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Fundamental solutions in the generalized theory of thermoelastic diffusion with triple porosity

Kansal Tarun

Engineering Transactions

2023

Vol. 71, iss. 4

473--505

The main aim of this paper is to derive the basic governing equations for an anisotropic thermoelastic medium with mass diffusion and triple porosity. Additionally, the fundamental solutions of a system of equations for steady, pseudo-, quasi-static oscillations and equilibrium are constructed.

A two dimensional axisymmetric thermoelastic diffusion problem of micropolar porous circular plate with dual phase lag model

Kumar R., Miglani A., Rani R.

Mechanics and Mechanical Engineering

2018

Vol. 22, nr 4

1389--1406

In the present work, we consider a two dimensional axisymmetric problem of micropolar porous circular plate with thermal and chemical potential sources in the context of the theory of dual phase lag generalized thermoelastic diffusion. The potential functions are used to analyze the problem. The Laplace and Hankel transforms techniques are used to find the expressions of displacements, microrotation, volume fraction field, temperature distribution, concentration and stresses in the transformed domain. The inversion of transforms based on Fourier expansion techniques is applied to obtain the results in the physical domain. The numerical results for resulting quantities are obtained and depicted graphically. Effect of porosity, LS theory and phase lag are presented on the resulting quantities. Some particular cases are also deduced.

Generalized theory of thermoelastic diffusion with double porosity

Kansal T.

Archives of Mechanics

2018

Vol. 70, nr 3

241--268

The present paper focuses on the derivation of the constitutive relations and field equations for anisotropic thermoelastic medium with mass diffusion and double porosity. The variational principle, uniqueness and reciprocity theorems are also derived.

Distributed loads in an elastic solid with generalized thermodiffusion

Choudhary S., Deswal S.

Archives of Mechanics

2008

Vol. 60, nr 2

139-160

The linear theory of generalized thermoelastic diffusion with one relaxation time is employed to study the interactions in a homogeneous, isotropic elastic solid, when a distributed instantaneous source is acting on the free surface of the body. The eigenvalue approach is adopted for the solution of a two-dimensional problem. The Laplace-Fourier transform technique is used. The expansions of the stresses, displacement components, temperature, concentration and chemical potential are obtained analytically. Numerical results are given and illustrated graphically, employing numerical methods for the inversion for transforms. Comparisons are made with the results predicted by the theory of generalized thermoelasticity and elasticity.