Thermoelastic interactions without energy dissipation in an unbounded body with a cylindrical cavity

In this work, we apply Green and Naghdi's generalized thermoelasticity theory to a one-dimensional problem of an infinitely long cylindrical cavity. Laplace transform techniques are used to solve the problem. A comparison of generalized thermoelasticity theory with one relaxation time is made. Numerical results are computed and represented graphically for the temperature,displacement, and stress distributions.     

A 2D problem of thermoelasticity without energy dissipation for a sphere subjected to axisymmetric temperature distribution

We solve a 2D problem for a sphere in the theory of thermoelasticity without energy dissipation WED. The sphere’s surface is taken to be traction free and subjected to an axisymmetric temperature distribution that is harmonic in time. A direct approach is used to solve the problem. We consider two different cases of the boundary conditions. The collocation method was used in one of them where we could not obtain the exact solution. Numerical results are represented graphically and discussed.     

A thermoelastic spherical shell with and without energy dissipation

In this work, we apply the Green and Naghdi generalized thermoelasticity theory to a one-dimensional problem of distribution of thermal stresses and temperature in a generalized thermoelastic medium in the form of a spherical shell subjected to sudden change in the temperature of its external boundary. The results are compared to the generalized thermoelasticity theory with one relaxation time. Numerical results are computed and represented graphically for temperature, displacement, and stress distributions.     

On an influence of thermal stresses and magnetic field in thermoelastic half-space without energy dissipation

In this article, a two-dimensional problem for a homogeneous, isotropic, and thermoelastic half-space subjected to magnetic field and time-dependent heat source is investigated. The boundary conditions at the surface have been considered in the context of Green-Naghdi’s second model (GN-II) of thermoelasticity. The normal mode analysis and eigenvalue approach techniques are used to solve the nondimensional coupled equations. The effect of magnetic field, frequency, wave number, and time is analyzed theoretically and computed numerically. Comparison was made with the results obtained in the presence and absence of the magnetic field. Numerical results for the displacement components, mean value of normal stresses, dilatation, and temperature have been represented graphically to show the physical meaning of the external parameters. The results indicate that the effect of magnetic field, frequency, wave number, and time is very pronounced and effective on the phenomena.     

Coupled thermoelasticity analysis of FGM plate integrated with piezoelectric layers under thermal shock

Abstract

Based on theory of piezoelectricity and using generalized coupled thermoelasticity, transient response of a simply supported functionally graded material rectangular plate embedded in sensor and actuator piezoelectric layers under applied electric field and thermal shock is studied. Thermoelastic properties of the plate vary continuously along the thickness direction according to exponential functions and Poisson ratio is assumed to be constant. Applying Fourier series state space technique to the basic coupled thermoelastic differential equations results in the ordinary differential equations which are solved analytically by using Laplace transform. Validation of the present approach is assessed by comparing the numerical results with the available results in literature. In parametric study, effect of the relaxation time, applied voltage and temperature and time history of the thermoelastic response of FGM plate attached to piezoelectric layers are investigated.     

Dynamic response of an infinite medium with a spherical cavity on temperature-dependent properties subjected to a thermal shock under fractional-order theory of thermoelasticity

In this work, we consider the problem for an infinite medium with a spherical cavity on temperature-dependent properties subjected to a stress shock and thermal shock under the fractional-order theory of generalized thermoelasticity. The modulus of elasticity and the coe?cient of thermal conductivity are taken as linear function of temperature. The governing equations for the problem are formulated and then solved by Laplace transform together with its numerical inversion. The nondimensional temperature, displacement, radial stress, and hoop stress are obtained and illustrated graphically. In the calculation, the emphasis is focused on investigating the effect of temperature-dependent properties on the variations of the considered variables. The graphical results indicate that the temperature-dependent modulus of elasticity plays a significant role on all the physical quantities.     

Spectral analysis of thermoelastic systems under nonclassical thermal models

We study some spectral properties of the solutions to generalized thermoelastic systems under Lord–Shulman, Green–Lindsay, and Green–Naghdi of type-II models. First, we prove that the linear operator of each model has compact resolvent and generates a C₀?semigroup in an appropriate Hilbert space. We also show that there is a sequence of generalized eigenfunctions of the linear operator that forms a Riesz basis. By a detailed spectral analysis, we obtain the expressions of the spectrum and we deduce that the spectrum-determined growth condition holds. Therefore, if the imaginary axis is not an asymptote of the spectrum, we prove that the energy of each model decays exponentially to a rate determined explicitly by the physical parameters. Finally, some simulations are given for each model to support our results.     

