The transient thermo-electro-elastic fields in a piezoelectric plate with a crack

This paper is concerned with a thin plate made by a piezoelectric ceramic material and containing a crack perpendicular to its surfaces. It is assumed that the transient thermal stress is set up by the application of a heat flux as a function of the time and position along the crack edge and the heat flow by convection from the plate surfaces. The plate is also subjected to mechanical and electric loadings. The exact analytical formulae are obtained for transient thermo-electro-elastic fields in the plate. The exact analytical solutions for the stress and electric displacement intensity factors and crack-opening displacement are obtained. Numerical examples show, among others, a dependence of the stress and electric displacement intensity factors on the thermal and elastic, piezoelectric and dielectric constants of the piezoelectric materials.     

Experimental investigation of impingement heat transfer on a flat and dimpled plate with different crossflow schemes

A nine-by-nine jet array impinging on a flat and dimpled plate at Reynolds numbers from 15,000 to 35,000 has been studied by the transient liquid crystal method. The distance between the impingement plate and target plate is adjusted to be 3, 4 and 5 jet diameters. Three jet-induced crossflow schemes, referred as minimum, medium and maximum crossflow correspondingly, have been measured. The local air jet temperature is measured at several positions on the impingement plate to account for an appropriate reference temperature of the heat transfer coefficient. The heat transfer results of the dimpled plate are compared with those of the flat plate. The best heat transfer performance is obtained with the minimum crossflow and narrow jet-to-plate spacing no matter on a flat or dimpled plate. The presence of dimples on the target plate produce higher heat transfer coefficients than the flat plate for maximum and minimum crossflow.     

EFFICIENCY OF AN INVERSE METHOD TO DETERMINE NATURAL-CONVECTION HEAT

The final aim of this study is to identify the value of convective heat transfer generated by a local perturbation analog to a sun patch. A first approach to this work consisted of developing a means of evaluating the local heat transfer based on the use of an inverse method. We first chose the well-known academic case of a vertical heated plane plate to generate natural heat convection transfer. Then, for several temperatures of the plate, a first validation of the chosen inverse method was obtained in the steady state. It consisted of a comparison between the results provided by the inverse method and those obtained by the use of thermocouples to measure the temperature inside the boundary layer. These two types of results are also compared with relations published in the literature. In conclusion, the authors observe that the inverse method is pertinent and gives satisfactory results.     

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.     

THERMAL-STRESS PROBLEMS IN INDUSTRY. 6: TRANSIENT THERMAL STRESSES IN A PLATE DUE TO ROLLING WITH CONSIDERATION OF COUPLING EFFECT

In this paper, the transient thermal-stress problem in a plate subjected to frictional heat generation in rolling ( or welding) is theoretically analyzed with the consideration of the thermomechanical coupling effect. Numerical evaluation is carried out for the temperature distribution, thermal stresses, and thermal deformation in a flat plate heated by linear heat sources which are located symmetrically on both surfaces and which move with constant velocity.     

An experimental study on the quantitative interpretation of local convective heat transfer for a plate fin and tube heat exchanger using the lumped capacitance method

An experimental study has been performed to investigate the heat transfer characteristics of a plate fin and tube heat exchanger. Existing transient and steady methods are inappropriate for the measurement of heat transfer coefficients of the thin heat transfer model. In this study, the lumped capacitance method based on liquid crystal thermography was adopted. The method is validated through impinging jet and plate flow experiments. The two experiments showed very good agreements with those of the well-known transient method with the thick acryl model. And the lumped capacitance method showed similar results regardless of the thickness of the polycarbonate model if the Bi of the fin is small enough. The method was also applied for the heat transfer coefficient measurements of a fin and tube heat exchanger. Quantitative heat transfer coefficients of the plate fin were successfully obtained.     

THERMAL STRESS IN AN ORTHOTROPIC PLATE CONTAINING A PAIR OF COPLANAR CENTRAL CRACKS

Abstract

The thermal stress problem for a pair of coplanar central cracks contained in an orthotropic plate is investigated using the techniques of Fourier transforms and finite Hilbert transforms. The crack surfaces are subjected to symmetrical thermal loadings. Exact expressions for the temperature field, the crack shapes, and the thermal stresses in the crack plane are obtained for the case of constant temperature. The opening-mode stress intensity factors at the inner and outer crack tips are also obtained in closed forms in terms of the material properties and the distance between the cracks. The properties of the stress intensity factors are shown to be different from the shear-mode stress intensity factors because of the disturbance of a uniform heat flow by a pair of central cracks.     

Free convection from a vertical plate in a porous media subjected to a sudden change in surface temperature

The unsteady heat transfer process involved in free convection flow along a vertical surface embedded in a porous medium is investigated. An analytical solution has been obtained for the temperature/velocity field for small times in which the transport effects are confined within an inner layer adjacent to the plate. Then, a numerical solution of the full boundary-layer equation is obtained for the whole transient from the initial unsteady state to the final steady state. Detailed results of the effect of the temperature inputs on the transient process are given.     

