Value Of Shape Factor Research Articles

Endometrial Biopsy: a Karyometric and Stereological Study

Background:Diagnosis of premalignant endometrial lesions is a major challenge to pathologists. The D-score system is more reproducible than the WHO scheme, however it is not widely available, this study attest a simple custom-made workstation for estimation of the “D-score”.Material and methods:Fifteen endometriam with low grade hyperplasia, fifteen proliferative and eight secretory phase endometria were analyzed by light microscopy and stereology. We determined the volume and surface density glands & stroma. karyometric parameters of the endometrial glandular epithelial cells were estimated. D-score was calculated from some architectural & karyometric parameters.Results:The volume of stroma (VPS) was significantly higher in proliferative than secretory and hyperplastic endometria. The glandular surface density were higher in secretory endometria than proliferative and hyperplastic endometria, however, the differences was statistically insignificant. The ratio of longest nuclear axis to shortest nuclear axis was significantly less in secretory than proliferative and hyperplastic endometria. Secretory endometria also have significantly lower mean values of shape factor & significantly higher mean values of contour index than proliferative and secretory endometria. 67% of hyperplastic endometria show D-score values < 0.Conclusion:It seems feasible to estimate D-score using a semi-automated workstation based on the simple stereologic and morphometric principles.

Determination of size and shape features of walnut ( Juglans regia L.) cultivars using image processing

The dimensions, mass, and shape are the most commonly measured physical properties of fruits. The size and shape features of 10 common walnut ( Juglans regia L.) cultivars grown in Turkey were investigated using an image processing technique. The walnut cultivars produced nuts longer than wide and wider than thick in shape except cvs. Bursa-95, Hartley, and Şebin. The thickness of cv. Şebin was 1.07 times greater than its width. All cultivars were spherical as determined by their shape index except cv. Bursa-95 (1.32). The highest values for shape factors were obtained from the horizontal orientation, followed by the suture and vertical orientations. Mean values for mass, volume, geometric mean diameter, sphericity, and surface area ranged between 11.42 and 18.28 g, 23.84 and 48.32 cm 3, 35.71 and 45.89 mm, 83.0 and 94.1%, and 42.73 and 66.16 cm 2 among cultivars, respectively, and cv. Şen-1 had the highest values for all of these parameters.

Fatigue behaviour of AA6082 friction stir welds under variable loadings

Welded components are often subjected to variable amplitude service loads, demanding fatigue life prediction methods that can take into account fatigue damage accumulation. In previous work the fatigue behaviour of friction stir welding of aluminium alloys under constant and variable amplitude loadings was analysed under the stress ratio R = 0. The objective of this work is to extend the study of the fatigue strength of friction stir welds in AA6082-T6 under constant and variable amplitude loadings under the stress ratio R = −1 and analyse the validity of Miners´s and Manson–Halford damage sum rules for both stress ratios R = 0 and R = −1. Fatigue tests were carried out in a servo-hydraulic testing machine using typified Gassner amplitude spectra, ranging the correspondent shape exponent between 1.5 and 5. Constant amplitude fatigue tests revealed that crack initiation occurs internally from tunnel defects or at the surface, near stress concentration due to shear lips, leading to fatigue life reduction relative to the base material. Tunnel defects showed to be more detrimental for fatigue resistance than the stress concentration created near shear lips. As expected, a significant mean stress influence was observed. Therefore, the assumption in design codes of no mean stress effect, based in the presence of high residual stresses close to the yield stress, seems not adequate to be applied for friction stir butt welds. Although residual stresses were not measured in this work, the small test samples (160 × 15 × 4 mm) tested transversely implies that they must be very small. The comparison of experimental fatigue lives with predictions calculated with both Miners´s Linear Damage Rule and Manson–Halford Double-Linear Damage Rule, using two stress ratios and four spectrum shape factor values, revealed a good agreement for R = 0. Under R = −1 both damage predictions methods were, in general, unconservative, with the Double-Linear Damage Rule being less unconservative. Therefore, the application of the Double-Linear Damage Rule can be considered advantageous as it requires no further input information than the required by the Linear Damage Rule and takes into account both loading level and loading sequence effects.

