopic insight into solvated Li(+), Li(+)···Cl(-) and Li(+)···ClO4(-) contact ion pairs formed in concentrated THF solutions. Symmetrical stretching vibrational mode of solvated Li(+) in LiCl and LiClO4 solutions was observed at ν = 181-184 and 140 cm(-1), respectively. The stretching vibrational mode of Li(+)···Cl(-) and Li(+)···ClO4(-) solvated contact ion pairs formed in 4 mol % (6)LiCl-THF-h8 and (7)LiCl-THF-h8 solutions was found at ν = 469 and 435 cm(-1), respectively. Detailed structural properties of solvated Li(+) and the contact ion pairs were derived from the least-squares fitting analyses of the first-order difference function, ΔLi(Q), obtained from neutron diffraction measurements on (6)Li/(7)Li isotopically substituted THF-d8 solutions. It has been revealed that Li(+) takes 4-fold coordination in the average local structure of Li(+)X(-)(THF)3, X = Cl and ClO4. The nearest neighbor Li(+)···O(THF) distance was determined to be 2.21 ± 0.01 Å and 2.07 ± 0.01 Å for 4 mol % *LiCl- and 10 mol % *LiClO4-THF-d8 solutions, respectively. The Li(+)···anion distances for Li(+)···Cl(-) and Li(+)···O(ClO4(-)) contact ion pairs were determined to be 2.4 ± 0.1 Å and 2.19 ± 0.01 Å, respectively. The nearest neighbor Li(+)···THF interaction is significantly modified by the anion in the first solvation shell.

Structure-stereospecificity relationships of propylene polymerization using substituted ansa-silylene(fluorenyl)(amido) titanium complexes

ansa-Fluorenylamidotitanium complexes bearing various substituents on the nitrogen and fluorene (2a-d) were synthesized. The structures of the complexes were characterized by 1H and 13C NMR, and X-ray crystal analyses were performed for complexes 2a, 2b and 2d. The coordination mode of the fluorenyl group to the metal center was changed from η3 to η1 when a bulky group was introduced on the nitrogen or 2,3-position of the fluorenyl ring. Syndiotactic-specificity of the catalyst for the propylene polymerization was reduced when bulky group was introduced on the nitrogen. Least-square fitting analysis of the steric pentad distributions revealed that the stereodefect was mainly formed by the chain migration without monomer insertion, which is accelerated by the η1-coordination of the fluorenyl group.

A robust circle detection algorithm based on top-down least-square fitting analysis

In this paper, we propose a robust and efficient circle detector, which achieves accurate results with a controlled number of false detections and requires no parameter tuning. The proposed algorithm consists of three steps as follows. First, we propose a novel edge point chaining method to extract Canny edge segments (i.e., contiguous and sequential chains of Canny edge points). Second, we split each edge segment into several smooth sub-segments, and detect candidate circles within each obtained sub-segment based on top-down least-square fitting analysis. Third, we employ Desolneux et al.’s method to reject the false detections. Experimental results demonstrate that the proposed method is efficient and more robust than the state-of-the-art algorithm EDCircles.

Studies on convective heat transfer through helical coils

An experimental investigation on steady state convection heat transfer from vertical helical coiled tubes in water was performed for laminar flow regime. Three coils with curvature ratios as 0.0757, 0.064, 0.055 and range of Prandtl number from 3.81 to 4.8, Reynolds number from 3,166 to 9,658 were considered in this work. The heat transfer data were generated from 30 experiments conducted at constant water bath temperature (60 °C) for different cold water flow rates in helical coils. For the first time, an innovative approach of correlating Nusselt number with ‘M’ number is proposed which is not available in the literature and the developed correlations are found to be in good agreement with the work of earlier researchers. Thus, dimensionless number ‘M’ was found to be significant to characterize the hydrodynamics of fluid flow and heat transfer correlations in helical coils. Several other correlations based on experimental data are developed. To cover wide range of industrial applications, suitable generalized correlations based on extended parameters beyond the range of present experimental work are also developed. All these correlations are developed by using least-squares power law fit and multiple-regression analysis of MATLAB software. Correlations so developed were compared with published correlations and were found to be in good agreement. Comparison of heat transfer coefficients, friction factor and Nusselt number for different geometrical conditions is presented in this paper.