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.     

Optimization of heat losses in normal and reverse flat-plate collector configurations: Analysis and performance

This communication presents a comparative analysis of flat-plate collector operated in normal and reverse configurations. Radiative and convective heat losses from the absorber and back collector have been minimised by optimizing the absorber to cover glass separation (gap width), providing low emissivity surfaces on the collector's back face and spacing an additional reflector supported on glasswool insulation behind the back face. Expressions for the transient and stagnation temperatures of the absorber plate have been derived. Experimental results are found to be in close agreement with the theory.     

板翅式换热器翅片及隔板动态特性分析

基于板翅式换热器翅片的非稳态导热方程，计算分析了翅片的动态特性，认为翅片的不稳定传热过程相对于换热器其它过程特征时间无限小，因此可以不考虑翅片的动态特性，从而简化了板翅式换热器动态模型，通过分析换热器动态过渡过程表明：隔板的热容对板翅式换热器的动态特性的影响是不容忽略的。     

MULTIPLE ENGAGEMENT WET CLUTCH HEAT TRANSFER MODEL

To optimize the thermal performance of transmission wet clutches during multiple engagements, a general thermal numerical model has been developed. At every cycle, temperatures are computed throughout the clutch materials until a periodic steady state is achieved. One cycle is characterized by (a) an engagement period where the separator plate is contacting the friction lining with heat being generated while some cooling is provided by the oil passing through friction material grooves; (b) a locked stage of separator plate and friction lining contact during which the heat generation is zero while oil cooling through the grooves continues; and (c) a cooling period with the separator plate completely disengaged from the friction lining while the oil cools both surfaces. Temperatures are calculated from the transient numerical solution of the heat conduction equation in two dimensions. The finite difference technique based on an implicit numerical scheme is employed. This approach is verified by comparison with a known solution as well as experimental data, and a sample run is presented for conditions representative of an actual clutch assembly.     

Evaluation of heat exchanger surface coatings

Compact heat exchangers are very popular due to their effectiveness, small footprint and low cost. In order to protect heat exchangers in dirty applications, coatings can be applied to the heat transfer surfaces to extend effectiveness and minimize fouling. Coating selection is extremely important since the wrong coating can decrease unit effectiveness, cause more fouling, and/or erode the surface.An experimental investigation of coating effectiveness in compact plate heat exchangers is presented. New, cleaned and coated plate heat exchangers are considered in this study. Heat exchangers have been exposed to untreated lake water for various time periods. Transient effectiveness results compare the rate of fouling for coated and uncoated heat exchangers. Additional results compare deposit weight gain at the end of the test period and transient observations of heat transfer surface appearance. All heat exchanger combinations showed some deposit accumulation for the period considered.Results indicate that the thermal performance of the unit decreases with time, resulting in an undersized heat exchanger. For the conditions considered here, uncoated plates accumulate deposits up to 50% faster than coated plates and show a decrease in performance of up to 40%. Surface coating, exposure time, fluid velocity and concentration of particles can affect fouling.     

GREEN'S FUNCTION APPROACH TO THREE-DIMENSIONAL HEAT CONDUCTION EQUATION OF FUNCTIONALLY GRADED MATERIALS

A Green's function approach based on the laminate theory is adopted to solve the three-dimensional heat conduction equation of functionally graded materials (FGMs) with one-directionally dependent properties. An approximate solution for each layer is substituted into the governing equation to yield an eigenvalue problem. The eigenvalues and the corresponding eigenfunctions obtained by solving an eigenvalue problem for each layer constitute the Green's function solution for analyzing the three-dimensional transient temperature. The eigenvalues and the corresponding eigenfunctions are determined from the homogeneous boundary conditions at outer sides and from the continuous conditions of temperature and heat flux at the interfaces. A three-dimensional transient temperature solution with a source is formulated by the Green's function. Numerical calculations are carried out for an FGM plate, and the numerical results are shown in tables and figures.     

Dynamic modeling and control of plate heat exchanger

A general model has been developed to suggest the transient responses of a plate heat exchanger. The predicted and experimental step responses of the system have been analyzed using the frequency response analysis. The results indicate that the system is represented by a first order lag and dead time. A closed fit between the simulated and experimental data has been obtained.To verify the presented model, temperature control has been applied on the plate heat exchanger using both conventional and fuzzy logic controllers. Results show that the performance of the fuzzy logic controller produces transient responses with less settling time and less oscillatory behavior compared to that under the conventional controller. Comparisons between simulated and experimental responses indicate that the developed model is capable of predicting the transient responses of the plate heat exchanger, satisfactory.     

