Stagnation is the transient state of a solar thermal system under high solar irradiation where the useful solar gain is zero. Both flat-plate collectors with selective absorber coatings and vacuum-tube collectors exhibit stagnation temperatures far above the saturation temperature of the glycol-based heat carriers within the range of typical system pressures. Therefore, stagnation is always associated with vaporization and propagation of vapor into the pipes of the solar circuit. It is therefore essential to design the system in such a way that vapor never reaches components that cannot withstand high temperatures. In this article, a thermal-hydraulic model based on the integral form of a two-phase mixture model and a drift-flux correlation is presented. The model is applicable to solar thermal flat-plate collectors with meander-shaped absorber tubes and selective absorber coatings. Experimental data from stagnation experiments on two systems, which are identical except for the optical properties of the absorber coating, allowed comparison with simulations carried out under the same boundary conditions. The absorber of one system features a conventional highly selective coating, while the absorber of the other system features a thermochromic coating, which exhibits a significantly lower stagnation temperature. Comparison of simulation results and experimental data show good conformity. This model is implemented into an open-source software tool called “THD” for the thermal-hydraulic dimensioning of solar systems. The latest version of THD, updated by the results of this article, enables planners to achieve cost-optimal design of solar thermal systems and to ensure failsafe operation by predicting the steam range under the initial and boundary conditions of worst-case scenarios.

Lithium titanates are used in various applications, such as anode materials for lithium intercalation (Li4Ti5O12) or breeding materials in fusion reactors (Li2TiO3). Here, we report the formation of nano-crystalline lithium titanates by a mechanochemical approach and present a deeper insight into their structural characteristics by PXRD and solid-state NMR spectroscopy. The compounds were synthesized in a high energy planetary ball mill with varying milling parameters and different grinding tools. NaCl type Li2TiO3 (α-Li2TiO3) was formed by dry milling of lithium hydroxide with titania (rutile or anatase) and by a milling induced structure transformation of monoclinic β Li2TiO3 or spinel type Li4Ti5O12. Heating of mechanochemical prepared α Li2TiO3 induces a phase transformation to the monoclinic phase similar to hydrothermal reaction products, but a higher thermal stability was observed for the mechanochemical formed product. Microstructure and crystallographic structure were characterized by PXRD via Rietveld analysis. Detailed phase analysis shows the formation of the cubic phase from the various educts. A set of two lattice parameters for α Li2TiO3 was refined, depending on the presence of OH- during the milling process. An average crystallite size of less than 15 nm was observed for the mechanochemical generated products. The local Li environment detected by 6Li SPE MAS NMR revealed Li defects in the form of tetrahedral instead of octahedral site occupation. Subsequent adjustment of the structural model for Rietveld refinement leads to better fits, supporting this interpretation.

The object of study is a transversely bent triangular plate made of orthotropic material fixed along the edges of the plate under the action of a uniformly distributed load. Fourth-order differential equilibrium equations with variable orthotropy parameters were used. The equations were approximated by finite differences for a grid of scalene triangles. This type of mesh accurately describes the boundary contour of the triangular-shaped plates. The boundary conditions for the mesh consider the orthotropy of the plate material. Seven standard finite-difference equations have been developed considering the boundary conditions along the three edges of the plate and the presence of three angles of an irregularly shaped triangle. A finite difference matrix is obtained. The matrix structure makes calculating a triangular plate at different base angles possible. The boundary conditions were varied in the form of rigid or hinged support of triangular plates. The calculation method considers the orthotropic parameters of the material in two mutually perpendicular planes. The adaptation of the numerical method to the calculation of orthotropic plates of arbitrary shape is described. Relationships are given for determining the rigidity characteristics of orthotropic materials. An algorithm for simple engineering calculation of triangular orthotropic plates is proposed, which makes it possible to perform accurate calculations in variant design.

