Thermoelastic behavior of elastic media with temperature-dependent properties under transient thermal shock

This article is concerned with thermoelastic behavior of an elastic media with temperature-dependent properties. The formulations of anisotropic media with variable material properties are proposed by the Clausius inequality and generalized theory of thermoelasticity with one relaxation time, where the higher-order expansion of the Helmholtz free energy with respect to increment temperature is used to obtain the relations between each parameter and real temperature. The governing equations of isotropic media with temperature-dependent properties are obtained based on these formulations. The problem of a half-space formed of an isotropic media with variable material properties and subjected to a sudden temperature rise in the boundary has been conducted. The propagations of thermoelastic wave and thermal wave, as well as the distributions of displacement, temperature, and stresses in the different cases, including constant properties and variable properties with specific temperature and real temperature, are obtained and plotted to reveal the effect of variable material properties on thermoelastic behavior.     

Rotation,electromagnetic field,and variable thermal conductivity effects on free convection flow past an eternity vertical porous plate

The present research may facilitate the reduction of the number of conversion steps required to include the low output voltages in an electrokinetic biomass process. Variable thermal conductivity and electroosmosis flow have already established great potential in the thermo-elastic models of various manufacturing industries and have been widely used in energy technologies. As a result, the current framework investigates the characteristics of natural convection flow with the influence of variable thermal conductivity and electroosmosis over an eternity vertical porous plate. Coriolis forces and Hall current effects are considered in the momentum equations, and also thermal radiation and variable thermal conductivity are taken as energy equations. A linear chemical reaction parameter is used in the concentration equation. The equation of Poisson–Boltzmann is exploited to depict the electric potential characteristics within the accelerated plate medium. The pdepe command in Matlab software is used to figure out the numerical solutions to equations about momentum, energy, and concentration. The expressions of fluid transverse velocity, fluid axial velocity, fluid temperature, and concentration profiles are presented as numerical results and also derived vital relevant stream parameters diagrammatically, whereas the numerical values of primary skin friction, secondary skin friction, and Nusselt number are presented in tabular form for various values of pertinent flow parameters. The temperature rises as the strength of the thermal conductivity variable parameter increases. Also, as the values of the Taylor number and the thermal conductivity variable parameter go up, the primary velocity goes down. Similarly, secondary velocity increases in the opposite direction as the Taylor number and thermal conductivity variable parameter increase.     

Normal Mode Analysis to a Two-Dimensional Generalized Electromagnetothermoelastic Problem with Diffusion

A two-dimensional generalized electromagnetothermoelastic problem for a half-space with diffusion is investigated in the present work. The problem is formulated in the context of the generalized thermoelastic diffusion theory. The half-space is initially placed in an external magnetic field with constant intensity, and its bounding surface in contact with a permeating substance is taken to be traction free and subjected to a time-dependent thermal load. The chemical potential is also assumed to be known function of time on the bounding surface. The half-space deforms because of the thermal load, and due to the application of magnetic field, there results in an induced magnetic field and an induced electric field in the half-space. The system of Maxwell's equations is given and the generalized electromagnetothermoelastic diffusive coupled governing equations are established. To solve the formulated equations, normal mode analysis is adopted and the exact expressions for the non-dimensional temperature, displacement, stress, induced magnetic field, induced electric field, and chemical potential and concentration are obtained and represented graphically.     

Three-dimensional thermoelastic problem in orthotropic medium

Abstract

The present article is concerned with a thermoelastic boundary-value problem with a time-dependent thermal shock on traction-free half-space for a homogeneous orthotropic heat-conducting solid. The governing equations of the three-dimensional problem of generalized thermoelasticity in orthotropic medium are obtained as a vector-matrix differential equation form by employing normal mode analysis to the considered equations which is then solved by the eigenfunction expansion method. The distribution of thermal stress, displacements, and temperature are presented graphically and compared with other thermoelastic models.     