Effect of fracture pressure depletion regimes on the dual-porosity shape factor for flow of compressible fluids in fractured porous media

A precise value of the matrix-fracture transfer shape factor is essential for modeling fluid flow in fractured porous media by a dual-porosity approach. The slightly compressible fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a compressible fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in dual-porosity media. Adv Water Res 2011;34(5):627–39. doi:10.1016/j.advwatres.2011.02.012]. However, for a compressible fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a compressible fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of slightly compressible fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of compressible fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of fluid flow in fractured porous media.

Numerical and Experimental Investigation of Bubbling Gas–Solid Fluidized Beds with Dense Immersed Tube Bundles

Numerical simulations of gas–solid bubbling fluidized beds with and without dense immersed horizontal tubes were performed using the Eulerian-Eulerian Two Fluid Model (TFM) and applying the Kinetic Theory of Granular Flow (KTGF). The results were compared with experimental data obtained from a pseudo-2D fluidized bed test rig using a developed digital image analysis technique (DIAT). The influences of dense immersed horizontal tubes on bed properties (bed pressure drop and expansion ratio) and bubble hydrodynamics (bubble size, rise velocity, aspect ratio, and shape factor) were investigated numerically as well as experimentally. In the first part grid sensitivity with different mesh sizes was checked and effects using 2D and 3D domains were examined. Simulations with 3D domains gave better agreement with experimental data but were seen to be computationally expensive. For conducting intensive parametric studies of fluidized bed behavior the use of 2D domains remains indispensable. In the second part it could be shown that dense tube arrangements in the fluidized bed lead to repeated bubble break-up and coalescence in the tube bank region and therefore to fluctuating values of bubble size, rise velocity, aspect ratio, and shape factor. For different superficial velocities similar results were found which shows the high influence of dense immersed tubes on fluidized bed behavior. In addition no significant differences between staggered and in-line tube arrangement were observed. In general the simulations based on the Two Fluid Model showed good agreement with the experimental results.

Experimental Study of Bite Mark Injuries by Digital Analysis

This study was based on a morphometric analysis of bite marks starting from the quantitative definition of the anterior teeth by the geometric acquisition of the "injuries," using bite marks impressed on pig skin and plastic. Each mark was photographed and acquired. A dedicated program automatically supplied the values of the shape factors and the areas of the pattern geometric figures. The values obtained for the homologous samples were compared to the heterologous values. Statistical comparison was made of the sets by linear regression, determining the correlation coefficient and the determination coefficient for each value. Results showed only 4.8% and 2% of overlap between homologous and heterologous values. This study was carried out in attempting to quantitatively define the anterior teeth of the human dentition and the procedure described and the results obtained support the advantage of morphometric studies and computer-aided programs in this study of bite marks.

Biometry of the Cornea in Myopic Chinese Patients

To develop a close-fit mathematical model of corneal anterior and posterior topography and investigate the variation of corneal topography with biometric parameters in a group of young adult myopic Chinese patients. Corneal topography data were acquired from 112 eyes of 61 myopic patients (mean age: 24.10±3.66 years). Videokeratoscopic images were recorded for anterior and posterior corneal surfaces using an Orbscan IIz topography system (Bausch & Lomb), and elevation data were fit to ellipsoid, hyperboloid, and paraboloid equations. Axial length, anterior chamber depth, refractive error, corneal curvature, central corneal thickness, and white-to-white distance were also measured and statistically analyzed. The ellipsoid equation provided the best fit for the anterior and posterior corneal surfaces in all patients. Corneal asymmetry slightly improved the accuracy of the mathematical model and reduced errors of fit with the clinical data. Strong evidence of right and left corneal symmetry was obtained in the form of similar corneal curvature, shape factor, and thickness values. The refractive error showed strong correlation with axial length (r=-0.586, P<.001) but not with corneal curvature or anterior chamber depth, indicating that myopia may be related to scleral stretching and globe elongation rather than changes in corneal curvature or anterior chamber depth. Axial length appears to be the main morphological parameter related to myopia. Myopic corneas took the form of a rotationally asymmetric prolate ellipsoid that gradually flattened towards the periphery. The study also provided evidence of symmetry between an individual's right and left corneas.