Background: The Stability Index estimation algorithm was derived and applied to develop and implement a balance ability diagnosis system that can be used at daily life. Methods: The system integrated an approach based on sensory function interaction, called the clinical test of sensory interaction with balance (CTSIB). The piezo-resistive force mat was fabricated, and a Stability Index prediction algorithm was developed and applied using the center of pressure (CoP) variables. The Stability Index prediction algorithm derived a CoP variable for 103 elderly people by Nintendo Wii Balance Board (WBB) to predict the Stability Index of the Balance System (Biodex SD). And, the accuracy was confirmed through the correlation between the real and predicted value. Results: As a result of testing with the test-set, the linear regression model confirmed that the r value ranged between 0.943 to 0.983. To confirm the similarity between the WBB and flexible force mat, each measured CoP value was input and calculated into the developed regression model, and the result of the correlation coefficient validation ​​confirmed an r value of 0.96. Conclusion: The system developed in this study will be applicable to the daily life of the home in the form of a floor mat.

The object of this paper is the analysis of isotropic rectangular thin plates supported (simply supported or clamped) along two opposite edges whereby the other edges have arbitrary support conditions; the plates are subjected to external bending moments, concentrated or distributed, and perpendicular to the supported edges. The standard approach to this problem is to replace the bending moment with a couple of forces infinitely close and to use the known expressions of efforts and deformations for the plate subjected to concentrated forces; the results are then related to the first derivatives of those efforts and deformations with respect to the position of application of the load. In this study, the external bending moment was expanded into a Fourier series, leading to a distributed external bending moment, and the boundary conditions and continuity equations were applied. Various types of rectangular plates were analyzed, as well as plates of infinite length whose results were identical to those in the literature. In addition, results for cantilever plates of infinite length were presented.

This paper aims to analyze arbitrarily loaded isotropic rectangular thin plates with two opposite edges supported (simply supported or clamped), from which one or both are clamped, and the other edges have arbitrary support conditions. Rectangular thin plates with two opposite edges simply supported are routinely analyzed using for the deflection the simple trigonometric series of Lévy or the double trigonometric series of Navier, while the loads are expanded in Fourier series. In this paper the flexibility method (or force method) of the linear beam theory was applied whereby the unknowns were the bending moments along the opposite edges; in this regard, the primary system was the plate simply supported along the above-mentioned opposite edges and subjected to the external loads, system solved using the Lévy solution, and the redundant system was the plate simply supported along the opposite edges and subjected to bending moments along those edges. In the redundant system, a modified Lévy solution was introduced to account for the edge moments. The compatibility equations (vanishing of the slopes at selected positions of the opposite edges) were set to determine the unknowns and so the efforts in the plate. The results obtained were in good agreement with the exact results.

Multi-gap Resistive Plate Chamber has been attracting increasing attention and has been studied in recent decades because of its good efficiency, high time resolution and relatively low cost. It has become a new standard technology for the Time of Flight system in particle and high energy physics experiments. In this paper, we introduce the operation principle and structure of the MRPC detector and review the applications on the Time of Flight system in several famous experiments, such as STAR, CBM and SoLID. The performances including time resolution and particle identification are discussed in detail. Some recent advances and perspectives with regard to the future development of the next generation MRPC are also outlined.

Let b∈Cn∖{0} be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e. we study functions which are analytic in intersection of every slice {z0+tb:t∈C} with the unit ball Bn={z∈C:|z|:=|z|12+…+|zn|2<1} for any z0∈Bn. For this class of functions there is introduced a concept of boundedness of L-index in the direction b where L:Bn→R+ is a positive continuous function such that L(z)>β|b|1−|z|, where β>1 is some constant. For functions from this class we describe local behavior of modulus of directional derivatives on every ’circle’ {z+tb:|t|=r/L(z)} with r∈(0;β],t∈C,z∈Cn. It is estimated by value of the function at center of the circle. Other propositions concern a connection between boundedness of L-index in the direction b of the slice holomorphic function F and boundedness of lz-index of the slice function gz(t)=F(z+tb) with lz(t)=L(z+tb). Also we show that every slice holomorphic and joint continuous function in the unit ball has bounded L-index in direction in any domain compactly embedded in the unit ball and for any continuous function L:Bn→R+.