The effects of Joule heating and variable thermal conductivity on peristaltic pumping of Jeffrey nanofluid in the presence of heat transfer

This investigation aims to study Hall's current effect on the peristaltic flow of a Jeffrey nanofluid with variable thermal conductivity in an inclined asymmetric channel. Joule heating and oblique magnetic field effects are taken into consideration. A system of ordinary differential equations is obtained under the approximation of low Reynolds number and long wavelength, which consists of momentum, energy, and concentration equations. The influences of penitent physical parameters on the distribution of velocity, temperature, and concentration have been discussed graphically. Streamline graphs are offered in the terminus, which elucidates the trapping bolus phenomenon. The resulting equations are solved numerically using the ND Solver technique. The thermal conductivity parameter causes the pressure gradient to increase while reducing the pressure rise. Our present model can be applied to physiological flow transportation in the veins with heat transfer.     

The phase change thermoelastic analysis of biological tissue with variable thermal properties during cryosurgery

Abstract

In this work, the coupling phase change heat transfer process and thermal stress behavior of biological tissue during cryosurgery are studied in the context of a generalized thermoelastic theory. The nonlinear governing equations are constructed while considering the variable thermal properties and solved by a time-domain finite element method based on the effective heat capacity formulation. A 2-D tumor and normal tissue model is adopted for simulating the freezing process in cryosurgery. The effects of temperature-dependent thermal properties and relaxation time on the responses of biological tissue are discussed and illustrated graphically.     

Three-dimensional generalized thermoelastic diffusion and application for a thermoelastic half-space subjected to rectangular thermal pulse

In this article, a model of three-dimensional generalized thermo-diffusion in a half-space thermoelastic medium subjected to permeating gas and the rectangular thermal pulse has been constructed. The half-space is considered to be made of an isotropic homogeneous thermoelastic material. The chemical potential is also assumed to be known on the bounding plane. Laplace transform techniques have been applied, and the solution is obtained in the Laplace transform domain using a direct approach. The solution of the problem in the physical domain is obtained numerically using a numerical method based on a Riemann-sum approximation for the inversion of Laplace transform. The temperature increment, stress, strain, diffusion concentration, and chemical potential distributions are represented graphically. The nonzero value of the relaxation time parameter predicts the finite speed of thermal, mechanical, diffusion waves.     

Analytical approaches for thermal analysis of radiative fin with a step change in thickness and variable thermal conductivity

In this paper, heat transfer in a straight fin with a step change in thickness and variable thermal conductivity which is losing heat by radiation to its surroundings is analyzed. The calculations are carried out by using the differential transformation method (DTM) and variational iteration method (VIM) that can be applied to various types of differential equations. The results obtained employing the DTM and VIM are compared with a finite difference technique with Richardson extrapolation which is an accurate numerical solution to verify the accuracy of the proposed methods. As an important result, it is depicted that the DTM results are more accurate in comparison with those obtained by VIM. After these verifications the effects of parameters such as thickness parameter α, dimensionless fin semi‐thickness δ, length ratio λ, thermal conductivity parameter β, and radiation–conduction parameter N_r, on the temperature distribution and fin efficiency are illustrated and explained. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj) . DOI 10.1002/htj.21000     

Flow and heat transfer in a power-law fluid over a stretching sheet with variable thermal conductivity and non-uniform heat source

In this paper the flow of a power-law fluid due to a linearly stretching sheet and heat transfer characteristics using variable thermal conductivity is studied in the presence of a non-uniform heat source/sink. The thermal conductivity is assumed to vary as a linear function of temperature. The similarity transformation is used to convert the governing partial differential equations of flow and heat transfer into a set of non-linear ordinary differential equations. The Keller box method is used to find the solution of the boundary value problem. The effect of power-law index, Chandrasekhar number, Prandtl number, non-uniform heat source/sink parameters and variable thermal conductivity parameter on the dynamics is analyzed. The skin friction and heat transfer coefficients are tabulated for a range of values of said parameters.     