Inverse Modeling of Respiratory System during Noninvasive Ventilation by Maximum Likelihood Estimation

We propose a procedure to estimate the model parameters of presented nonlinear Resistance-Capacitance (RC) and the widely used linear Resistance-Inductance-Capacitance (RIC)models of the respiratory system by Maximum Likelihood Estimator (MLE). The measurement noise is assumed to be Generalized Gaussian Distributed (GGD), and the variance and the shape factor of the measurement noise are estimated by MLE and Kurtosis method, respectively. The performance of the MLE algorithm is also demonstrated by the Cramer-Rao Lower Bound (CRLB) with artificially produced respiratory signals. Airway flow, mask pressure, and lung volume are measured from patients with Chronic Obstructive Pulmonary Disease (COPD) under the noninvasive ventilation and from healthy subjects. Simulations show that respiratory signals from healthy subjects are better represented by the RIC model compared to the nonlinear RC model. On the other hand, the Patient group respiratory signals are fitted to the nonlinear RC model with lower measurement noise variance, better converged measurement noise shape factor, and model parameter tracks. Also, it is observed that for the Patient group the shape factor of the measurement noise converges to values between 1 and 2 whereas for the Control group shape factor values are estimated in the super-Gaussian area.

Combined Effects of Pipe Diameter, Reynolds Number and Wall Heat Flux and on Flow, Heat Transfer and Second-Law Characteristics of Laminar-Transitional Micro-Pipe Flows

Fluid flow, heat transfer and entropy generation characteristics of micro-pipes are investigated computationally by considering the simultaneous effects of pipe diameter, wall heat flux and Reynolds number in detail. Variable fluid property continuity, Navier-Stokes and energy equations are numerically handled for wide ranges of pipe diameter (d = 0.50–1.00 mm), wall heat flux (q''= 1000–2000 W/m2) and Reynolds number (Re = 1 – 2000), where the relative roughness is kept constant at e/d = 0.001 in the complete set of the scenarios considered. Computations indicated slight shifts in velocity profiles from the laminar character at Re = 500 with the corresponding shape factor (H) and intermittency values (γ) of H = 3.293→3.275 and γ = 0.041→0.051 (d = 1.00→0.50 mm). Moreover, the onset of transition was determined to move down to Retra = 1,656, 1,607, 1,491, 1,341 and 1,272 at d = 1.00, 0.90, 0.75, 0.60 and 0.50 mm, respectively. The impacts of pipe diameter on friction mechanism and heat transfer rates are evaluated to become more significant at high Reynolds numbers, resulting in the rise of energy loss data at the identical conditions as well. In cases with low pipe diameter and high Reynolds number, wall heat flux is determined to promote the magnitude of local thermal entropy generation rates. Local Bejan numbers are inspected to rise with wall heat flux at high Reynolds numbers, indicating that the elevating role of wall heat flux on local thermal entropy generation is dominant to the suppressing function of Reynolds number on local thermal entropy generation. Cross-sectional total entropy generation is computed to be most influenced by pipe diameter at high wall heat flux and low Reynolds numbers.

Spherical indentation of metallic foams

Metallic foams are a new class of functional materials. They have found their applications as sandwich cores in lightweight structures and as implant materials in bioengineering. To characterize the mechanical properties of these materials becomes an interesting and relevant research topic. In the mean time, indentation method has been well accepted as a simple and effective way to measure the mechanical properties of solid materials. We believe that it is possible to study the averaged mechanical properties of a metallic foam from a spherical indentation test. In this paper, theoretical investigation to understand the spherical indentation responses of metallic foams is presented. Based on the dimensional analysis, several scaling relationships in the indentation of metallic foams with a spherical indenter are obtained. Numerical results from the finite element simulations are used to examine the dependence of the indentation response on the basic material parameters, such as the porosity, the work hardening exponent and the shape factor, which characterizes the plastic deformation of metallic foams due to hydrostatic loading. Our numerical results show that the maximum indentation force has a linear relationship with the indentation depth for different shape factor values. It is therefore proposed to calibrate the shape factor value from the slope of the maximum indentation force versus the indentation depth from a spherical indentation test, instead of a complicated hydrostatic loading test. We also find that the spherical indentation hardness varies about 11% within the examined indentation depths. The range of the ratio of the hardness to the yield strength of metallic foams is from 2.17 to 2.95, which is different from that of solid materials. Our study provides the basis for applying a simple spherical indentation test to investigate the mechanical properties of metallic foams.