Derivation of light paths in the Michelson interferometer is based on the hypothesis that the speed of light does not change after reflection by a mirror in motion. The Michelson-Morley experiment predicts a fringe shift of 0.40. The same fringe shift is predicted for a particular Michelson interferometer in which the beam splitter of the interferometer makes an angle of 45° with the direction of light from the source. Light behaves like a wave and also as a particle. Thus, it is reasonable to consider the reflection of light as a mechanical phenomenon. With this hypothesis, the speed of light changes after reflection, and the predicted fringe shift for the particular Michelson interferometer is zero which is in accordance with the result of the Michelson-Morley experiment. Apparently, light travels in any inertial frame as if this particular interferometer belongs to a fixed frame. The velocity of light is considered independent of the velocity of its source, which is in accordance with astronomers’ observations of the binary stars, and the experiment performed at CERN, Geneva, in 1964.

The article is devoted to the analytical and numerical study of the pattern of propagation and attenuation, due to Coulomb friction, of shear waves in an infinite thin elastic plate with a circular orifice of radius lying on a rough base. In the field of motion, an exact analytical solution of a nonlinear boundary value problem for tangential stresses and transversal velocities is obtained in quadratures by the method of Laplace transformations. It turned out that the complete exhaustion of the wave front of a strong rupture occurs at a finite distance from the center of the hole and an elementary formula is given for this distance (the case of tangential forces instantly applied to the orifice boundary, and then constant in time, is considered). For various ratios of the magnitude of the limiting friction force to the amplitude of the applied load, the trailing wave fronts are obtained, after which a state of static equilibrium between the elastic and friction forces with a nonlinear distribution of residual deformations is established in the region .

Flails are one of the more contentious and misunderstood classes of medieval weaponry, despite their prevalence in popular media: some researchers question their existence entirely and the bulk of historians are sceptical of widespread temporal and geographical prevalence while others, and a significant volume of period evidence, would argue the contrary. While the expansive use of flails in Eastern Europe and Byzantium is familiar, many Central, Western, and Southern European sources are less well-known or largely forgotten, especially those stemming from the later-early and early-high medieval eras (up to 1250). In this work, I collate and discuss the bulk of the available literary references and artistic depictions of flails and their use alongside some of the archaeological finds from Western, Central, and Southern Europe, with an emphasis on the 12^th and 13^th Centuries. The significance of this volume of evidence is examined, and an assessment of flails as a part of medieval culture and warfare is considered. Collectively, this would suggest that knowledge of flails as instruments of war and associated cultural connotations, if not their actual prevalence and use in warfare, was far more widespread across Europe this time period than has been previously estimated.

The main goal of this article is the characterization of Herz-type Besov-Morrey spaces K˙p,qαN˙μ,rs and Triebel-Lizorkin-Morrey spaces K˙p,qαE˙μ,rs via ball means of differences, atomic, molecular and wavelet decompositions. There are provided necessary facts for implying these results, which can help to explore such spaces on different domains in further researches. Proposed spaces allow to extend the class of studying functions, containing Leray projection, heat semi-group and other operators, which can be helpful in exploring weak, strong and mild solutions of nonlinear partial differential equations.

The famous singlet correlations of a composite quantum system consisting of two spatially separated components exhibit notable features of two kinds. The first kind consists of striking certainty relations: perfect correlation and perfect anti-correlation in certain settings. The second kind consists of a number of symmetries, in particular, invariance under rotation, as well as invariance under exchange of components, parity, or chirality. In this note, I investigate the class of correlation functions that can be generated by classical composite physical systems when we restrict attention to systems which reproduce the certainty relations exactly, and for which the rotational invariance of the correlation function is the manifestation of rotational invariance of the underlying classical physics. I call such correlation functions classical EPR-B correlations. It turns out that the other three (binary) symmetries can then be obtained "for free": they are exhibited by the correlation function, and can be imposed on the underlying physics by adding an underlying randomisation level. We end up with a simple probabilistic description of all possible classical EPR-B correlations in terms of a "spinning coloured disk" model, and a research programme: describe these functions in a concise analytic way.

