Axisymmetric mechanical and thermal stresses in thick short length FGM cylinders

The exact solution of steady-state two-dimensional axisymmetric mechanical and thermal stresses for a short hollow cylinder made of functionally graded material is developed. Temperature, as functions of radial and longitudinal directions, is solved analytically, using the generalized Bessel function. A standard method is used to solve a non-homogeneous system of partial differential Navier equations with non-constant coefficients, using Fourier series, rather than potential functions method.     

Axisymmetric thermoelastic analysis in a finite hollow cylinder due to nonuniform thermal shock

An exact solution is obtained for two-dimensional elastodynamic analysis of finite hollow cylinder excited by nonuniform thermal shock. The cylinder is simply-supported at the two ends and is traction-free at the internal and external cylindrical surfaces. Based on the uncoupled linear thermoelastic theory, the solution is developed by employing the expansion of trigonometric series method and the separation of variables technique. The obtained solution contains two infinite series. One is trigonometric function and the other is Bessel function. The coefficients in the series solution are determined by the orthogonal properties of the functions. Numerical experiments are presented for describing the thermal dynamic behaviors of finite hollow cylinder.     

A criterion-selection diagram for the thermal shock resistance of a hollow circular cylinder

Abstract

The characteristics of thermally induced failure are investigated for a hollow circular cylinder exposed to a convective cooling at the inner surface. The transient fields of both temperature and thermal stresses are given in closed forms over the full range of Biot number. The thermal shock resistance (TSR) is analyzed based on two distinct failure criteria. Namely, the strength-based failure criterion is adopted for a nearly flaw-free cylinder while the fracture toughness-based one is used for the counterpart with an inner crack-like flaw. From each criterion, the admissible maximum temperature drop is obtained assuring that a hollow cylinder can tolerate without failure. The influence of flaw size on the TSR is quantified and a criterion-selection diagram is proposed for the TSR characterization. These results are deemed to be of importance from the perspective of estimating the TSR of a hollow circular cylinder.     

Inverse problem on the identification of temperature and thermal stresses in an FGM hollow cylinder by the surface displacements

A problem on the identification of time-dependent temperature on one of the limiting surfaces of a radially inhomogeneous hollow cylinder is formulated and solved under the temperature and radial displacement given on the other limiting surface. The analysis of temperature and thermal stress distribution in the cylinder is performed. The solution has been constructed by the reduction to an inverse thermoelasticity problem. By making use of the finite difference method, a stable solution algorithm is suggested for the analysis of inverse problem. The solution technique is verified numerically by making use of the solution to a relevant direct problem. It is shown that the proposed technique can be e?ciently used for the identification of a heat flux or unknown parameters (the surrounding temperature or the heat-exchange coe?cient) in the third-kind boundary conditions.     

Transient thermal stress analysis of a functionally graded thick hollow cylinder with temperature-dependent material properties

This article deals with the study of temperature distribution and thermal stresses of a functionally graded thick hollow cylinder with temperature dependent material properties. All the material properties except Poisson’s ratio are assumed to be dependent on temperature and spatial coordinate z. The two-dimensional transient heat conduction equation is solved under convective heat transfer condition with varying point heat source. The influence of inhomogeneity parameters on the thermal and mechanical behavior is examined. Numerical computations are performed for ceramic-metal-based functionally graded material, in which alumina is selected as ceramic and nickel as metal.     

Heat transfer from hollow cylinder using optimal homotopy asymptotic method

Optimal homotopy asymptotic method (OHAM) is employed to investigate steady‐state heat conduction with temperature dependent thermal conductivity and uniform heat generation in a hollow cylinder. Analytical models are developed for dimensionless temperature distribution and heat transfer for two cases using mixed boundary conditions (Dirichlet, Neumann, and Robin). The inner cylinder is assumed to be insulated in both cases. In the first case, the outer cylinder is assumed to be isothermal whereas in the second case, the outer cylinder is convectively cooled by a fluid of temperature T₂ through a uniform heat transfer coefficient h. The effects of Biot number, dimensionless heat generation, and thermal conductivity parameters on the temperature distribution and heat transfer are determined analytically and validated numerically using MAPLE 14. In both cases, the results obtained by OHAM are found to be in good agreement with the numerical results. It is found that as the Biot number increases, the results approach that of the isothermal case. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20407     

Determination of dynamic pressure on infinite piezoelectric hollow cylinder from electric potential difference measurement

An analytical method is developed for evaluating the dynamic pressure acted at the surface of infinite piezoelectric hollow cylinder by measuring the electric potential difference between the internal and external surfaces. By virtue of the separation of variables method and the orthogonal expansion technique, the inverse boundary problem is transformed to a second kind Volterra integral equation about the unknown dynamic pressure. The interpolation method is employed to solve the integral equation and the dynamic pressure is determined. The present method is suitable for the hollow cylinder with arbitrary thickness subjected to arbitrary dynamic pressure. Numerical experiments are also presented.     