Analytical solution of generalized coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads

In this article, a fully analytical solution of the generalized coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads, based on Lord–Shulman model, is presented. The general forms of axisymmetric thermal and mechanical boundary conditions as arbitrary time-dependent heat transfer and traction, respectively, are considered at the inner and outer radii of the disk. The governing equations are solved analytically using the principle of superposition and the Fourier–Bessel transform. The general closed form solutions are presented for temperature and displacement fields. To validate the solutions, the results of this study are compared with the numerical results available in the literature, which show good agreement. For the temperature, displacement and stresses, radial distributions, and time histories are plotted and discussed. The propagation of thermoelastic waves and their reflection from the boundary of the disk are clearly shown. Moreover, effects of relaxation time and angular velocity on temperature, displacement, and stress fields are investigated.     

Investigation of the thermal-elastic problem in cracked semi-infinite FGM under thermal shock using hyperbolic heat conduction theory

In this paper, a thermoelastic analytical model is established for a functionally graded half-plane containing a crack under a thermal shock in the framework of hyperbolic heat conduction theory. The moduli of functionally graded materials (FGMs) are assumed to vary exponentially with the coordinates. By employing the Fourier transform and Laplace transform, coupled with singular integral equations, the governing partial differential equations under mixed, thermo-mechanical boundary conditions are solved numerically. For both the temperature distribution and transient stress intensity factors (SIFs) in FGMs, the results of hyperbolic heat conduction model are significantly different than those of Fourier’s Law, which should be considered carefully in designing FGMs.     

Dynamic simulation of hydrogen-based off-grid zero energy buildings with hydrogen storage considering Fanger model thermal comfort

In this study, some locations with different climates, off-grid zero energy buildings with hydrogen energy storage systems are designed, and transient analysis is conducted. These considered buildings supply their electricity consumption without using the electrical grid and PV panels or wind turbines. Also, they supply thermal comfort to occupants by using a vapor compression chiller and humidifier. Domestic hot water of occupants is supplied using solar collectors. For analyzing building's performance and objectives achievement, TRNSYS software is used. Also, for evaluating occupant thermal comfort, the Fanger model is used. The considered building is a one-story building with a 150 m² area. Four occupants are considered. Both of them are seated at rest, and another is seated with light working such as typing. Using the Fanger model equation and MATLAB software, the thermal comfort of occupants is determined. For domestic hot water consumption, verified profiles that vary during 24 h of the day are considered. Achieved results show that for humid and cold cities, PV panels with an area of 73 and 76 m² can be supplied the required electricity of considered building with four occupants and battery state of charge is higher than 50% and 10%, respectively. Moreover, with a suitable air conditioner system, the predicted percentage of dissatisfied (PPD) can be lower than 12% and 8% for humid and cold cities. Therefore, the building can be converted to a zero-energy building using its rooftop area.     

Deterministic assessment of reactor pressure vessel integrity under pressurised thermal shock

Numerical investigations were carried out to assess the integrity of reactor pressure vessels under pressurised thermal shock (PTS). The 4-loop reactor pressure vessel with cladding was subjected to thermo-mechanical loading owing to loss of coolant accident. The loss of coolant accident corresponding to small break as well as hot leg breaks were considered separately, which led to axisymmetric and asymmetric thermal loading conditions respectively. Three different crack configurations, 360° circumferential part through, circumferential semi-elliptical surface and circumferential semi-elliptical under-clad cracks, were postulated in the reactor pressure vessel. Finite element method was used as a tool for transient thermo-elastic analysis. The various fracture parameters such as crack mouth opening displacement (CMOD), stress intensity factor (SIF), nil ductility transition temperature (RT_NDT) etc. were computed for each crack configuration subjected to various type of loading conditions. Finally for each crack a fracture assessment was performed concerning crack initiation based on the fracture toughness curve. The required material RT_NDT was evaluated to avoid crack initiation.     

Numerical study on thermal energy storage performance of phase change material under non-steady-state inlet boundary

Due to the solar radiation intensity variation over time, the outlet temperature or mass flow rate of heat transfer fluid (HTF) presents non-steady-state characteristics for solar collector. So, in the phase change thermal energy storage (PCTES) unit which is connected to solar collector, the phase change process occurs under the non-steady-state inlet boundary condition. In present paper, regarding the non-steady-state boundary, based on enthalpy method, a two dimensional physical and mathematical model for a shell-and-tube PCTES unit was established and the simulation code was self-developed. The effects of the non-steady-state inlet condition of HTF on the thermal performance of the PCTES unit were numerically analyzed. The results show that when the average HTF inlet temperature in an hour is fixed at a constant value, the melting time (time required for PCM completely melting) decreases with the increase of initial inlet temperature. When the initial inlet temperature increases from 30 °C to 90 °C, the melting time will decrease from 42.75 min to 20.58 min. However, the total TES capacity in an hour reduces from 338.9 kJ/kg to 211.5 kJ/kg. When the average inlet mass flow rate in an hour is fixed at a constant value, with the initial HTF inlet mass flow rate increasing, the melting time of PCM decreases. The initial inlet mass flow rate increasing from 2.0 × 10⁻⁴ kg/s to 8.0 × 10⁻⁴ kg/s will lead to the melting time decreasing from 37.42 min to 23.75 min and the TES capacity of PCM increasing from 265.8 kJ/kg to 273.8 kJ/kg. Under all the studied cases, the heat flux on the tube surface increases at first, until it reaches a maximum then it decreases over time. And the larger the initial inlet temperature or mass flow rate, the earlier the maximum value appearance and the larger the maximum value.     