THERMAL STRESSES AROUND TWO PARALLEL CRACKS IN AN INFINITE ORTHOTROPIC PLATE UNDER UNIFORM HEAT FLOW

Stress intensity factors around two parallel cracks in an infinite orthotropic plate have been determined. Uniform heat flows normally to the cracks. Thermal insulation is assumed on the surfaces of the cracks. The mixed boundary value conditions are reduced to dual integral equations using the Fourier transform technique. In order to solve the equations, the temperatures and displacements at the two cracks are expanded in a series of functions that are zero outside the cracks. The unknown coefficients in each series are solved by the Schmidt method. The stress intensity factors are calculated numerically for steel and ceramic-fiber-reinforced ceramics.     

A simplified approach for the thermoelastic large deflection in the thin clamped annular sector plate

The present article is concerned with analysis of large deflection of a heated thin annular sector plate with clamped edges under transient temperature distribution using Berger’s approximate methods. The prescribed surface temperature is at the top face of the plate whereas the bottom face is kept at zero temperature. In this study, the Laplace transform as well as the classical method have been used for the solution of heat conduction equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained using resultant bending moment and resultant forces per unit length. The calculations are obtained for the aluminium plate in the form of an infinite series involving Bessel functions, and the numerical results for temperature, deflection, resultant bending moments, and thermal stresses have been illustrated by graphs.     

Experimental study of the interactions between long and short-term unsteady heat transfer responses on the in-cylinder and exhaust manifold diesel engine surfaces

The paper presents the results from the analysis of an experimental investigation with the aim to provide insight to the cyclic, instantaneous heat transfer phenomena occurring in both the cylinder head and exhaust manifold wall surfaces of a direct injection (DI), air-cooled diesel engine. The mechanism of cyclic heat transfer is investigated during engine transient events, viz. after a sudden change in engine speed and/or load, both for the combustion chamber and exhaust manifold surfaces. These results are then compared with relevant experimental data from steady state operation which in the present case are used as reference helping to reveal any potential influences of each transient event on cyclic heat transfer. The experimental installation allowed both long- and short-term signal types to be recorded on a common time reference base during the transient event. Processing of experimental data was accomplished using a modified version of one-dimensional heat conduction theory with Fourier analysis, capable to cater for the special characteristics of transient engine operation. Based on this model, the evolution of local surface heat flux during a transient event was calculated. Two engine transient events are examined, which present a key difference in the way the load and speed changes are imposed on each one of them. From the analysis of experimental results it is confirmed that each thermal transient event consists of two distinguished phases the “thermodynamic” and the “structural” one which are appropriately configured and analyzed. In the case of a severe variation, in the first 20 cycles after the beginning of the transient event, the wall surface temperature amplitude on cylinder head was almost three times higher than the one observed at the “normal” temperature oscillations occurring during the steady state operation. At the same time, peak pressure values in the same cycles are increased by almost 15% above their corresponding values at the final steady state. The same phenomena are valid for the exhaust manifold surfaces but on a moderated scale.     

A quasi-3D analysis of the thermal performance of a flat heat pipe

The thermal performance of a flat heat pipe thermal spreader has been described by a quasi-3D mathematical model and numerically modeled. An explicit finite volume method with under-relaxation was used for computations in the vapor phase. This was combined with a relatively small time step for the analysis. The physical problem consisted of an evaporator surface that was transiently heated non-uniformly for a short period of time and the heat source then removed. Then the system was cooled by natural convection and radiative heat transfer at the condenser region. The transient temperature distributions at the front and back of the heat spreader were obtained for different times during the transient period. The velocity distribution in the vapor core was also obtained. Due to the effect of phase change at the evaporator and condenser sides, a significant amount of energy is found to be absorbed and partially released during the transient heating and cooling processes. The numerical results indicate that advection and the high thermal diffusivity of the vapor phase accelerate the propagation of the temperature distribution in the vapor core, making it uniform during this process. The condenser temperature distribution was almost uniform at the end of the transient heating process. The transient temperature distribution on a solid aluminum plate was compared with the flat heat pipe results and indicated that the flat heat pipe successfully spread the heat uniformly at the condenser side of the structure.     

The Investigation of Flow Boiling for Flows in Channels with Cross-Corrugated Walls

The problem of heat transfer for flows in channels with corrugated walls is very complicated. Previously most investigators have focused their attention on studies of forced-convection, single-phase flow, and condensation of pure vapors and vapor gas mixtures. The results of new experimental investigations into heat transfer and pressure drop, for flow boiling in channels with corrugated walls, are discussed. The experimental section was a part of a pack of an industrial plate exchanger, which contained several pressed plates with longitude corrugations located under an angle to flow direction and had many contact points on the heat transfer area. The condensation method was used for the investigations. The relationship between the heat transfer ratios of the Nusselt number for single-phase flow was obtained. This correlation compares very favorably with the similar relationship obtained for flow bubble boiling in tubes proposed by Sterman [11]. For correlation of the pressure drop data, the Martinelli-Lockart approach was used, which also correlated well with the results of this study and the results of other investigations. The relationship obtained may be used in calculations for various types of industrial units which have corrugated patterns on their heat transfer surfaces.