The paper presents new data on mineralogical-geochemical peculiarities of the granites and pegmatites of the Baikal area (Olkhon Region) with implications for the age, generation conditions and geodynamic settings of magmatism. The early Paleozoic granitoids of the Olkhon region are syncollisional formations produced from the gneiss-schistose substratum of the Olkhon metamorphic sequences. Pegmatoid granites and pegmatites of the Region were generated within a wide age range (458-390 Ma) and include different mineralogical and geochemical types. Amongst the Early Paleozoic granitoids, pegmatoid rocks are products of the collisional magmatism evolution and are similar to granites in terms of the mineral composition and distribution patterns of rare and rare earth elements. On the Olkhon island (Baikal lake) the pegmatite of the Tashkiney vein belong to the Be-Nb-Ta mineralogical-geochemical type demonstrating high contents of W, Sn U, Th and very low concentrations of Li and volatile components (F, B). In the Pryolkhonye area, vein pegmatite Iliksin is with Li, Be, Nb, Ta mineralization (lepidolite, vorobyevite, samarskite et al). The studied pegmatite veins are similar both by the profound negative Ba, Sr, Eu, and Zr anomalies. The zircons from the Tashkiney vein (390±5.0 Ma) and of the Iliksin vein (430.1±2.2 Ma, U-Pb isotope LA ICP MS metod) indicate the formation of pegmatite at the late post-collisional stage of magmatism in the Olkhon Region. As regard to mineralogical and geochemical characteristics, vein pegmatites with amazonite (Ainsky and Ulan-Nur) belong to the Li-F type. The tantalum mineralization, represented by microlites and minerals of the columbite-tantalite group is associated with the Ainsky amazonite pegmatite. As opposed to the Early Paleozoic syncollisional granitoids and pegmatoid formations, the middle Paleozoic vein bodies of pegmatites (Tashkiney, Iliksin, Ainsky, Ulan-Nur) are regarded as rare-metal pegmatites. In terms of geochemical characteristics, they are similar to the rare-metal pegmatoid granites and pegmatites of the intra-plate setting widespread in Mongolia and Transbaikalia. The rare-metal mineralization in the Olkhon region may be genetically related to the evolution of Be-Nb-Ta and Li-F types of the post-collisional granites and pegmatites.

This paper draws an earlier book (with Evans and Higgins) entitled Bad Call: Technology’s Attack on Referees and Umpires and How to Fix It (hereafter Bad Call) and its various precursor papers. These show why it is that current match officiating aids are unable to provide the kind of accuracy that is often claimed for them and that sports aficianados have been led to expect from them. Accuracy is improving all the time but the notion of perfect accuracy is a myth because, for example, lines drawn on sports fields and the edges of balls are not perfectly defined. The devices meant to report the exact position of a ball – for instance ‘in’ or ‘out’ at tennis – work with the mathematically perfect world of virtual reality, not the actuality of an imperfect physical world. Even if ball-trackers could overcome the sort of inaccuracies related to fast ball speeds and slow camera frame-rates the goal of complete accuracy will always be beyond reach. Here it is suggested that the purpose of technological aids to umpires and referees be looked at in a new way that takes the viewers into account.

Modular steel buildings (MSBs) interlocking inter-module connections (IMCs) have piqued researchers’ interest. However, the existing literature has not yet studied the optimisation of its plate thicknesses. This paper, therefore, focuses on optimising interlocking (IMCs) plate thickness in (MSBs), leveraging previous experimental and numerical simulation methodologies. Various numerical models for four MSBs interlocking (IMCs) with plate thicknesses (4 mm, 6 mm, 10 mm, and 12 mm) were developed under compression loading conditions. The study’s novelty lay in its comprehensive parametric analysis, which evaluated the slip phenomenon in (MSBs) connections and introduced a slip prediction model validated against empirical data. Further innovative machine learning approach was utilised to predict slip values based on applied force through a random forest regression model trained using the 'Treebagger' function. Sensitivity analysis and comparisons with alternative methods were utilised to underscore the reliability and applicability of the findings. The results showed that 11.03 mm was the optimal plate thickness for interlocking (IMCs) in modular steel buildings, with up to 8.08% reduced material costs. Increasing plate thickness boosts its deformation resistance by up to 50.75%. ‘TreeBagger’ random forest for anomaly detection and machine learning improves slip prediction up to 7% at higher force levels.