Application of a novel symmetrical shape factor to gastroretentive matrices as a measure of swelling synchronization and its impact on drug release kinetics under standard and modified dissolution conditions

Abstract Objectives We have assessed the kinetics of drug release in relation to the full or partial hydration and swelling of matrices under standard and modified United States Pharmacopeia (USP) apparatus II using a novel index, defined as the symmetrical shape factor. The symmetrical shape factor describes the regularity of the hydration rate of the matrix perimeter relative to its central regions. Methods Monolithic and three-layer matrices based on hypromellose, polyethylene oxide, Kollidon SR, theophylline, diltiazem hydrochloride and alfuzosin hydrochloride were subjected to dissolution testing. Key findings Our results indicated that Kollidon SR matrices and the three-layer composite systems with and without effervescing components were not significantly affected by the dissolution conditions. However, in the case of the floating monolithic systems based on hypromellose and polyethylene oxide, both release profiles and swelling dynamics in accordance with the similarity factor (f2) and symmetrical shape factor values were significantly influenced. Conclusions The symmetrical shape factor values were positively impacted. Consequently the drug release kinetics were more predictable and reproducible. The modified USP method resulted in a more synchronized axial and radial swelling with symmetrical shape factor values approaching unity. Data further indicated that the modified USP method provided for complete matrix hydration and swelling as the dosage form remained fully submerged, allowing for more reliable release mimicking the in-vivo conditions.

Modeling the effect of species retention on the band broadening in perfectly ordered silica monolithic column mimics with variable external porosity and intra‐skeleton diffusivity

Computational fluid dynamics simulations of the band broadening in an idealized, and highly ordered 3-D model of silica monoliths are reported. As this high degree of order induces only a minimal eddy-dispersion, the band broadening is very sensitive to the intra-skeleton diffusivity and retention factor of the analytes. The simulations hence provide a maximal view on how the C(m)- and C(s)-contributions to the band broadening depend on the intra-skeleton diffusivity and retention factor. By comparing two model-structures with different external porosities, some interesting qualitative insights on the effect of the through-pore diameter are obtained as well. Because of the precisely known intra-skeleton diffusivity, the obtained plate height data also provide an ideal test case for the general plate height expression of chromatography. Writing out this model, identifying the geometrical parameters, and determining their value using a parameter fitting algorithm, a set of parameter values can be found which allows to accurately predict the retention factor dependency of the band broadening over a very broad range of mobile phase velocities. Remaining modeling problems are the apparent intra-skeleton diffusion dependency of the shape factor describing the intra-skeleton mass transfer, and the absence of mathematical expressions to predict the model shape factor values.

Application of a novel symmetrical shape factor to gastroretentive matrices as a measure of swelling synchronization and its impact on drug release kinetics under standard and modified dissolution conditions

We have assessed the kinetics of drug release in relation to the full or partial hydration and swelling of matrices under standard and modified United States Pharmacopeia (USP) apparatus II using a novel index, defined as the symmetrical shape factor. The symmetrical shape factor describes the regularity of the hydration rate of the matrix perimeter relative to its central regions. Monolithic and three-layer matrices based on hypromellose, polyethylene oxide, Kollidon SR, theophylline, diltiazem hydrochloride and alfuzosin hydrochloride were subjected to dissolution testing. Our results indicated that Kollidon SR matrices and the three-layer composite systems with and without effervescing components were not significantly affected by the dissolution conditions. However, in the case of the floating monolithic systems based on hypromellose and polyethylene oxide, both release profiles and swelling dynamics in accordance with the similarity factor (f(2)) and symmetrical shape factor values were significantly influenced. The symmetrical shape factor values were positively impacted. Consequently the drug release kinetics were more predictable and reproducible. The modified USP method resulted in a more synchronized axial and radial swelling with symmetrical shape factor values approaching unity. Data further indicated that the modified USP method provided for complete matrix hydration and swelling as the dosage form remained fully submerged, allowing for more reliable release mimicking the in-vivo conditions.