Mechanical and thermal stresses of a functionally graded circular hollow cylinder with finite length

By using a multi-layered approach based on the theory of laminated composites, the solutions of temperature, displacements, and thermal/mechanical stresses in a functionally graded circular hollow cylinder are presented in this paper. The cylinder has finite length and is subjected to axisymmetric thermal and mechanical loads. The material properties are assumed to be temperature-independent and radially dependent, but are assumed to be homogeneous in each layer. As an illustration, the numerical results for a mullite/molybdenum functionally graded circular hollow cylinder are also presented.     

Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads

In this paper, a general analysis of one-dimensional steady-state thermal stresses in a hollow thick cylinder made of functionally graded material is developed. The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions along the inside and outside surfaces. The material properties, except Poisson's ratio, are assumed to depend on variable the r and they are expressed as power functions of r. The direct method is used to solve the heat conduction and Navier equations.     

Thermoelastic interaction in functionally graded thick hollow cylinder with temperature-dependent properties

The prediction of thermoelastic behavior induced by transient thermal shock is important to evaluate the durability of functionally graded materials. The purpose of this article is to study the axisymmetric thermoelastic interaction in a functionally graded thick hollow cylinder by an asymptotic approach. The governing equations with variable material properties, which are spatially graded and temperature dependent, are proposed based on the generalized theory of thermoelasticity with one relaxation time (L–S theory). The Laplace transform technique is used to derive the general solutions with the cylinder divided into thin cylinders and material properties assumed constant in each thin cylinder. The inverse Laplace transform is then conducted analytically by some approximations in the time domain, and the short-time solution of the problem with its interior boundary subjected to a sudden temperature rise and the outer surface maintained at constant temperature are obtained. Utilizing these asymptotic solutions, the propagation of thermal and thermoelastic waves are studied, which display dependence of each wave’s propagation upon the relaxation time, volume fraction parameter and temperature. The distributions of the radial displacement, temperature and stresses are also plotted and discussed. These results reveal effects of these variable material properties with spatial position and temperature on thermoelastic behavior.     

Transient solution of temperature field of conjugate laminar forced convection heat transfer in functionally graded hollow cylinder

In this study, the numerical analysis of conjugate heat transfer of laminar flow in a functionally graded hollow cylinder (FGHC) made of metal/ceramic for a two‐dimensional fluid and wall conduction subject to Newton boundary condition is considered. The fluid and FGHC energy equations are coupled through the continuity of temperature and heat flux at the inner wall‐fluid interface while the outer surface is subject to convective heat transfer. The continuity, momentum, and energy equations of the fluid are discretized using the finite volume approach. The effects of fluid and functionally graded material parameters, such as volume fraction index, volume composition, time history, wall‐to‐fluid thermal diffusivity ratio, wall‐to‐fluid thermal conductivity ratio, Biot number, Peclet number, and Prandtl number are investigated on the temperature field in the FGHC. The result shows that on account of the inhomogeneity of the material property, the volume fraction index has a significant effect on the other parameters and the temperature variation along the thickness. The lower the volume fraction index, the higher the inner wall (metal side) temperature, and the temperature gradient along the thickness. However, except for the variation in the wall‐to‐fluid thermal conductivity ratio, the lower the volumetric fraction, the lower the outer wall (ceramic side) temperature distribution.     

Development of new analytical solutions for elastic thermal stress components in a hollow cylinder under sinusoidal transient thermal loading

For the analysis of high-cycle thermal fatigue due to striping (such as has been observed due to turbulence at mixing tees of class 1–2–3 piping of nuclear power reactors) it can be necessary to consider the time-dependent temperature gradient within the pipe wall thickness rather than just at the surface. To address this, a set of analytical solutions with several new features has been developed for the temperature field and the associated elastic thermal stress distributions for a hollow circular cylinder subjected to sinusoidal transient thermal loading at the inner surface. The approach uses a finite Hankel transform and some properties of Bessel functions. The analytical predictions have been successfully benchmarked by comparison with results from finite element analysis, and also with some results of independent studies.     

Numerical and experimental analysis of chemical dehydration, heat and mass transfers in a concrete hollow cylinder submitted to high temperatures

This paper presents a thermo-hydro-chemical model for concrete at high temperatures. Non-linear phenomena, heat and mass transfers, evolution of the phases constituting the porous medium are taken into account in a full three phases coupled analysis. The proposed model does not take into account mechanical aspects, i.e. the solid skeleton is considered as rigid. An experimental set-up and a numerical simulation are also presented. A hollow cylinder has been heated up to 523.15 K (250 °C) on the internal side and submitted to gas pressure/temperature measurements. A numerical simulation of the cylinder has been performed, showing a good correlation with the experimental observations.     

Effects of buoyancy and conjugate heat transfer on non-Darcy mixed convection about a vertical slender hollow cylinder embedded in a porous medium with high porosity

This study investigates mixed convection heat transfer about a vertical slender hollow cylinder in the buoyancy and conjugate heat transfer effects in the porous medium with high porosity. The non-similar solutions using the Keller box method are obtained. The wall conduction parameter p, the porous medium parameter k₁, the Forchheimer parameter F∗ and the Richardson number are the main parameters. For various values of these parameters the local skin friction and local heat transfer parameters are determined. The validity of the methodology is checked by comparing the results with those available in the open literature and a fairly good agreement is observed. Finally, it is determined that the local skin friction and the local heat transfer coefficients increase with an increase buoyancy parameter Ri, porous medium parameter k₁, Forchheimer parameter F∗ and decrease with conjugate heat transfer parameter p.     

