Jyoti Verma, Navneet Kumar Lamba and K.C. Deshmukh
The purpose of the paper is to prepare the hygrothermal model with fraction order theory in a mathematical aspect.
Abstract
Purpose
The purpose of the paper is to prepare the hygrothermal model with fraction order theory in a mathematical aspect.
Design/methodology/approach
In this study, linear hygrothermoelastic theory is adopted to analyze and discuss the memory effect in a finite length hollow cylinder subjected to hygrothermal loading.
Findings
Analytical solutions of temperature, moisture and stresses are obtained in this study by using the decoupling technique and the method of Integral transform.
Originality/value
The paper deals with the original work based on hygrothermal response in hollow cylinder by theory of uncoupled-coupled heat and moisture.
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V.R. Manthena, G.D. Kedar and K.C. Deshmukh
The purpose of this paper is to determine the temperature distribution of a thin rectangular plate made of thermosensitive functionally graded (FG) material. By finding out…
Abstract
Purpose
The purpose of this paper is to determine the temperature distribution of a thin rectangular plate made of thermosensitive functionally graded (FG) material. By finding out thermal deflection and stress resultants, the thermal stresses have been obtained and analyzed.
Design/methodology/approach
Initially, the rectangular plate is kept at the surrounding temperature. The upper, lower and two parallel sides (y=0, b and z=0, c) are thermally insulated, while other parallel sides (x=0, a) are given convective-type heating, that is, the rate of change of the temperature of the rectangular plate is proportional to the difference between its own temperature and the surrounding temperature. The non-linear heat conduction equation has been converted to linear form by introducing Kirchhoff’s variable transformation and the resultant heat conduction equation is solved by integral transform technique with hyperbolic varying point heat source.
Findings
A mathematical model is prepared for FG ceramic–metal-based material, in which alumina is selected as the ceramic and nickel as the metal. The thermal deflection and thermal stresses have been obtained for the homogeneous and nonhomogeneous materials. The results are illustrated numerically and depicted graphically for comparison. During this study, one observed that variations are seen in the stresses, due to the variation in the inhomogeneity parameters.
Research limitations/implications
The paper is constructed purely on theoretical mathematical modeling by considering various parameters and functions.
Practical implications
This type of theoretical analysis may be useful in high-temperature environments like nuclear components, spacecraft structural members, thermal barrier coatings, etc., as the effect of temperature and evaluation of temperature-dependent and nonhomogeneous material properties plays a vital role for accurate and reliable structural analysis.
Originality/value
In this paper, the authors have used thermal deflection and resultant stresses to determine the thermal stresses of a thin rectangular plate with temperature- and spatial variable-dependent material properties which is a new and novel contribution to the field.
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Navneet Kumar Lamba and K.C. Deshmukh
In this paper, a solid circular cylinder of finite length occupying the space 0⩽r⩽1, 0⩽z⩽h is considered. The purpose of this paper is to adopt a linear hygrothermal effect to…
Abstract
Purpose
In this paper, a solid circular cylinder of finite length occupying the space 0⩽r⩽1, 0⩽z⩽h is considered. The purpose of this paper is to adopt a linear hygrothermal effect to analyze the unsteady state responses in a finite long solid cylinder subjected to axisymmetric hygrothermal loading T=TR and C=CR at the surface. The analytical solution of temperature, moisture and thermal stresses is obtained by using the integral transform technique. The coupling and uncoupling effects of temperature, moisture and thermal stresses are discussed for a graphite fiber-reinforced epoxy matrix composite material (T300/5208). The numerical results of transient response hygrothermoelastic field are presented graphically.
Design/methodology/approach
In the present problem, hygrothermoelastic response of a finite solid circular cylinder has been investigated by integral transform technique consisting of Laplace transform, Hankel transform and Fourier-cosine transform. The problem is investigated subjected to prescribed sources. Numerical algorithm has been developed for numerical computation.