Numerical investigation of the influence of kinetics and shape factor on barium sulfate precipitation in a continuous stirred tank

The effect of kinetics and shape factor on barium sulfate precipitation in a continuous stirred tank has been investigated numerically through solving the standard momentum and mass transport equations in combination with the moment equations for crystal population balance. The numerical method was validated with the literature data. The simulated results include the distribution of the local supersaturation ratio in the reactor, the mean crystal size, and the coefficient of variation. The simulation results show that the value of shape factor used in the model affected greatly the mean crystal size and the moments of the crystal size distribution. The influence of the kinetic expressions on the simulation is also analyzed. It is important to investigate the relationship of the shape factor with the precipitator type and other operation conditions to obtain reliable simulation results and suitable kinetic equations of crystal nucleation and growth rates.

Predictive model of Vibrio parahaemolyticus growth and survival on salmon meat as a function of temperature

The growth and survival curves of a strain of pandemic Vibrio parahaemolyticus TGqx01 (serotype O3:K6) on salmon meat at different storage temperatures (range from 0 °C to 35 °C) were determined. In order to model the growth or inactivation kinetics of this pathogen during storage, the modified Gompertz and Weibull equations were chosen to regress growth and survival curves, respectively, and both equations produced good fit to the observed data (the average R 2 value equals to 0.990 for modified Gompertz and 0.920 for Weibull equation). The effect of storage temperature on the specific growth rate ( μ) was modeled by square root type equation, and the relationship between μ and lag time ( λ) was described by a rule of μ × λ = constant. The shape factor ( n) and scale factor ( b) values of the Weibull equations versus the temperature (°C) were plotted and the temperature effects on these parameters were described by two linear empirical equations. The predicted growth and survival curves from the model were compared to real enumeration results, using the correlation coefficient ( R 2), bias factor ( B f) and accuracy factor ( A f), to assess the performance of the established model. The results showed that the overall predictions for V. parahaemolyticus TGqx01 growth or inactivation on salmon at tested temperatures agreed well with observed plate counts, and the average R 2, B f and A f values were 0.958, 1.019 and 1.035, respectively.

Network flow modeling via lattice-Boltzmann based channel conductance

Lattice-Boltzmann (LB) computations of single phase, pore-to-pore conductance are compared to models in which such conductances are computed via standard pore body–channel–pore body series resistance (SR), with the conductance of each individual element (pore body, channel) based on geometric shape factor measurements. The LB computations, based upon actual channel geometry derived from X-ray computed tomographic imagery, reveal that the variation in conductance for channels having similar shape factor is much larger than is adequately captured by the geometric models. Fits to the dependence of median value of conductance versus shape factor from the LB-based computations show a power law dependence of higher power than that predicted by the geometric models. We introduce two network flow models based upon the LB conductance computations: one model is based upon LB computations for each pore-to-pore connection; the second is based upon a power law fit to the relationship between computed conductance and throat shape factor. Bulk absolute permeabilities for Fontainebleau sandstone images are computed using the SR-based network models and the two LB-based models. Both LB-based network models produce bulk absolute permeability values that fit published data more accurately than the SR-based models.

Thermal and Hydraulic Matrix-Fracture Interaction in Dual-Permeability Simulation

Summary The shape factor concept, originally introduced by Barenblatt in 1960, provides an elegant and powerful upscaling method for fractured reservoir simulation. The shape factor determines the fluid and heat transfer between matrix and fractures when there is a difference in pressure or temperature between matrix blocks and the surrounding fractures. An appropriate specification of the shape factor is therefore critical for accurate modeling. Since its introduction, many different values for the shape factor have been proposed in the literature, among which the well-known Warren-Root and Kazemi shape factors. The aim of this paper is to show that the selection of the appropriate shape factor should not only depend on the “shape” and dimensions of matrix blocks, but should also take into consideration the character of the dominant underlying physical recovery mechanisms. We will show that by taking into account the dominant physical recovery mechanism, the apparent discrepancies in the shape factor values reported in the literature can be overcome. We derive a general expression for the shape factor that not only captures existing shape factor expressions, but also allows extensions to recovery mechanisms requiring a dual permeability approach. The paper is organized as follows. First, we briefly review the shape factors presented in the literature. We then derive the general expression for the (single-phase) matrix-fracture shape factor. Subsequently, we analytically derive a new shape factor that captures the transient in pressure/temperature diffusion processes. To compare and contrast the impact of the various shape factors, we consider three cases of increasing complexity. First, we consider pressure/temperature diffusion in a single 1D matrix block following a step change in the boundary conditions. Next, we consider isothermal gas/oil gravity drainage from a homogeneous stack. We compare fine-grid single-porosity simulations (in which the matrix is finely gridded and in which the fractures are explicitly represented) with coarse-grid dual-permeability simulations (in which the matrix-fracture interaction is modeled by shape factors). In the third step, we consider gas-oil gravity drainage of the same stack model, but now under steam injection. In this case, steam is injected at the top, and oil recovered from the base of the fracture system. Again, we compare fine-grid single-porosity simulations with coarse-grid dual-permeability simulations. We show that in this case, the constant (asymptotic) shape factor provides a good approximation to the heating of the stack. We will show, however, that with a constant (time-independent) shape factor, the initial fast heating of the matrix blocks cannot be captured. We show that the new transient shape factor, however, enables coarse-grid dual-permeability modeling of thermal recovery processes such that they reproduce fine-grid results.

