THERMAL BUCKLING ANALYSIS OF INHOMOGENEOUS RECTANGULAR PLATE DUE TO UNIFORM HEAT SUPPLY

This paper is concerned with the thermal buckling analysis of an isotropic inhomogeneous rectangular plate subjected to the arbitrary thermal loads. The fundamental equations system is derived by introducing the technique of the newly defined position of the reference plane, which allows us to analyze the problem using an elementary plate theory. It is assumed that the material properties such as the coefficient of linear thermal expansion α, the thermal conductivity λ, and Young's modulus of elasticity, E, are changed in the thickness direction with the power law of the coordinate variable, whereas Poisson's ratio ν is assumed to be constant. As an illustrative example, we consider the thermal buckling problem of a simply supported inhomogeneous rectangular plate due to uniform heat supply. Numerical calculations are carried out for several cases taking into account the variations of the inhomogeneous material properties, aspect ratio, and width-to-thickness ratio.     

Numerical and experimental study of a solar equipped with offset rectangular plate fin absorber plate

A mathematical model that allows the determination of the thermal performances of the single-pass solar air collector with offset rectangular plate fin absorber plate is developed. The model can predict the temperature profile of all the components of the collector and of the air stream in the channel duct. Into the latter are introduced the offset rectangular plate fins, which increase the thermal heat transfer between the absorber plate and the fluid. The offset rectangular plate fins, mounted in a staggered pattern, are oriented parallel to the fluid flow and are soldered to the underside of the absorber plate. They are characterized by high heat transfer area per unit volume and generate the low pressure losses. The experimental results of the air stream temperature will be compared with the results obtained by the theoretical model suggested.     

STUDY ON LOCAL DELAMINATED THERMAL BUCKLING OF COMPOSITE LAMINATED PLATES

Based on the Whitcomb delaminated buckling model, a Rayleigh-Ritz analysis is presented to study the local thermal buckling problem of elliptical, rectangular, triangular, and lemniscate delaminations in a symmetric composite laminated plate. The critical temperatures of the laminated plate with various shaped local delaminations and different stacking patterns are obtained by utilizing the energy principle. The geometrical axis of various shapes of local delamination is arbitrary. The stacking sequence of base laminated plates is symmetric, but the stacking sequence of the sublayer is asymmetric. Finally, our experimental study on the mechanism of delaminated buckling failure in a laminated plate with a single elliptical and rectangular delamination near the surface of the laminated plate under thermal load was accomplished. Analytical predictions for the critical temperature yielding the local delamination buckling are shown to correlate well with experimental results for a number of different delamination shapes.     

Study and optimization of the thermal performances of the offset rectangular plate fin absorber plates, with various glazing

The low thermophysical characteristics of air used as a heat transfer fluid in the solar collectors with thermal conversion require a fully developed turbulent flow. This increases the thermal heat transfer between the absorber plate and the fluid, which clearly improves the thermal performances of the solar collector with obstacles arranged into the air channel duct. In the present work, we introduce, in solar collector, the offset rectangular plate fins, which are used in heat exchangers. An experimental investigation carried out showed the generated enhancement of thermal performance. The offset rectangular plate fins, mounted in staggered pattern, are oriented parallel to the fluid flow and are soldered to the underside of absorber plate. They are characterized by high heat transfer area per unit volume. High thermal performances are obtained with low pressure losses and in consequence a low electrical power consumption by the fan in comparison to the flat plate collector. The experimental results are all so compared by using two types of transparent cover; double and triple.     

Effect of Initial Imperfections on Thermal Buckling of Functionally Graded Plates

ABSTRACT

Thermal buckling analysis of rectangular functionally graded plates with initial geometrical imperfections is presented in this article. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the first-order shear deformation plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through the thickness, are described by a power function of the thickness variable. The plate is assumed to be under three types of thermal loading, namely: uniform temperature rise, nonlinear temperature rise through the thickness, and axial temperature rise. Resulting equations are employed to obtain the closed-form solutions for the critical buckling temperature change of an imperfect functionally graded plate. The influence of transverse shear on thermal buckling load is discussed.     

Experimental study of thermal performance of offset rectangular plate fin absorber-plates

A new technique was developed to enhance the heat transfer more than with fully developed turbulent flow. Commonly the offset rectangular plate fins are used in heat exchangers; they alternate with the periodically interruptions. The fluid homogenization depends on the length of interruption, and new velocity and thermal boundary layers were developed at each encountered offset fin located downstream of interruption. This technique characterizes a higher heat transfer than in fully developed turbulent flow. In the present work this technique of periodically interrupted offset fins is adapted to solar collector. An experimental investigation carried out showed the generated enhancement of thermal performance. The offset rectangular plate fins, mounted in staggered pattern, are oriented parallel to the fluid flow and are soldered to the underside of absorber plate. High thermal performances are obtained with low flow friction and in consequence a low electrical power consumption by the fan in comparison to the flat plate collector.     