Findings
The analytical solution of temperature, moisture and thermal stresses is obtained by using the integral transform technique. The coupling and uncoupling effects of temperature, moisture and thermal stresses are discussed for a graphite fiber-reinforced epoxy matrix composite material (T300/5208). The numerical results of transient response hygrothermoelastic field are presented graphically.
Research limitations/implications
The work presented here is mostly hypothetical in nature and totally mathematical.
Practical implications
It may be useful for composite materials, composite laminated plates in hygrothermal environment. Also it is having the applications in hygrothermal field where porous media exposed to heat and moisture. The problem investigated will be beneficial for the researcher working in the field thermoelastic diffusion and hygrothermoelastic materials.
Originality/value
Till date, the other authors did the research work on hygrothermal effect of an infinitely long cylinder without thickness. In this paper, the authors consider finite solid cylinder with finite length and discuss the hygrothermal effect within a small range. Second, the material properties are both homogenous and isotropic and are independent of both temperature and moisture.
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Jitesh Tripathi, Shrikant Warbhe, K.C. Deshmukh and Jyoti Verma
The present work is concerned with the solution of a fractional-order thermoelastic problem of a two-dimensional infinite half space under axisymmetric distributions in which…
Abstract
Purpose
The present work is concerned with the solution of a fractional-order thermoelastic problem of a two-dimensional infinite half space under axisymmetric distributions in which lower surface is traction free and subjected to a periodically varying heat source. The thermoelastic displacement, stresses and temperature are determined within the context of fractional-order thermoelastic theory. To observe the variations of displacement, temperature and stress inside the half space, the authors compute the numerical values of the field variables for copper material by utilizing Gaver-Stehfast algorithm for numerical inversion of Laplace transform. The effects of fractional-order parameter on the variations of field variables inside the medium are analyzed graphically. The paper aims to discuss these issues.
Design/methodology/approach
Integral transform technique and Gaver-Stehfast algorithm are applied to prepare the mathematical model by considering the periodically varying heat source in cylindrical co-ordinates.
Findings
This paper studies a problem on thermoelastic interactions in an isotropic and homogeneous elastic medium under fractional-order theory of thermoelasticity proposed by Sherief (Ezzat and El-Karamany, 2011b). The analytic solutions are found in Laplace transform domain. Gaver-Stehfast algorithm (Ezzat and El-Karamany, 2011d; Ezzat, 2012; Ezzat, El Karamany, Ezzat, 2012) is used for numerical inversion of the Laplace transform. All the integrals were evaluated using Romberg’s integration technique (El-Karamany et al., 2011) with variable step size. A mathematical model is prepared for copper material and the results are presented graphically with the discussion on the effects of fractional-order parameter.
Research limitations/implications
Constructed purely on theoretical mathematical model by considering different parameters and the functions.
Practical implications
The system of equations in this paper may prove to be useful in studying the thermal characteristics of various bodies in real-life engineering problems by considering the time fractional derivative in the field equations.
Originality/value
In this problem, the authors have used the time fractional-order theory of thermoelasticity to solve the problem for a half space with a periodically varying heat source to control the speed of wave propagation in terms of heat and elastic waves for different conductivity like weak conductivity, moderate conductivity and super conductivity which is a new and novel contribution.
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Tasneem Firdous Islam, G.D. Kedar and Sajid Anwar
The purpose of this paper is to examine the impact of moisture and temperature changes on the behavior of a semi-infinite solid cylinder made of T300/5208 composite material. This…
Abstract
Purpose
The purpose of this paper is to examine the impact of moisture and temperature changes on the behavior of a semi-infinite solid cylinder made of T300/5208 composite material. This study aims to provide analytical solutions for temperature, moisture and thermal stress through the de-coupling technique and the method of integral transforms. Both coupled and uncoupled cases are considered.
Design/methodology/approach
This study investigates the hygrothermo-elastic response of a semi-infinite solid circular cylinder using an integral transform technique that includes Hankel and Fourier transforms. The cylinder is subjected to prescribed sources, and a numerical algorithm is developed for the numerical computation of the results. The goal is to understand how the cylinder responds to changes in temperature and moisture.
