Thermodynamical interactions in a double porosity model with diffusion and microtemperatures

This study investigates the two-dimensional behavior of a nonlocal micropolar double-porous thermoelastic material with voids (MDPTMWV) within the framework of the Moore–Gibson–Thompson (MGT) theory. An isotropic, homogeneous, initially stressed, rotating thermoelastic half-space with double porosity is considered. The MGT heat conduction model, incorporating memory-dependent derivatives and variable thermal conductivity, is employed. Governing equations are derived using generalized thermoelasticity, and analytical solutions for displacement, temperature, equilibrated stress, and thermal stress components are obtained via Lame’s potentials combined with normal mode analysis. The model is analyzed under boundary conditions including variable temperature, normal stress, constant equilibrated stress, and stress-free surfaces. Numerical evaluations using MATHEMATICA illustrate the effects of time, rotation, initial stress, and nonlocal parameters. The results indicate that double porosity and the considered parameters significantly amplify material responses, particularly under increasing time, rotation, initial stress, and nonlocal effects. Several special cases are discussed and validated against the literature. These findings provide insights relevant to geophysics, seismology, and earthquake engineering.

In this article, a two-dimensional problem is studied in a homogeneous isotropic thermoelastic medium with double porosity in the context of nonlocal thermoelasticity and the problem is treated in the presence of the Green–Naghdi model of type-III. Constitutive relations and field equations are derived and the state space approach is employed to solve this problem. Thermal shock is applied on the boundary of the surface. From these relations and expressions, we have calculated stress components, displacement components, and temperature for different values of distance and time numerically and plotted graphically to demonstrate and compare theoretical results. The influences of void parameters, locality, and nonlocality on the various physical quantities are also analyzed. Some particular and special cases are also deduced from this study and compared with the existing results.

Purpose The purpose of this study is to obtain a general solution to the field equations of thermoelastic solid with voids and micro-temperatures under the gravitational field in the context of the three theories, namely, coupled theory (CT), Lord and Shulman theory and Green and Lindsay theory. Design/methodology/approach The normal mode analysis is used to obtain the exact expressions for the considered variables. Comparisons are made with the results obtained in the three theories with and without gravity. Some particular cases are also deduced from the present investigation. Findings The effect of the gravity on the displacement, the micro-temperature vector, the temperature distribution, the normal stress, the changes in the volume fraction field and the heat flux moments have been depicted graphically. Research limitations/implications Some particular cases are also deduced from the present investigation. Originality/value The results of the physical quantities have been illustrated graphically by a comparison between three different theories in the presence and absence of gravity.

This study presents the application of a new analytical model for analyzing pressure transient data for wells intercepted by a finite-conductivity vertical fracture in a closed square multilayered reservoir using the concept of a dual-porosity system. The solution takes into account the effect of wellbore storage. Our specific objectives are twofolded: first, to estimate fracture half-length, fracture conductivity and to correlate multilayered (two-layered) solution with the single-layer solution; secondly, to verify the numerical solution with the analytical solution. A set of asymptotic analytical (early-, intermediate-and late-time) solutions is also presented. In addition, we developed constant rate drawdown type curves applicable for analyzing transient pressure data. These type curves are used to match drawdown and buildup curves to determine fracture half-length, reservoir permeability and fracture conductivity. The results obtained from our type curves indicate that if the reservoir conductivity is known or can be calculated from given data, the estimated values of the aforementioned parameters compared favorably with the value? of the designed parameter. Although this study presents the solution to a twolayered system, it can be extended to a n-layered reservoir system.

Numerical simulations on the influence of matrix diffusion to carbon sequestration in double porosity fissured aquifers

In the present work, the 2D problem of a magneto-micropolar thermoelastic medium in the context of the dual-phase-lag model with the frame of the memory-dependent derivative is established. Normal mode analysis and an eigenvalue expansion technique are used to solve the resulting non-dimensional coupled governing equations. The variations of the physical quantities with the vertical distance are illustrated graphically. The effects of the time-delay parameter, magnetic field, rotation, and the variable thermal conductivity on the variations of different field quantities inside the half-space are analyzed graphically.

The three-phase-lag model, thermoelasticity without energy dissipation (G-N II) theory and thermoelasticity with energy dissipation (G-N III) theory are applied to study the effect of rotation on a fiber-reinforced thermoelastic medium. The exact expressions for the physical quantities were obtained by using the normal mode analysis. The numerical results for the field quantities are given in the physical domain and illustrated graphically in the absence and presence of rotation, Coriolis acceleration as well as reinforcement parameters.

The aim of this investigation is making mathematical model for the variation in laser pulse, rotational gravity, and magnetic fields on the generalized thermoelastic homogeneous isotropic half‐space. The governing dynamical system equations have been formulated considering the four thermoelastic models: coupled (CT) model, Lord and Shulman (LS) model, Green and Lindsay (GL) theory, and Green and Naghdi (GN III) model. Normal mode analysis technique is used to obtain the analytical expressions for the displacement components, temperature, and mechanical and Maxwell’s stresses distribution. The effect of laser pulse, gravity, and magnetic field is studied by numerical examples and displayed graphically. A comparison has been made between the theories as well as the present results and agreement with it as a special case from this study. The results predict the strong effect of magnetic field, laser pulse, and gravity field on the wave propagation phenomenon.