THERMAL STRESS ANALYSIS OF A RECTANGULAR PLATE AND ITS THERMAL STRESS INTENSITY FACTOR FOR COMPRESSIVE STRESS FIELD

Abstract

In this study, a transient thermal stress problem of a rectangular plate due to a nonuniform heat supply is treated theoretically and, thereafter, fracture behaviors of the plate with a crack are examined for compressive stress states. Assuming that a crack located on an arbitrary position, with an arbitrary direction, is sufficiently small and is closed because of the compressive stress field, a temperature field, in a transient state, is analyzed by taking into account the effect of relative heat transfer on both surfaces of the plate. Thereafter, the corresponding thermal stress analysis is developed on the basis of the two-dimensional plane stress problem using Airy's stress function method, and the stress intensity factor is analyzed for the biaxial stress state. As an analytical model, we consider mechanical boundary conditions of prescribed displacement and estimate the stress intensity factor of a crack tip using parameters of the crack configuration such as the location, direction, length, and coefficient of friction. These numerical results are shown in graphical form.     

The experimental study of energy features for solar air heaters with different turbulator configurations

To assess the thermal performance in the climate conditions of western and central Iraq, the advantages of using a solar air collector with various turbulator absorber plates are experimentally explored. Four distinct kinds of absorber plates are provided flat plate (F), triangular (T), rectangular (R), and circular (C) turbulators at different air mass flow rates. The collector's economic properties and overall thermal performance are compared to the conventional flat plate turbulator heating systems. The main findings suggest that delta turbulators improve collector economics and overall thermal performance by generating vortex and dampening the formation of the thermal boundary layer in the direction of airflow. Furthermore, when the mass flow rate increases, the thermal performance improves, and the efficiency increases for all mass flow rates, resulting in good thermal performance for the rectangular plate collector when compared to other collectors. When compared to other types of configurations, the daily average efficiency of solar air collectors for flat plate (F), triangular (T), rectangular (R), and circular (C) turbulators are 28%, 67%, 39%, and 48%, respectively, at 50° tilt angle while at 90° tilt angle they are 44%, 76%, 54%, and 63%, respectively, as ṁ = 0.0377 kg/s. The maximum daily average efficiency fitted with rectangular turbulators have about 86% at the largest ṁ = 0.1 kg/s. This study will also give a unique direction to the work trend in the western and central parts of Iraq throughout the winter months.     

THERMAL BUCKLING OF FUNCTIONALLY GRADED PLATES BASED ON HIGHER ORDER THEORY

Equilibrium and stability equations of a rectangular plate made of functionally graded material (FGM) under thermal loads are derived, based on the higher order shear deformation plate theory. Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental partial differential equations is established. The derived equilibrium and stability equations for functionally graded plates (FGPs) are identical to the equations for laminated composite plates. A buckling analysis of a functionally graded plate under four types of thermal loads is carried out and results in closed-form solutions. The critical buckling temperature relations are reduced to the respective relations for functionally graded plates with a linear composition of constituent materials and homogeneous plates. The results are compared with the critical buckling temperatures obtained for functionally graded plates based on classical plate theory given in the literature. The study concludes that higher order shear deformation theory accurately predicts the behavior of functionally graded plates, whereas the classical plate theory overestimates buckling temperatures.     

An Extension of the Flow Boiling Correlation to Transition,Laminar, and Deep Laminar Flows in Minichannels and Microchannels

The thermal performance of rectangular plate fins circumscribing elliptic tubes is presented in this paper. Based on the assumption of uniform convective heat transfer the two-dimensional conduction equation has been formulated, and the solution has been obtained through the finite element method. Performance of rectangular plate fins for both inline and staggered arrangement of tubes has been investigated for a variation of geometric and thermo-geometric parameters. The necessity of optimizing the fin geometry for a given fin surface area has also been highlighted.     

THERMAL STRESSES AND DEFLECTIONS OF CROSS-PLY LAMINATED PLATES USING REFINED PLATE THEORIES

Exact analytical solutions of refined plate theories are developed to study the thermal stresses and deflections of cross-ply rectangular plates. The state-space approach in conjunction with the Levy method is used to solve exactly the governing equations of the theories under various boundary conditions. Numerical results of the higher-order theory of Reddy for thermal stresses and deflections are compared with those obtained using the classical and first-order plate theories.     

TRANSIENT THERMAL STRESSES IN A RECTANGULAR PLATE DUE TO NONUNIFORM HEAT TRANSFER COEFFICIENTS

Abstract

The linear problems of transient temperature and thermal stresses in a thin, finite, rectangular plate subjected to heat losses due to nonuniform heat transfer coefficients on the upper and lower plate surfaces are solved by a direct power series approach through the application of the Lanczos-Chebyshev and the discrete least-squares methods. A numerical example demonstrates the accuracies that can be achieved by using only a small number of terms.     