Findings
The paper presents an analytical solution for temperature, moisture and thermal stress in a semi-infinite solid cylinder obtained through the use of an integral transform technique. The study focuses on a graphite fiber-reinforced epoxy matrix composite material (T300/5208) and discusses the coupled and uncoupled effects of temperature, moisture and thermal stress on the material. The results of the transient response hygrothermo-elastic field are presented graphically to provide a visual representation of the findings.
Research limitations/implications
The research presented in this article is primarily hypothetical and focused on the analysis of mathematical models.
Originality/value
To the authors' best knowledge, this study is the first to investigate the hygrothermal effect in a semi-infinite circular cylinder. Additionally, the material properties used in the analysis are both homogenous and isotropic and independent of both temperature and moisture. These unique aspects of the study make it a novel contribution to the field.
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Rajneesh Kumar, Shaloo Devi and Veena Sharma
The purpose of this paper is to investigate the two-dimensional axisymmetric problem in a homogeneous, isotropic modified couple stress thermoelastic diffusion (TD) medium in the…
Abstract
Purpose
The purpose of this paper is to investigate the two-dimensional axisymmetric problem in a homogeneous, isotropic modified couple stress thermoelastic diffusion (TD) medium in the context of dual-phase-lag model.
Design/methodology/approach
The Laplace and Hankel transforms have been applied to find the general solution to the field equations. The components of displacement, stresses, temperature change and chemical potential are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique.
Findings
The components of normal stress, tangential stress, tangential couple stress, temperature change and chemical potential are obtained numerically and depicted graphically to see the effect of dual-phase-lag diffusion (DLD), dual-phase-lag heat transfer (DLT) and TD models in the absence and presence of couple stress parameter.
Originality/value
Comparisons are made in the absence and presence of couple stress DLD, DLT and TD models.
Details
Keywords
The thermo-diffusion analysis of an isotropic cylinder under thermal flux and chemical potential impacts has been discussed. Improvements of Green and Naghdi generalized…
Abstract
Purpose
The thermo-diffusion analysis of an isotropic cylinder under thermal flux and chemical potential impacts has been discussed. Improvements of Green and Naghdi generalized thermoelasticity theory have been proposed.
Design/methodology/approach
Some models with and without energy dissipation have been presented as well as the simple forms of Green–Naghdi (G–N) theories. These novel multi- and single-/dual-phase-lag models are presented to investigate the thermo-diffusion of the solid cylinder. The closed-form solution of thermo-diffusion governing equations of solid cylinder has been obtained to deduce all field variables.
Findings
A comparison study between the simple G–N II and III models and their improved models has been presented. The validations of outcomes are acceptable and so benchmarks are reported to help other investigators in their future comparisons.
Originality/value
The modified Green and Naghdi theories of types II and III are presented to get novel and accurate models of single- and dual-phase-lag of multiterms. The heat of mass diffusion equation as well as the constitutive equations for the stresses and chemical potential of a solid cylinder is added to the present formulation. The system of three differential coupled equations is solved, and all field variables are obtained for the thermal diffusion of the solid cylinder. Some validation examples and applications are presented to compare the simple and modified Green and Naghdi theories of types II and III. Sample plots are illustrated along the radial direction of the solid cylinder. Some results are tabulated to serve as benchmark results for future comparisons with other investigators. The reported and illustrated results show that the simple G–N II and III models yield the largest values of all field quantities. The single-phase-lag models give the smallest values. However, the dual-phase-lag model yields results that are intermediate between those of the simple and single-phase-lag G–N models.
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Chandra Sekhar Mahato and Siddhartha Biswas
This paper is concerned with the study of the propagation of Rayleigh waves in a homogeneous isotropic, generalized thermoelastic medium with mass diffusion and double porosity…
Abstract
Purpose
This paper is concerned with the study of the propagation of Rayleigh waves in a homogeneous isotropic, generalized thermoelastic medium with mass diffusion and double porosity structure using the theoretical framework of three-phase-lag model of thermoelasticity.