One of the most important pieces of equipment used in labs in culturing populations of fruit flies (Drosophila sp.) is that of the “CO₂ gas plate”, which is used to anesthesize individuals during “fly-pushing”. This piece of equipment consists of a box with a porous top into which carbon-dioxide is pumped. Flies placed on its surface are left immobilized, permitting the sorting, categorizing and/or counting of flies during population culturing and experimental assays. Unfortunately, commercially available gas plates are typically expensive. Here, we describe a new design for a gas plate that can be easily produced using a 3D printer and a laser cutter, which we are making freely available to the fly community.

This article develops algorithms for the characterization and the visualization of micro-scale features by using a small number of sample points, and with a goal to mitigate for the measurement shortcomings which are often destructive or time consuming. We implement the algorithms to rapidly examine the microscopic features of a Microelectromechanical System (MEMS) surface. Such images are highly dense; therefore, traditional image processing techniques might be computationally expensive. The contribution of this research include first, we develop local and global algorithm based on modified Thin Plate Spline (TPS) model to reconstruct high resolution images of the micro-surface’s topography, and its derivatives by using low resolution images. Second, we obtain a bending energy algorithm from our modified TPS model, and use it to filter out image defects. Finally, we develop a computationally efficient Windowing technique, which combines TPS and Linear Sequential Estimation (LSE), to enhance the visualization of images. The Windowing technique allows rapid image reconstruction based on the reduction of inverse problem.

This research aims to study the ultimate limit state (ULS) behaviour of stiffened panel under longitudinal compression by non-linear finite element method (NLFEM). There are different types of stiffeners being used in shipbuilding i.e. T-bar, flat-bar and angle-bar. However, this research focuses on the ultimate compressive strength behaviour of flat-bar stiffened panel. A total of 420 of reliable scenarios of flat-bar stiffened panel are selected for numerical simulation by ANSYS NLFEM. The ultimate strength behaviours obtained were used as data for the development of closed form shape empirical formulation. Recently, Kim et al. [1] proposed for advanced empirical formulation for T-bar stiffened panel and the applicability of the proposed formulation to flat-bar stiffened panel will be confirmed by this study. The accuracy of the empirical formulation obtained for flat-bar stiffened panel has been validated by FE simulation results of statistical analysis (R2 = 0.9435). The outcome obtained will be useful for ship structural designers in predicting the ultimate strength performance of flat-bar type stiffened panel under longitudinal compression.

Pin-on-plate and pin-on-disk wear tests are typically used for assessing the wear behavior of a given material coupling. Such a behavior is frequently described by a wear coefficient k, which is estimated, according to the Archard’s law, as the ratio between the measured wear volume V and the product of the applied normal force F and the sliding distance s, i.e. k=V/(F s). This study demonstrates that such a relationship is correct for pin-on-plate but not for pin-on-disk, particularly for flat-ended pins. Both analytical and finite element models of the two tests were developed, considering three different distances pin-disk axis. As results, wear volumes, pressure and wear depth maps were examined and compared for the same sliding distance. Though this study is focused only on the initial transient part of the wear tests, some interesting aspects arose: i) rotational effect in pin-on-disk tests affects k estimation, especially when the pin is near to the disk axis; ii) a simple analytical function is defined to correct the wear volume estimation for pin-on-disk tests; iii) due to the different sliding distances of contact points in pin-on-disk tests, pressure redistribution occurs with higher values on the inner side (closer to disk axis); the opposite trend is observed in wear depth maps. From a computational point of view, the pin-on-disk problem, only apparently simple, required very small time increments to correctly describe the circular trajectories of points, with high computational costs. Numerical strategies are currently under investigation to extend the study to the steady state phase of both tests.

