Laminar counterflow parallel-plate heat exchangers: Exact and approximate solutions

Multilayered, counterflow, parallel-plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for the temperature field involves eigenfunction expansions that can be solved in terms of Whittaker functions using standard symbolic algebra packages, leading to analytical expressions that provide the eigenvalues numerically. It is seen that the approximate solution obtained by retaining the first two modes in the eigenfunction expansion provides an accurate representation for the temperature away from the entrance regions, specially for long heat exchangers, thereby enabling simplified expressions for the wall and bulk temperatures, local heat-transfer rate, overall heat-transfer coefficient, and outlet bulk temperatures. The agreement between the numerical and theoretical results suggests the possibility of using the analytical solutions presented herein as benchmark problems for computational heat-transfer codes.

Analysis of plate bending by means of high order finite hyperelements

The possibilities and limitations of high order hyperelements in plate bending analysis are discussed. Explicit shape functions for some types of triangular elements are given. These elements are applied to simple cases to assess their computational efficiency.

A C1 finite element for Kirchhoff plate bending

After a short introduction the possibilities and limitations of polynomial simple elements with C1 continuity are discussed with reference to plate bending analysis. A family of this kind of elements is presented.. These elements are applied to simple cases in order to assess their computational efficiency. Finally some conclusions are shown, and future research is also proposed.

A computer formulation for the analysis on continuous non prismatic folded plate structures of arbitrary cross-section

A computer solution to analyze nonprismatic folded plate structures is shown. Arbitrary cross-sections (simple and multiple), continuity over intermediate supports and general loading and longitudinal boundary conditions are dealt with. The folded plates are assumed to be straight and long (beam like structures) and some simplifications are introduced in order to reduce the computational effort. The formulation here presented may be very suitable to be used in the bridge deck analysis.

A survey on folded plate structures

A compact formulation of the linear theory of folded plate structures utilizing matrix methods is given. Different usual approximations and comparison between them are also shown

A plastic analysis of nonprismatic folded plate structures

A computer method for the plastic analysis of folded plate structures is presented. The method considers the specific characteristics of the folded plate structural model using a simplified one-dimensional theory. and it can be applied to the analysis of any type of folded pIates, either prismatic or nonprismatic, with arbitrary cross-section. A simple example is analyzed in order to show the possibilities of the procedure and some results of interest are presented

The folded plate model in structural analysis. Elastic, plastic and dynamic formulations for nonprismatic structures

A specific numerical procedure for the analysis of arbitrary nonprismatic folded plate structures is presented. An elastic model is studied and compared with a harmonic solution for a prismatic structure. An extension to the plastic analysis is developed, and the influence of the structural geometry and loading pattern is analyzed. Nonprismatic practical cases, with arbitrary geometry and loading are shown, as well in the elastic range as in the plastic one. Finally, a dynamic formulation is outlined

Application of the dynamic models to the detection of imperfections in plate Structures

This paper is part of a set of publications related with the development of mathematical models aimed to simulate the dynamic input and output of experimental nondestructive tests in order to detect structural imperfections. The structures to be considered are composed by steel plates of thin thickness. The imperfections in these cases are cracks and they can penetrate either a significant part of the plate thickness or be micro cracks or superficial imperfections. The first class of cracks is related with structural safety and the second one is more connected to the structural protection to the environment, particularly if protective paintings can be deteriorated. Two mathematical groups of models have been developed. The first group tries to locate the position and extension of the imperfection of the first class of imperfections, i.e. cracks and it is the object of the present paper. Bending Kirchoff thin plate models belong to this first group and they are used to this respect. The another group of models is dealt with membrane structures under the superficial Rayleigh waves excitation. With this group of models the micro cracks detection is intended. In the application of the first group of models to the detection of cracks, it has been observed that the differences between the natural frequencies of the non cracked and the cracked structures are very small. However, geometry and crack position can be identified quite accurately if this comparison is carried out between first derivatives (mode rotations) of the natural modes are used instead. Finally, in relation with the analysis of the superficial crack existence the use of Rayleigh waves is very promising. The geometry and the penetration of the micro crack can be detected very accurately. The mathematical and numerical treatment of the generation of these Rayleigh waves present and a numerical application has been shown.

Application of the homogenization techniques to the determination of the effective flexure constants of plate structural systems

A Mindlin plate with periodically distributed ribs patterns is analyzed by using homogenization techniques based on asymptotic expansion methods. The stiffness matrix of the homogenized plate is found to be dependent on the geometrical characteristics of the periodical cell, i.e. its skewness, plan shape, thickness variation etc. and on the plate material elastic constants. The computation of this plate stiffness matrix is carried out by averaging over the cell domain some solutions of different periodical boundary value problems. These boundary value problems are defined in variational form by linear first order differential operators on the cell domain and the boundary conditions of the variational equation correspond to a periodic structural problem. The elements of the stiffness matrix of homogenized plate are obtained by linear combinations of the averaged solution functions of the above mentioned boundary value problems. Finally, an illustrative example of application of this homogenization technique to hollowed plates and plate structures with ribs patterns regularly arranged over its area is shown. The possibility of using in the profesional practice the present procedure to the actual analysis of floors of typical buildings is also emphasized.

Effects of estrogen on growth plate senescence and epiphyseal fusion

Estrogen is critical for epiphyseal fusion in both young men and women. In this study, we explored the cellular mechanisms by which estrogen causes this phenomenon. Juvenile ovariectomized female rabbits received either 70 μg/kg estradiol cypionate or vehicle i.m. once a week. Growth plates from the proximal tibia, distal tibia, and distal femur were analyzed after 2, 4, 6, or 8 weeks of treatment. In vehicle-treated animals, there was a gradual senescent decline in tibial growth rate, rate of chondrocyte proliferation, growth plate height, number of proliferative chondrocytes, number of hypertrophic chondrocytes, size of terminal hypertrophic chondrocytes, and column density. Estrogen treatment accelerated the senescent decline in all of these parameters. In senescent growth plates, epiphyseal fusion was observed to be an abrupt event in which all remaining chondrocytes were rapidly replaced by bone elements. Fusion occurred when the rate of chondrocyte proliferation approached zero. Estrogen caused this proliferative exhaustion and fusion to occur earlier. Our data suggest that (i) epiphyseal fusion is triggered when the proliferative potential of growth plate chondrocytes is exhausted; and (ii) estrogen does not induce growth plate ossification directly; instead, estrogen accelerates the programmed senescence of the growth plate, thus causing earlier proliferative exhaustion and consequently earlier fusion.

Control of somite patterning by signals from the lateral plate.

The body musculature of higher vertebrates is composed of the epaxial muscles, associated with the vertebral column, and of the hypaxial muscles of the limbs and ventro-lateral body wall. Both sets of muscles arise from different cell populations within the dermomyotomal component of the somite. Myogenesis first occurs in the medial somitic cells that will form the epaxial muscles and starts with a significant delay in cells derived from the lateral somitic moiety that migrate to yield the hypaxial muscles. The newly formed somite is mostly composed of unspecified cells, and the determination of somitic compartments toward specific lineages is controlled by environmental cues. In this report, we show that determinant signals for lateral somite specification are provided by the lateral plate. They result in a blockade of the myogenic program, which maintains the lateral somitic cells as undifferentiated muscle progenitors expressing the Pax-3 gene, and represses the activation of the MyoD family genes. In vivo, this mechanism could account for the delay observed in the onset of myogenesis between muscles of the epaxial and hypaxial domains.