Upshot of radiative rotating Prandtl fluid flow over a slippery surface embedded with variable species diffusivity and multiple convective boundary conditions

Here, modeling and computations are performed to explore the impact of variable molecular diffusivity, nonlinear thermal radiation, convective boundary conditions, momentum slip, and variable molecular diffusivity on Prandtl fluid past a stretching sheet. By using the compatible transformation, the partial differential equations regarding momentum, energy, and concentration are reformed into ordinary differential equations and furthermore, these equations are handled numerically via the shooting method. The behavior of intricate parameters that emerge during numerical simulation is displayed in the form of tables and graphs. These outcomes are supplemented with the information for the heat transfer rate and surface drag coefficients. It is perceived that an uplift in the temperature profile occurs by virtue of augmentation in the temperature convection parameter, and furthermore, mass fraction field escalates owing to an amplification in the chemical reaction coefficient.     

TWO-DIMENSIONAL PROBLEM OF A MOVING HEATED PUNCH IN GENERALIZED THERMOELASTICITY

The two-dimensional equations of generalized thermoelasticity are solved for the case of a heated punch moving across the surface of a semi-infinite thermoelastic half-space subject to appropriate boundary conditions. The exponential Fourier transform with respect to one space variable in a coordinate system moving with the punch is applied. The resulting equations are solved and numerical results are given. The results are compared with those obtained by Roberts for the coupled thermoelastic case.     

A revised viscoelastic micropolar nanofluid model with motile micro‐organisms and variable thermal conductivity

In the present study, a magnetized micropolar nanofluid and motile micro‐organism with variable thermal conductivity over a moving surface have been discussed. The mathematical modeling has been formulated using a second‐grade fluid model and a revised form of the micropolar fluid model. The governing fluid contains micro‐organisms and nanoparticles. The resulting nonlinear mathematical differential equations have been solved with the help of the homotopy analysis method. The graphical and physical features of buoyancy force, micro‐organisms, magnetic field, microrotation, and variable thermal conductivity have been discussed in detail. The numerical results for Nusselt number, motile density number, and Sherwood number are presented with the help of tables. According to the graphical effects, it is noted that the buoyancy ratio and the bioconvection parameter resist the fluid motion. An enhancement in the temperature profile is observed due to the increment in thermal conductivity. Peclet number tends to diminish the motile density profile; however, the viscoelastic parameter magnifies the motile density profile.     

Measurement of thermal conductivity, thermal diffusivity and heat capacity of highly porous building materials using transient plane source technique

This paper presents both experimental and theoretical works concerning evaluation of the thermal conductivity, thermal diffusivity and heat capacity of wood composites. Moreover, the aim of this study is to show that the transient plane source technique originally used for measuring thermal properties of isotropic materials can be spread worthy of heat capacity, thermal conductivity and thermal diffusivity measurements of highly porous materials. Measurements of the thermal conductivity, thermal diffusivity and heat capacity have been performed at room temperature (20 ± 0.5°C) and normal pressure. An attempt has been made to predict the thermal diffusivity of wood composites from the predicted values of thermal conductivity using a Verma et al's model based on Ohms law and the calculated values of heat capacity using the enthalpy concept. The predicted values by the proposed model are compared with the values of the thermal diffusivity measured using the TPS method. A comparison shows a good agreement.     

Symmetry analysis of MHD Casson fluid flow for heat and mass transfer near a stagnation point over a linearly stretching sheet with variable viscosity and thermal conductivity

In this article, the impacts of variable viscosity and thermal conductivity on magnetohydrodynamic, heat transfer, and mass transfer flow of a Casson fluid are analyzed on a linearly stretching sheet inserted in a permeable medium along with heat source/sink and viscous dissipation. To reduce the ascendant partial differential equations into ordinary differential equations, Lie group transformation is utilized. Further, the fourth-order Runge–Kutta strategy is utilized to solve the ordinary differential equations numerically. The numerical results obtained for various parameters by employing coding in MATLAB programming are investigated and considered through graphical representation and tables. We anatomize the impacts of distinctive parameters on velocity, temperature, and concentration distributions.     

