The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governi...The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governing equations of fractional order generalized thermoelasticity with three-phase lag model for functionally graded materials(FGM)(i.e., material with spatially varying material properties) are established. The analytical solution in the transform domain is obtained by using the eigenvalue approach.The inversion of Laplace transform is done numerically. The graphical results indicate that the fractional parameter has significant effects on all the physical quantities. Thus, we can consider the theory of fractional order generalized thermoelasticity an improvement on studying elastic materials.展开更多
In this paper, we construct the equations of generalized thermoelasicity for a non-homogeneous isotropic hollow cylider with a variable modulus of elasticity and thermal conductivity based on the Lord and Shulman theo...In this paper, we construct the equations of generalized thermoelasicity for a non-homogeneous isotropic hollow cylider with a variable modulus of elasticity and thermal conductivity based on the Lord and Shulman theory. The problem has been solved numerically using the finite element method. Numerical results for the displacement, the temperature, the radial stress, and the hoop stress distributions are illustrated graphically. Comparisons are made between the results predicted by the coupled theory and by the theory of generalized thermoelasticity with one relaxation time in the cases of temperature dependent and independent modulus of elasticity.展开更多
An analysis is performed to study the magnetohydrodynamic flow of an electrically conducting, viscous incompressible fluid past a semi-infinite vertical plate with variable surface temperature under the action of tran...An analysis is performed to study the magnetohydrodynamic flow of an electrically conducting, viscous incompressible fluid past a semi-infinite vertical plate with variable surface temperature under the action of transversely applied magnetic field. The heat due to viscous dissipation and the induced magnetic field are assumed to be negligible. The dimensionless governing equations are unsteady, two-dimensional, coupled and non-linear governing equations. It is found that the magnetic field parameter has a retarding effect on the velocities of air and water.展开更多
The disturbance due to mechanical and thermal sources in saturated porous media with incompressible fluid for two-dimensional axi-symmetric problem is investigated.The Laplace and Hankel transforms techniques are used...The disturbance due to mechanical and thermal sources in saturated porous media with incompressible fluid for two-dimensional axi-symmetric problem is investigated.The Laplace and Hankel transforms techniques are used to investigate the problem.The concentrated source and source over circular region have been taken to show the utility of the approach.The transformed components of displacement,stress and pore pressure are obtained.Numerical inversion techniques are used to obtain the resulting quantities in the physical domain and the effect of porosity is shown on the resulting quantities.All the field quantities are found to be sensitive towards the porosity parameters.It is observed that porosity parameters have both increasing and decreasing effect on the numerical values of the physical quantities.Also the values of the physical quantities are affected by the different boundaries.A special case of interest is also deduced.展开更多
The two-dimensional problem of generalized thermoelastic diffusion material with thermal and diffusion relaxation times is investigated in the context of the Lord-Shulman theory. As an application of the problem, a pa...The two-dimensional problem of generalized thermoelastic diffusion material with thermal and diffusion relaxation times is investigated in the context of the Lord-Shulman theory. As an application of the problem, a particular type of thermal source is considered and the problem is solved numerically by using a finite element method. The components of displacement, stress, temperature distribution chemical potential and mass concentration are obtained. The resulting quantities are depicted graphically for a special model. An appreciable effect of relaxation times is observed on various resulting quantities.展开更多
文摘The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governing equations of fractional order generalized thermoelasticity with three-phase lag model for functionally graded materials(FGM)(i.e., material with spatially varying material properties) are established. The analytical solution in the transform domain is obtained by using the eigenvalue approach.The inversion of Laplace transform is done numerically. The graphical results indicate that the fractional parameter has significant effects on all the physical quantities. Thus, we can consider the theory of fractional order generalized thermoelasticity an improvement on studying elastic materials.
文摘In this paper, we construct the equations of generalized thermoelasicity for a non-homogeneous isotropic hollow cylider with a variable modulus of elasticity and thermal conductivity based on the Lord and Shulman theory. The problem has been solved numerically using the finite element method. Numerical results for the displacement, the temperature, the radial stress, and the hoop stress distributions are illustrated graphically. Comparisons are made between the results predicted by the coupled theory and by the theory of generalized thermoelasticity with one relaxation time in the cases of temperature dependent and independent modulus of elasticity.
文摘An analysis is performed to study the magnetohydrodynamic flow of an electrically conducting, viscous incompressible fluid past a semi-infinite vertical plate with variable surface temperature under the action of transversely applied magnetic field. The heat due to viscous dissipation and the induced magnetic field are assumed to be negligible. The dimensionless governing equations are unsteady, two-dimensional, coupled and non-linear governing equations. It is found that the magnetic field parameter has a retarding effect on the velocities of air and water.
文摘The disturbance due to mechanical and thermal sources in saturated porous media with incompressible fluid for two-dimensional axi-symmetric problem is investigated.The Laplace and Hankel transforms techniques are used to investigate the problem.The concentrated source and source over circular region have been taken to show the utility of the approach.The transformed components of displacement,stress and pore pressure are obtained.Numerical inversion techniques are used to obtain the resulting quantities in the physical domain and the effect of porosity is shown on the resulting quantities.All the field quantities are found to be sensitive towards the porosity parameters.It is observed that porosity parameters have both increasing and decreasing effect on the numerical values of the physical quantities.Also the values of the physical quantities are affected by the different boundaries.A special case of interest is also deduced.
文摘The two-dimensional problem of generalized thermoelastic diffusion material with thermal and diffusion relaxation times is investigated in the context of the Lord-Shulman theory. As an application of the problem, a particular type of thermal source is considered and the problem is solved numerically by using a finite element method. The components of displacement, stress, temperature distribution chemical potential and mass concentration are obtained. The resulting quantities are depicted graphically for a special model. An appreciable effect of relaxation times is observed on various resulting quantities.