Absence of Prognostic Value of Nuclear Shape Factor Analysis in Colorectal Carcinoma: Relevance of Interobserver and Intraobserver Variability

Several retrospective studies, including our previous investigation, have shown a prognostic value of nuclear shape factor in colorectal carcinomas. This prospective study was designed to assess the reliability of nuclear shape factor determined by nuclear morphometry and to confirm its prognostic value. Ninety-eight patients who underwent colorectal carcinoma resection were prospectively enrolled. Measurement of nuclear shape factor was performed by using a computer-based image analysis system. Nuclear shape factor was defined as the degree of circularity of the nucleus (1.0 for a perfect circle and <1.0 for any other elliptical shape). The prognostic impact of nuclear shape factor on ten-year survival and the intraobserver and interobserver agreement were assessed. The nuclear shape factor mean values by American Joint Committee on Cancer stage were: 0.73 (0.07) in Stage I, 0.74 (0.06) in Stage II, and 0.75 (0.05) in Stage III carcinomas (P = 0.78, ANOVA). The intraobserver agreement was poor for observer A (r = 0.28) and practically nonexistent for observer B (r = -0.004, Pearson correlation). The intraclass coefficient for interobserver agreement was practically nonexistent. No significant association between nuclear shape factor and ten-year survival was found. Our prospective results, as opposed to our previous retrospective results, suggest that the reliability for nuclear shape factor morphometric analysis is very poor. We failed to confirm a prognostic value for nuclear shape factor in colorectal carcinoma.

Fruit Shape Analysis of Vitis Using Digital Photography

Quantifying fruit shape is challenging, particularly when measurements are made on segregating populations of plants. Objective manual measurements can be performed on small samples of fruit, but this method is difficult and very time-consuming when dealing with larger samples or when shapes are complex or shape variations are slight. Subjective rating scales can also be used, but their effectiveness is questionable when done by multiple raters resulting from varying descriptive standards among individuals. Therefore, a method was developed to analyze digital images containing multiple fruits to characterize fruit shapes. Each segregant of a population of table grapes (Vitis spp.) with parents of wide shape variation was photographed and analyzed for shape using SigmaScan® software. The program discriminately selected image pixels representing the fruit and determined the area and perimeter of a grape berry, which were subsequently used to calculate the major:minor axis ratio, shape factor, and compactness values. Computer findings were compared with data from human raters using a simple correlation. When compared with the human ratings, results showed strong correlations of r = 0.941 for major:minor axis ratio, r = –0.804 for shape factor, and r = 0.744 for compactness. This analysis method was a reasonably quick and simple way to quantify grape berry shape, yielding valuable phenotypic data in numerical form. This technology should be useful for shape characterizations in other fruits as well.

Optimization of a reversed trapezoidal fin using a 2-D analytic method

A reversed trapezoidal fin with variable fin base thickness is optimized based on the fixed fin volume by using a two-dimensional analytic method. The variation of temperature along the normalized Y position at the fin tip is presented. For fixed fin volumes, the maximum heat loss, the corresponding optimum fin effectiveness, fin base height and fin tip length as a function of the fin base thickness, fin shape factor and the fin volume are presented. One of the results shows that both the optimum heat loss and the optimum fin length increase with the increase of the value of fin shape factor.