Radially Symmetric Steady State Thermal and Mechanical Stresses of a Poro FGM Hollow Sphere

Jabbari, Mohsen; Karampour, S.; Eslami, M. R.

doi:10.5402/2011/305402

Cited by 12 publications

(6 citation statements)

References 21 publications

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“…Nayak et al [37] determined analytically the displacements, strains, and stresses of a power-law graded thick spherical vessel under the third kind thermal boundary conditions, with steady-state unidirectional radial heat conduction and general mechanical boundary conditions. Jabbari et al [38] presented a general solution for the one-dimensional steady-state thermal and mechanical stresses in a hollow thick sphere made of porous power-law graded material. Bayat et al [39] carried out a thermo-mechanical analysis of a power-law graded hollow sphere subjected to pressure and one-dimensional steady-state thermal loads.…”

Section: Introductionmentioning

confidence: 99%

Exact Thermomechanical Analysis of Functionally Graded (FG) Thick-Walled Spheres

Yıldırım

2018

Mechanics and Mechanical Engineering

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The present study aims to provide a deeper understanding for the thermo-mechanical analysis of spheres made of non-homogeneous isotropic materials. To this end, Navier equations are solved analytically based on the spherically-symmetric plain-strain assumptions and closed-form formulas are proposed for the elastic fields in a simple-power-law graded spheres subjected to steady-state thermal and internal/external pressure loads. A comprehensive parametric study is then performed with both functionally-graded hypothetical and physical materials. Two benchmark examples are reconsidered with hypothetically chosen inhomogeneity indexes. Effects of inhomogeneity indexes are reviewed in these examples. Differently from the literature, thickness effects are also examined under separate and combined loads together with the thermo-mechanical behavioral differences in spheres and cylinders. Finally three physical metal-ceramic pairs are studied originally with appropriate inhomogeneity indexes which are defined as the inner surface is full ceramic and the outer surface is full metal. Results are presented in graphical and tabular forms.

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Section: Introductionmentioning

confidence: 99%

Exact Thermomechanical Analysis of Functionally Graded (FG) Thick-Walled Spheres

Yıldırım

2018

Mechanics and Mechanical Engineering

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“…У працях [3], [6], [7] удосконалено наявні та розроблено нові підходи до створення математичних моделей аналізу теплообміну між кусково-однорідними конструкціями та навколишнім середовищем і методів розв'язування лінійних і нелінійних крайових задач для кусково-однорідних середовищ. Розглянуто дво-та тривимірні моделі, що містять рівняння, коефіцієнти яких є функціями теплофізичних властивостей фаз і геометричної структури [2], [4], [8], [12]. Наведено методи визначення аналітичних та аналітично-числових розв'язків крайових задач теплопровідності.…”

Section: ʑ˔˕˖˒unclassified

Mathematical Models of Heat Transfer in Elements of Turbogenerators

Havrysh¹,

Korol²,

Shkrab³

et al. 2019

UJIT

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Separate mathematical models for determining the temperature distribution in the elements of turbogenerators have been developed, which are described geometrically by an isotropic half-space and a heat-sensitive space with locally concentrated sources of heating. For this purpose, using the theory of generalized functions in a convenient form, we write the initial differential equations of thermal conductivity with boundary conditions. For thermosensitive space (thermophysical parameters are temperature dependent), the original nonlinear thermal conductivity equation and the nonlinear boundary conditions are linearized using the Kirchhoff transform, for which a linear differential equation is obtained. An integral Hankel transform was used to solve the boundary value problems of thermal conductivity, and as a result analytical solutions in the images were obtained. These solutions were applied by the inverted Hankel integral transformation, which made it possible to obtain the final analytical solutions of the original problems. The analytical solutions obtained are presented in the form of non-native convergent integrals. For the construction material of the heat-sensitive space, a linear dependence of the thermal conductivity coefficient on the temperature was used. The result is a convenient formula for determining the temperature field, which allows to analyze temperature regimes in a heat-sensitive environment. To determine the numerical values of temperature in the above structures, as well as to analyze the heat exchange in the elements of the turbogenerators caused by different temperature regimes due to the heating of locally concentrated heat sources, computational programs have been developed. Using these programs are graphs that show the behavior of surfaces constructed using numerical values of the dimensionless temperature distribution depending on the spatial dimensionless coordinates. The obtained numerical values of temperature indicate that the mathematical models of determining the distribution of temperature to the actual physical process are consistent. The software also allows you to analyze locally heated environments for their heat resistance. As a consequence, it becomes possible to raise it, to determine the allowable temperatures of normal operation of the turbogenerators, to protect them from overheating, which can cause destruction not only of individual elements, but also of the whole structure.

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“…A one-dimensional stationary temperature problem and a mechanical problem have been solved, and relationships for determination of thermal and mechanical loadings in a hollow thick-walled sphere are presented. The distribution of temperature is depicted by means of a function of radial coordinate for the given general thermal and mechanical boundary conditions at inner and outer surfaces of the sphere (Jabbari, Karampour & Eslami, 2011). In the paper (Bayat, Moosavi & Bayat, 2015) a non-station of problem of heat conduction and thermoelasticity for functional-gradient thick-walled spheres is solved.…”

Section: Introductionmentioning

confidence: 99%

Thermal 3D model for non-homogeneous elements in mobile devices

Havrysh

Korol

Shkrab

et al. 2019

SBUNFU

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A mathematical model for the analysis of heat exchange between the environment and an isotropic space layer with an alien inclusions is developed, which is heated by a heat flux centered on one of the boundary surfaces. For this purpose, using the theory of generalized functions, the coefficient of thermal conductivity of this structure is depicted as one unit for the whole system. In view of this, instead of two equations of thermal conductivity for the layer and the inclusion and conditions of perfect thermal contact on the surfaces of the junction between them, one equation of thermal conductivity was obtained in the generalized derivatives with breaking coefficients. We consider the case when the inclusion sizes are small compared to the distances from the inclusion surfaces to the boundary surfaces of the layer. In this connection, the combined thermophysical parameters were introduced and the thermal coefficients of the thermal conductivity equation were transformed into singular ones. For the solution of the boundary value problem of thermal conductivity containing this equation and boundary conditions on the boundary surfaces of the layer, an integral Fourier transform was used and, as a result, an analytical solution of the problem in the images was obtained. The inverse integral Fourier transform was applied to this solution, which made it possible to obtain the final analytical solution of the original problem. The analytical solution obtained is presented as a non-native double convergent integral. To determine the numerical values of the temperature in the above design, as well as to analyze the heat exchange between the layer and the environment caused by different temperature regimes due to the heating of the inhomogeneous layer by a heat source concentrated in the area of inclusion, computational programs have been developed. Using these programs, graphs are displayed showing the behavior of curves constructed using numerical values of the temperature distribution depending on the spatial coordinates for different inclusion materials. The obtained numerical values of temperature indicate a significant influence of the inclusion on its distribution in the design "layer-inclusion". The software also makes it possible to analyze these inhomogeneous media with respect to their heat resistance during heating. As a consequence, it becomes possible to raise and protect it from overheating, which can cause destruction not only of individual elements, but also of the whole structure.

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Radially Symmetric Steady State Thermal and Mechanical Stresses of a Poro FGM Hollow Sphere

Cited by 12 publications

References 21 publications

Exact Thermomechanical Analysis of Functionally Graded (FG) Thick-Walled Spheres

Exact Thermomechanical Analysis of Functionally Graded (FG) Thick-Walled Spheres

Mathematical Models of Heat Transfer in Elements of Turbogenerators

Thermal 3D model for non-homogeneous elements in mobile devices

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