Design/methodology/approach
Using Eringen’s nonlocal elasticity theory and normal mode analysis technique, this paper solves the problem. The medium is subjected to isothermal, thermally insulated stress-free, and chemical potential boundary conditions.
Findings
The frequency equation of Rayleigh waves for isothermal and thermally insulated surfaces is derived. Propagation speed, attenuation coefficient, penetration depth and specific loss of the Rayleigh waves are computed numerically. The impact of nonlocal, void and diffusion parameters on different physical characteristics of Rayleigh waves like propagation speed, attenuation coefficient, penetration depth and specific loss with respect to wave number for isothermal and thermally insulated surfaces is depicted graphically.
Originality/value
Some limiting and particular cases are also deduced from the present investigation and compared with the existing literature. During Rayleigh wave propagation, the path of the surface particle is found to be elliptical. This study can be extended to fields like earthquake engineering, geophysics and the degradation of old building materials.
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Manish Garg, B S Salaria and V K Gupta
– The purpose of this paper is to investigate steady state creep behavior of a functionally graded rotating disc under varying thermal gradient (TG).
Abstract
Purpose
The purpose of this paper is to investigate steady state creep behavior of a functionally graded rotating disc under varying thermal gradient (TG).
Design/methodology/approach
The steady state creep in a rotating FGM disc with linearly varying thickness has been investigated by using von-Mises yield criterion. The disc under investigation is assumed to be made of FGM containing non-linear distribution of silicon carbide particle (SiCp) in a matrix of pure aluminum along the radial distance. The creep behavior of the FGM composite disc is described by threshold stress-based law. The stresses and strain rates in the FGM disc have been estimated for different kinds of TG.
Findings
The results indicate that when the FGM disc is subjected to a radial TG, with temperature increasing with increasing radius, the radial stress in the disc increases over the entire disc but the tangential and effective stresses increase near the inner radius and decrease toward the outer radius. The imposition of such a radial TG in the FGM disc leads to significant reduction in the radial and tangential strain rates. With the increase in magnitude of TG in the FGM disc, the inhomogeneity in creep stresses increases but the inhomogeneity in strain rates decreases significantly, thereby reducing the chances of distortion in the FGM disc.
Originality/value
The creep strain rates in rotating FGM disc could be significantly reduced when the disc is subjected to a radial TG, with temperature increasing with increasing radius.
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Chenghui Xu, Sen Leng, Deen Li and Yajun Yu
This paper aims to focus on the accurate analysis of the fractional heat transfer in a two-dimensional (2D) rectangular monolayer tissue with three different kinds of lateral…
Abstract
Purpose
This paper aims to focus on the accurate analysis of the fractional heat transfer in a two-dimensional (2D) rectangular monolayer tissue with three different kinds of lateral boundary conditions and the quantitative evaluation of the degree of thermal damage and burn depth.
Design/methodology/approach
A symplectic method is used to analytically solve the fractional heat transfer dual equation in the frequency domain (s-domain). Explicit expressions of the dual vector can be constructed by superposing the symplectic eigensolutions. The solution procedure is rigorously rational without any trial functions. And the accurate predictions of temperature and heat flux in the time domain (t-domain) are derived through numerical inverse Laplace transform.
Findings
Comparison study shows that the maximum relative error is less than 0.16%, which verifies the accuracy and effectiveness of the proposed method. The results indicate that the model and heat source parameters have a significant effect on temperature and thermal damage. The pulse duration (Δt) of the laser heat source can effectively control the time to reach the peak temperature and the peak slope of the thermal damage curve. The burn depth is closely correlated with exposure temperature and duration. And there exists the delayed effect of fractional order on burn depth.
Originality/value
A symplectic approach is presented for the thermal analysis of 2D fractional heat transfer. A unified time-fractional heat transfer model is proposed to describe the anomalous thermal behavior of biological tissue. New findings might provide guidance for temperature prediction and thermal damage assessment of biological tissues during hyperthermia.