Transient stress analysis of sandwich plate and shell panels with functionally graded material core under thermal shock

A finite element formulation for stress analysis of functionally graded material (FGM) sandwich plates and shell panels under thermal shock is presented in this work. A higher-order layerwise theory in conjunction with Sanders’ approximation for shells is used to develop the finite element formulation for transient stress analysis of FGM sandwich panels. The top and the bottom surfaces of FGM sandwich panels are made of pure ceramic and metal, respectively, and core of the sandwich is assumed to be made of FGM. The temperature profile in the thickness direction of the panels is considered to be varying as per the Fourier’s law of heat conduction equation for unsteady state. The heat conduction equations are solved using the central difference method in conjunction with the Crank–Nicolson approach. Transient thermal displacements of the sandwich panels are obtained using Newmark average acceleration method and the transient thermal stresses are obtained using stress–strain relations, subsequently. Results obtained from the present layerwise finite element formulations are first validated with available solutions in literature. Parametric studies are taken up to study the effects of volume fraction index, temperature dependency of material properties, core thickness, panel configuration, geometric and thermal boundary conditions on transient thermal stresses of FGM sandwich plates and shells.     

Analysis of activation energy and thermal radiation on convective flow of a power‐law fluid under convective heating and chemical reaction

The purpose of the present article is to explore the influence of activation energy in the mixed convective flow of a power‐law fluid over a permeable inclined plate. The energy expression is incorporated with thermal radiation effect. Additionally, the suction/injection effect and convective thermal conditions are considered at the surface of the inclined plate. The convection along with a nonlinear Boussinesq approximation (i.e., quadratic or nonlinear convection) and usual boundary‐layer assumptions are used in the mathematical formulation. A combined local non‐similarity and successive linearization techniques are used to evaluate the highly complicated governing equations. The effect of pertinent parameters on the fluid flow characteristics and its solutions are conferred using this study with the help of graphs. This kind of investigation is useful in the mechanism of combustion, aerosol technology, high‐temperature polymeric mixtures, and solar collectors, which operate at moderate to very high temperatures.     

Weight function method for transient thermomechanical fracture analysis of a functionally graded hollow cylinder possessing a circumferential crack

This article introduces a weight function method for fracture analysis of a circumferentially cracked functionally graded hollow cylinder subjected to transient thermomechanical loading. Analytical solutions for transient temperature and stress distributions in the uncracked cylinder are derived by applying finite Hankel transformation. These solutions are utilized to determine stress acting on the faces of the circumferential crack in the local perturbation problem. Thermomechanical material properties are assumed to be power functions of the radial coordinate in the derivations. Coefficients of the weight function are found using reference stress intensity factors computed through the finite element method. Domain form of the J-integral is used in the finite element calculations. Comparisons of the numerical results calculated by the proposed weight function method to those generated by finite element analysis demonstrate the high level of accuracy attained by the application of the developed procedures. Further parametric analyses are presented to illustrate the influences of dimensionless time, crack depth to thickness ratio, power law index, and convection coefficient upon transient mode I thermomechanical stress intensity factors.     

Analysis of an interface crack of arbitrary shape in a three-dimensional transversely isotropic magnetoelectrothermoelastic bimaterial—part 2: Numerical method

The extended displacement discontinuity (EDD) boundary integral equation and boundary-element method are extended and developed to analyze an arbitrarily shaped, planar interface crack in a three-dimensional, transversely isotropic, magnetoelectrothermoelastic bimaterial under combined, thermoelectromagnetomechanical loadings. The fundamental solutions for uniformly distributed EDDs applied over a constant triangular element are obtained through integrating the fundamental solutions for the unit-point EDDs given by Part 1 over the triangular area. To eliminate the oscillatory singularity near the crack front, the Dirac delta function in the integral–differential equations is approximated by the Gaussian distribution function, and accordingly, the Heaviside step function is replaced by the Error function. The extended stress intensity factors without oscillatory singularities, the energy release rate, and the local J-integral in terms of intensity factors are all obtained. To validate the solution, the EDD boundary-element method is proposed. As an application, an elliptical interface crack is numerically simulated. The influences of the applied combined loadings and material-mismatch as well as the ellipticity ratio on the multiphysical response are studied.