Carbon fiber reinforced polymer (CFRP) bending structure is widely used in the aviation field. The occurrence and propagation of delamination damage will reduce the safety of in-service bending structures. As a detection tool with high damage sensitivity, Lamb wave can effectively identify delamination damage. In this study, the signal difference coefficient (SDC) was introduced to quantify delamination damage and evaluate the sensitivity of A0 and S0 mode lamb waves to delamination damage. The simulation results show that compared with the S0 mode Lamb wave, the A0 mode Lamb wave exhibits higher delamination damage sensitivity. The delamination damage can be quantified based on the strong correlation between the SDC and the delamination damage size. The control effect of the linear array PZT phase time-delay method on Lamb wave mode was investigated by simulation. The phase time-delay method realizes the generation of a single-mode Lamb wave, which can separately excite the A0 mode and S0 mode Lamb wave to identify delamination damage of different sizes. The A0 mode Lamb wave was excited by the developed one-dimensional linear comb transducer (LCT), which was used to conduct the detection experiment on the CFRP bending plate with delamination damage sizes of Φ6.0 mm, Φ10.0 mm, and Φ15.0 mm. The experimental results verify the correctness of the simulation. According to the Hermite interpolation results of the finite-element simulation data, the relationship between the delamination damage size and the SDC was fitted by the Gaussian function, which can accurately quantify the delamination damage. The absolute error of the delamination damage quantification with fitting expression is not larger than 0.8 mm, and the percentage error is not more than 8%.

Understanding behavioral factors associated with obesity is of importance in addressing this issue. This study examined the association between cognitive restraint, uncontrolled eating, emotional eating and body mass index (BMI) and amount of food plated, consumed, leftovers, and leftover food thrown into the trash (food wasted) in early adolescent girls nine to 13 years in O’ahu, Hawai’i (n = 93). Food plated, consumed, leftovers, and food wasted were estimated using a three-day mobile food record (mFR). Weight and height were measured to compute BMI (kg/m2). The three-factor eating questionnaire provided a score from 0 to 100 for cognitive restraint, uncontrolled eating, and emotional eating. Higher scores are indicative of greater cognitive restraint, uncontrolled eating, and emotional eating. Pearson’s correlation and general linear models were computed to examine the relationship between three factor eating scores, BMI, and food plated, consumed, leftovers, and food wasted. There was no clinically significant association between cognitive restraint and amount of food wasted. Cognitive restraint was positively correlated with BMI (r=0.36, p<0.001) and with BMI z score (r=0.40, p<0.001). Uncontrolled eating and emotional eating were positively correlated with amount of leftover food at dinner (r=0.30, p=0.006; r=0.33, p=0.003, respectively). Emotional eating was positively associated with percentage of leftover food at dinner (r=0.24, p=0.30). Additional research should examine the specific roles of cognitive restraint, uncontrolled eating, emotional eating and food waste in the development of obesity in adolescents.

Background. The markerless motion capture system (MLS) is a new technology that uses deep learning to detect body segments from digital images. This study tested the agreement between the MLS and a force-plate based system (FPS, “gold standard”) to quantify stability control and motor performance (MP) during gait initiation (GI). Methods. Healthy adults (young and elderly) and patients with Parkinson’s disease (PD) performed GI series at spontaneous and maximal velocity on an FPS while being filmed by an MLS. Signals from both systems were used to compute the peak of forward center-of-mass velocity (indicator of MP) and the braking index (BI, indicator of stability control). Results. Descriptive statistics indicated that both systems detected between-groups differences and velocity effects similarly, while a Bland-Altman (BA) plot anal-ysis showed that BI and MP mean biases were virtually zero in all groups and conditions. Bayes factor 01 indicated strong (for BI) and moderate (for MP) evidence that both systems provided equivalent values. However, trial-by-trial analysis of BA plots revealed the possibility of differ-ences > 10% between the two systems. Conclusion. Although non-negligible differences do occur, MLS appears to be as efficient as FPS in detecting PD and velocity condition effects on BI and MP