Nonsymmetric thermomechanical analysis of a functionally graded cylinder subjected to mechanical,thermal, and magnetic loads

Thermoelastic analysis of a functionally graded cylinder under nonsymmetric thermal and mechanical loadings subjected to uniform magnetic field is presented in this article. All material properties are assumed to be variable along the thickness direction based on the power law. Due to nonsymmetric thermal and mechanical loadings and boundary conditions, a two-dimensional displacement field along the radial and circumferential directions is assumed for our analysis. The complex form of Fourier series is used as the method of solution. The nonsymmetric analysis of this problem for Lorentz force leads to radial and circumferential force components. The obtained results of this analysis indicate that the different parameters of material and loading have a considerable effect on the nonsymmetric behavior of cylinder.     

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.     

Enhanced thermal performance and entropy generation analysis in a novel cavity design with circular cylinder

Analyzing fluid dynamics and heat transfer holds significant importance in the design and enhancement of engineering systems. The current investigation utilizes the finite element method to explore natural convection and heat transfer intricacies within a novel cavity containing an inner circular cylinder under steady and laminar flow conditions. The principal aim of this study is to assess the impact of Rayleigh number (Ra), Bejan number (Be), and the presence of adiabatic, hot, and cold cylinders on heat transfer, entropy generation, and fluid flow. The range of Ra considered in this investigation spans from 10³ to 10⁶, while the Prandtl number for the air is fixed at 0.71. The findings illustrate that the presence of a cylinder leads to higher Be as Ra increase, compared to scenarios where no cylinder is present. This observation suggests that buoyancy forces dominate in the absence of a cylinder, resulting in significantly enhanced convective heat transfer efficiency. However, the presence of a heated cylinder within the tooth-shaped cavity exerts a substantial influence on the overall thermal performance of the system. Notably, the average Nusselt Number (Nu) experiences a remarkable increase of 41.97% under the influence of a heated cylinder, when compared to situations where a cold cylinder is present. This elevated average Nu signifies improved heat transfer characteristics, ultimately resulting in an overall improvement in the thermal system's efficiency.     

Effect of stochastic thermal input on elastic and thermal properties of an infinitely long annular cylinder

Random elastic and thermal properties for an infinitely long solid conducting circular cylinder are investigated under the effect of random thermal input. The problem is considered in the context of a generalized thermoelasticity theory with one relaxation time. The lateral surface of the solid is traction free and subjected to known stochastic temperature, driven by an additive Gaussian white noise. Laplace transform technique is used to obtain the solution in the transformed domain. Statistically, we derive and analyze the mean and variance for temperature, displacement and stress. Numerical inversion of the transformed solution is carried out, represented graphically and discussed.     

Numerical analysis of fluid flow due to mixed convection in a lid-driven cavity having a heated circular hollow cylinder

Mixed convection heat transfer in a lid-driven cavity along with a heated circular hollow cylinder positioned at the center of the cavity has been analyzed numerically. The present study simulates a realistic system such as air-cooled electronic equipment with a heat component or an oven with heater. A Galerkin weighted residual finite element method with a Newton–Raphson iterative algorithm is adopted to solve the governing equations. The computation is carried out for wide ranges of the Richardson numbers, cylinder diameter and solid fluid thermal conductivity ratio. Results are presented in the form of streamlines, isothermal lines, average Nusselt number at the heated surface and fluid temperature in the cavity for the mentioned parameters. It is found that the flow field and temperature distribution strongly depend on the cylinder diameter and also the solid–fluid thermal conductivity ratio at the three convective regimes.     

A numerical study on the effect of a heated hollow cylinder on mixed convection in a ventilated cavity

The present work is aimed to study mixed convection heat transfer characteristics within a ventilated square cavity having a heated hollow cylinder. The heated hollow cylinder is placed at the center of the cavity. In addition, the wall of the cavity is assumed to be adiabatic. Flows are imposed through the inlet at the bottom of the left wall and exited at the top of the right wall of the cavity. The present study simulates a practical system such as air-cooled electronic equipment with a heat component or an oven with heater. Emphasis is sited on the influences of the cylinder diameter and the thermal conductivity of the cylinder in the cavity. The consequent mathematical model is governed by the coupled equations of mass, momentum and energy and solved by employing Galerkin weighted residual method of finite element formulation. A wide range of pertinent parameters such as Reynolds number, Richardson number, cylinder diameter and the solid-fluid thermal conductivity ratio are considered in the present study. Various results such as the streamlines, isotherms, heat transfer rates in terms of the average Nusselt number and average fluid temperature in the cavity are presented for different aforesaid parameters. It is observed that the cylinder diameter has significant effect on both the flow and thermal fields but the solid-fluid thermal conductivity ratio has significant effect only on the thermal field.