Comparative Study of Thermal Performance of Parallel Plate and Rectangular Microchannel Counter Flow Heat Exchangers

This paper is aimed at comprehensive investigations of the thermal performance of parallel plate and rectangular microchannel counter flow heat exchangers based on axial conduction, number of transfer units, and non-dimensional power density. The geometrical parameters of the two configurations are optimized for a given heat transfer rate, effectiveness, and pressure drop. A reduced order model of rectangular micro channel counter flow heat exchanger is developed in which it is transformed into a hydrodynamically and thermally equivalent parallel plate micro heat exchanger. To improve the accuracy of the model, correction factors obtained from detailed computational fluid dynamics model are introduced. Various factors affecting the dimensionless power density of both the counter flow micro heat exchangers are studied. It is found that the axial conduction plays an important role on the performance of rectangular channel counter flow micro heat exchanger. In the limiting case where the channel aspect ratio tends to zero, the dimensionless power density of rectangular channel is found to approach that of a parallel plate counter flow micro heat exchanger.     

Thermal Buckling of Piezolaminated Plates Subjected to Different Loading Conditions

A thermal buckling analysis is presented for simply supported rectangular laminated composite plates that are covered with top and bottom piezoelectric actuators, and subjected to the combined action of thermal load and constant applied actuator voltage. The thermomechanical properties of composite and piezoelectric materials are assumed to be linear functions of the temperature. The formulations of the equations are based on the higher-order laminated plate theory of Reddy and using the Sanders nonlinear kinematic relations. The closed-form solutions for the buckling temperature are obtained through the Galerkin procedure and solving the resultant eigenvalue problem, which are convenient to be used in engineering design applications. Numerical examples are presented to verify the proposed method. The effects of the plate geometry, fiber orientation in composite layers, lay-up configuration, different utilized piezoelectric materials, temperature dependency of material properties, thermal conductivity, and energy generation on the buckling load are investigated.     

FAILURE-MODE TRANSITION SPEED IN THREE-DIMENSIONAL TRANSIENT DEFORMATIONS OF A MICROPOROUS HEAT-CONDUCTING THERMOELASTOVISCOPLASTIC PRENOTCHED PLATE

ABSTRACT

We analyze three-dimensional finite coupled thermomechanical deformations of a rectangular plate with two parallel notches placed symmetrically about the horizontal centroidal plane of the plate. The edge surface of the plate between the two notches is struck by a cylindrical projectile of diameter equal to the distance between the notches and made of the same material as the plate. The plate material is modeled as heat-conducting, microporous, elastoviscoplastic, and isotropic. Both the brittle and the ductile failures initiate at points adjoining the notch-tip surface that are on the midplane of the plate and propagate toward the outer surfaces. Even for a relatively thin plate, the difference in the times of initiation of failures on the mid and front surfaces is significant. Also the two failure modes on the mid surface initiate much later than that predicted by the plane strain analysis. Thus an experimentalist observing fracture on the front or the back face of the plate will see it initiate much later than the times given by the plane strain analysis of the problem. For a steel plate, it is found that the failure mode transitions from brittle to ductile at an impact speed of about 21.8 m/s.     

On thermoelastic problem of a thermosensitive functionally graded rectangular plate with instantaneous point heat source

The present article attempts to investigate transient thermoelastic problem of a functionally graded thin rectangular plate with thermosensitive and spatial variable dependent material properties. All the material properties are assumed to be isotropic. Kirchhoff’s variable transformation is used to deal with the nonlinearity of the three dimensional heat conduction equation and that equation is solved by the integral transform method considering an instantaneous point heat source. The thermoelastic behavior of the rectangular plate is studied together with the thermal deflection and thermally induced resultant moments. Numerical computations are carried out for ceramic-metal-based functionally graded material, in which alumina is selected as ceramic and nickel as metal. The results are illustrated graphically.     

Thermal Postbuckling Behavior of 3D Braided Rectangular Plates

Thermal postbuckling characteristics of 3D braided rectangular plates are investigated. A 3D braided composite may be treated as a cell system and the geometry of each cell is deeply dependent on its position in the cross-section of the plate. Based on Reddy's higher-order shear deformation plate theory, a perturbation technique is employed to determine buckling temperatures and postbuckling equilibrium paths of simply supported 3D braided rectangular plates. The results reveal that the temperature-dependent properties, geometric parameter, fiber volume fraction and braiding angle have a significant effect on thermal postbuckling behavior of braided composite plates.     

Performance analysis and optimization of absorber plates of different geometry for a flat-plate solar collector: a comparative study

This paper presents a comparative study on the performance and optimization of several profile shapes namely, rectangular, trapezoidal and rectangular profile with a step change in local thickness (RPSLT). This analysis concentrates on the performance and optimization of RPSLT. A modification has been suggested for the analysis of RPSLT absorber plate that was observed by Hollands and Stedman [Solar Energy 49 (1992) 493]. The result indicates that there is optimum fin efficiency of trapezoidal profile for constant plate volume. The RPSLT profile of absorber plate is superior to other profiles because of higher performance and less difficulties in fabrication.     

Experimental and Three—Dimensional Numerical Study on Under—Expanded Impinging Jets

IntroductionUnder-expanded impinging jets have attracted theinterest of many researchers not only because they havepotentially engineering applications such as surfacecooling devicesl'], and plasma spray coating['], alsobecause they are not fully understood yet[' 5]. Goldsteinet al. confirmed that the stagnation temperature near thestagnation region on the impinging plate is larger thanthat in the settling chamber despite no heat added to theflow during its process from the settling chamber to…