Understanding and predicting damage progression within thin plain-woven CFRP components is an essential issue for scheduling maintenance intervals and structural inspections, and typically require extensive test series. However, uncertainties always remain and result in conservative design and unnecessary downtimes due to the repeated inspections of a healthy structure. SHM can be used to reduce these uncertainties, as it allows to evaluate the condition of a mechanical structure during operation. Numerous SHM methods are developed , that achieve different levels of damage identification but are often investigated at small coupons with non-realistic structural damages and loading conditions on both, structure and sensor. The present research investigates the electrical impedance tomography (EIT) featuring an elastoresistive thin-film sensor to evaluate damage that propagates from a circular hole in a large plate under cyclic tensile-tensile multi-block loading. Applied fatigue loads were increased multiple times up to a total number of two million cycles. During the loading damage initiated at the hole and continuously propagated into the plate. Repeated EIT evaluations of the applied sensor and validating evaluations by means of digital image correlation clearly revealed the robustness of the hardware and the potential of the SHM method for damage evaluation of plain-woven CFRP components.

The object of this work is to determine the correlation on the Nusselt number on the individual rows of a four-row tubular finned heat exchanger with continuous fins with a staggered tube arrangement using CFD modelling. Correlations for calculating Darcy-Weisbach friction factors on individual tube rows were also determined. Relationships for the Nusselt number and friction factor derived for the entire exchanger based on CFD modelling were compared with those available in the literature determined using experimental data. The maximum relative differences between the Nusselt number for a four-row exchanger determined experimentally and by CFD modelling are in the range from 22% for a Reynolds number based on a tube's outside diameter of 1,000 to 30% for a Reynolds number of 13,000. The maximum relative differences between the friction factor for a four-row exchanger determined experimentally and by CFD modelling are in the range of 50% for a Reynolds number based on a tube outer diameter of 1,000 to 10% for a Reynolds number of 13,000. The CFD modeling performed shows that in the range of Reynolds numbers based on hydraulic diameters from 150 to 1,400, the Nusselt number for the first row in a four-row finned heat exchanger is about 22% to 15% higher than the average Nusselt number for the entire exchanger. In the range of Reynolds number changes based on hydraulic diameter from 2,800 to 6,000, the Nusselt numbers on the first and second rows of tubes are close to each other. Correlations on Nusselt numbers and friction factors derived for individual tube rows can be used in the design of plate-fin and tube heat exchangers used in equipment such as air-source heat pumps, automotive radiators, air-conditioning systems and in air hot-liquid coolers. In particular, the correlations can be used to select the optimum number of tube rows in the exchanger.

The ocean of the planet Earth, which is as thin as a cicada's wings, play a role of catalyst to the evolving of the ancient plates. The ocean and the ancient plates of the planet Earth formed a magic Whirlpool of the Cross “十” shape with double whirl arms. The central core of the Cross “十” shape Ocean-Plate Whirlpool is the Hint Black Hole (HBH) located at the Northwestern Pacific Ocean floor which is decorated with invisible geological age distribution of clam shell. The double whirl arms of ancient plates are distinguished to be left and right at Bering Strait and just formed the ring of fire of the Pacific Ocean.The Cross “十” shape Ocean-Plate Whirlpool of the planet Earth was born at the equatorial area about 66 Ma ago and is rotating anticlockwise and drifting northward by a mini footprint of spiral at s speed of as slow as a snail moves. Obviously, it would come to an end at the North Pole about 100 Ma in the future. So, the lifespan of the Cross “十” shape Ocean-Plate Whirlpool would be about 166 Ma, from birth to death on the planet Earth.What is hidden behind of the evolving of the oceans and the ancient plates is the golden law of geometrical progression of ladder pagoda of attributes evolving of them, which is “1➨2➨4➨2➨1”, including upgrading and downgrading process. It seems to hint that what is happening on the planet Earth, including the top-level species of human race, is actually unique in the Milky Way galaxy in essence.The property roles of expanding and shrinking are existing in the Cross “十” shape Ocean-Plate Whirlpool by face to face and the exchange of property roles took place tens of millions of years ago. And that situation would happen again tens of millions of years in the future. It seems a giant circle of evolving of the exchange of property roles would be drawn by the Cross “十” shape Ocean-Plate Whirlpool in her lifetime.