Simultaneous measurements of thermal conductivity and thermal diffusivity of insulators,fluids and conductors using the transient plane source (TPS) technique

Simultaneous measurements of thermal conductivity and thermal diffusivity of composite red-sand bricks, glycerine and mercury have been made at room temperature by the recently developed transient plane source (TPS) technique. This paper describes, in brief, the theory and the experimental conditions for the simultaneous measurements of thermal conductivity and thermal diffusivity of insulators, fluids and metals. The source of heat is a hot disc made out of bifilar spirals. The disc also serves as a sensor of temperature increase in the sample. The measured values of the thermal conductivity and thermal diffusivity of these samples are in agreement with the values reported earlier using other methods. The advantage of the TPS technique is the simplicity of the equipment, simultaneous information on thermal conductivity and thermal diffusivity, and also the applicability of the technique to insulators, fluids and metals.     

Viscous dissipation effect on mixed convective heat transfer of MHD flow of Williamson nanofluid over a stretching cylinder in the presence of variable thermal conductivity and chemical reaction

The effect of viscous dissipation and thermal radiation on mixed convective heat transfer of an MHD Williamson nanofluid past a stretching cylinder in the existence of chemical reaction is analyzed in this study. When energy equation is formulated, the variable thermal conductivity is deliberated. By proposing applicable similarity transformations, nonlinear ordinary differential equations (ODEs) are attained from partial differential equations. These nondimensional ODEs are computed through Runge-Kutta method integrated with shooting method using MATLAB software. The results found numerically are in agreement with that of the published works of similar nature in a limiting case. The results of the local Nusselt number, skin friction coefficient, and Sherwood numbers are organized in tables. The influence of protuberant parameters on temperature, velocity, and concentration is presented by graphs. From the results, it is seen that for higher values of variable thermal conductivity parameter, the local Sherwood number and skin friction coefficient upsurge, whereas the local Nusselt number diminishes.     

Temperature dependence of thermal conductivity and thermal diffusivity of some composites using the transient plane source technique

The recently developed transient plane source (TPS) technique has been applied for the simultaneous measurement of thermal conductivity and thermal diffusivity of two composite materials namely, marble and magnesium oxychloride cement in the range of temperatures from 30 to 150°C. The experimental results of these samples show that there is very slight variation in thermal conductivity and thermal diffusivity of these materials in this range of temperature. An effort has been made to express this variation of thermal conductivity and diffusivity with temperature by a linear relation, in these materials.     

Coupled thermoelasticity analysis of FGM plate integrated with piezoelectric layers under thermal shock

Abstract

Based on theory of piezoelectricity and using generalized coupled thermoelasticity, transient response of a simply supported functionally graded material rectangular plate embedded in sensor and actuator piezoelectric layers under applied electric field and thermal shock is studied. Thermoelastic properties of the plate vary continuously along the thickness direction according to exponential functions and Poisson ratio is assumed to be constant. Applying Fourier series state space technique to the basic coupled thermoelastic differential equations results in the ordinary differential equations which are solved analytically by using Laplace transform. Validation of the present approach is assessed by comparing the numerical results with the available results in literature. In parametric study, effect of the relaxation time, applied voltage and temperature and time history of the thermoelastic response of FGM plate attached to piezoelectric layers are investigated.     

DERIVATION OF SYSTEMS OF FUNDAMENTAL EQUATIONS FOR A THREE-DIMENSIONAL THERMOELASTIC FIELD WITH NONHOMOGENEOUS MATERIAL PROPERTIES AND ITS APPLICATION TO A SEMI-INFINITE BODY

A method of analytical development of three-dimensional thermoelastic problems for a medium with nonhomogeneous material properties is developed in this article. Assuming that the shear modulus elasticity G, the thermal conductivity lambda, and the coefficient of linear thermal expansion alpha vary with the power product form of axial coordinate variable z and introducing two kinds of displacement functions and the thermoelastic displacement function, the system of fundamental differential equations for such a three-dimensional field is established. As an illustrative example, we consider the thermoelastic problem of a semi-infinite body. The three-dimensional temperature solution in a steady state is obtained and the associated components of thermal displacement and stress are evaluated theoretically. Numerical calculations are carried out for several cases taking into account the variety of the nonhomogeneous material properties of G, lambda, and alpha, and these results are shown graphically.