In this manuscript, we investigate the propagation of plane time-harmonic waves in an infinite linear thermoelastic medium, assuming a known wavelength. For the thermodynamic response, we adopt the Lord–Shulman (L-S) theory of generalized thermoelasticity. Our analysis reveals two uncoupled, undamped transverse waves, along with possibly two to three coupled, temporally damped, and dispersive longitudinal waves. The speed of transverse waves remains unaffected by thermal effects, whereas longitudinal waves exhibit thermal dependence. Indeed, we observe a time-damped longitudinal quasi-elastic wave, with its amplitude exponentially decreasing to zero as time approaches infinity. Furthermore, there may be two possible longitudinal quasi-thermal waves that are damped in time with different decreasing rates or a single plane harmonic in time longitudinal quasi-thermal wave. We also examine surface wave propagation in a semi-infinite thermoelastic medium, considering a stress-free, heat-exchanging half-space boundary. The explicit forms of the dispersion relation and the secular equation are derived. Numerical computations for both plane and surface waves are conducted using a specific model, with graphical representations of the results and corresponding analytical discussions. Finally, we present generalized observations regarding the surface wave profile.

The propagation of plane waves in a rotating homogeneous, isotropic, thermoelastic solid with double porosity following Lord-Shulman’s theory of thermoelasticity has been investigated. It is assumed that the medium rotates about an axis normal to the surface with a uniform angular velocity. There may exist five coupled waves that evolved due to the longitudinal, transverse disturbance, voids of type-I and type-II, and temperature change in the medium. The secular equation for the model under consideration has been derived with the help of formal solutions and boundary conditions. The amplitude of displacements, temperature change and volume fraction fields for voids of type-I and type-II have also been computed analytically. Finally, numerical computations have been carried out for magnesium crystal material to understand the behavior of amplitude of phase velocity, penetration depth, specific loss, displacement components, temperature change, and volume fraction field due to type-I and type-II voids corresponding to the different rotation rates. Various graphs have been plotted to support the analytical findings. The study may be used in the development of rotation sensors, material design and thermal efficiency.

The aim of the present investigation is to study the effects of laser heat source and phase lags on a microstretch thermoelastic mass diffusion medium including dual phase lag model. The normal mode analysis technique has been adopted to obtain the components of displacement, microrotation, microstress, mass concentration and temperature distribution due to the presence of ultra-laser heat source. The numerical computation has been performed (using Matlab software) on the resulting quantities. The computed numerical results are shown graphically to depict the effect of laser heat source and diffusion phase-lags. Some particular cases of interest are also deduced from the present investigation.

In the present paper, the theory of multi‐phase‐lags with fractional derivative heat transfer thermoelasticity was used to study the wave propagation on a nonlocal fiber‐reinforced thermoelastic medium. The exact expressions for the displacement components, temperature, and stress components are obtained by using the Fourier and Laplace transforms. The comparisons are shown graphically to explore the effects of rotation, initial stress and fractional order parameters as well as a nonlocal parameter on different physical quantities. Numerical computations are carried out with the help of Matlab software.

The aim of the present study is to predict the functional adaptation of bone in response to changes in mechanical loading using a new biothermodynamic model for bone remodeling. In our approach, which fits into the framework of open systems, changes in the density are governed by balance of mass and balance of entropy supplemented by additional mass and entropy sources. The governing equations of bone remodeling process are based on irreversible thermodynamics and kinetics of chemical reactions. The key feature of this model is its ability to simulate the coupling between the mechanical and biochemical parameters that control bone remodeling, in particular the effect of dynamical loading, frequency of load and nutrition. Besides, the model can be used to predict some skeletal diseases such as bone fractures and osteoporosis. In the present paper, a biothermodynamic model was applied to the design of prosthetic implants. Numerical computations of bone density distributions after Total Hip Replacement (THR) using 3D finite element analysis showed that the biomimetic composite stem exhibit a better density patterns compared to the conventional titanium stem, indicating that the biomimetic prosthesis promotes higher remodeling rate and consequently less stress shielding. Furthermore, the model showed that the concentration of a new bone strongly depends on the history and intensity of loading and also on nutrition.

In this paper, we have studied a model of finite linear Mode-I crack in a thermoelastic transversely isotropic medium under Green Naghdi theory. The crack is subjected to a prescribed temperature and a known tensile stress. The plane boundary surface is considered as isothermal and all the field variables are sufficiently smooth. The heat conduction equation is written under two temperature theory (2TT) for Green Naghdi model which contains absolute temperature as well as conductive temperature. The analytical expressions of displacement components, stress components and temperature variables are obtained by normal mode analysis and matrix inversion method. Comparisons have been made within Green Naghdi (G-N) theory of type I, type II and type III for displacement, stress and absolute temperature variables against the crack width for a transversely isotropic material (Cobalt) by virtues of graphs. Also, Comparison have been made among displacement, thermal stress and absolute temperature for different depths.

The present article deals with the propagation of Rayleigh surface waves in a homogeneous orthotropic medium based on Eringen’s nonlocal thermoelasticity. This thermoelastic problem is studied under the purview of Green–Naghdi model type III of hyperbolic thermoelasticity in the presence of voids. The normal mode analysis is employed to obtain a vector matrix differential equation which is then solved by an eigenvalue approach. The frequency equations for different cases are derived. The path of surface particles during Rayleigh wave propagation is found to be elliptical. In order to illustrate the analytical developments, the numerical solution is carried out and the computer-simulated results with respect to phase velocity, attenuation coefficient and specific loss are presented graphically.