Thermal Relaxation Parameter Research Articles

THE ONSET OF CONVECTION IN A GRAVITY-MODULATED VISCOELASTIC FLUID-SATURATED ANISOTROPIC POROUS LAYER

This study presents a linear stability analysis of thermal convection in a porous layer saturated with viscoelastic fluid subjected to harmonic vertical vibrations so that the gravity varies periodically with time. The fluid obeys an Oldroyd-B constitutive relationship. The porous layer is considered to be densely packed and to possess vertical anisotropy in both mechanical and thermal properties. The onset threshold in terms of correction to a critical Rayleigh number is computed using the regular perturbation method based on small amplitude of modulation. Due to the imposed gravity modulation, there is a shift in the onset criteria. It is found that the low-frequency gravity modulation advances the convection, while for moderate and large frequencies stabilization occurs. The thermal anisotropy, normalized porosity, Darcy-Prandtl number, and relaxation parameter reinforce-while the mechanical anisotropy and retardation parameters suppress-the stabilizing effect of g-jitter. © 2013 by Begell House, Inc.

Transient hyperbolic heat conduction in thick-walled FGM cylinders and spheres with exponentially-varying properties

Abstract This paper focuses on non-Fourier hyperbolic heat conduction analysis for heterogeneous hollow cylinders and spheres made of functionally graded material (FGM). All the material properties vary exponentially across the thickness, except for the thermal relaxation parameter which is taken to be constant. The cylinder and sphere are considered to be cylindrically and spherically symmetric, respectively, leading to one-dimensional heat conduction problems. The problems are solved analytically in the Laplace domain, and the results obtained are transformed to the real-time space using the modified Durbin’s numerical inversion method. The transient responses of temperature and heat flux are investigated for different inhomogeneity parameters and relative temperature change values. The comparisons of temperature distribution and heat flux between various time and material properties are presented in the form of graphs.

Propagation of P waves from stress-free surface elastic half-space with voids under thermal relaxation and magnetic field

In this paper, an attempt is allocated to investigate the influence of the magnetic field and voids on the reflection of P waves under LS model. The basic governing equations for isotropic and homogeneous generalized thermoelastic half-space with voids under Maxwell’s stress are formulated in the context of the Lord Shulman theory. The boundary conditions at stress-free thermally insulated surface are satisfied to obtain a system of four equations in the reflection coefficients of various reflected waves. It is shown that there exist four plane waves; P 1 , P 2 , P 3 and SV waves. In addition, the reflection coefficients from insulated and isothermal stress-free surface for the incidence of P waves are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of the magnetic field, thermal relaxation and voids parameters.

Effects of thermal relaxation time on plane wave propagation under two-temperature thermoelasticity

The present paper is concerned with an in-depth investigation of the propagation of harmonic plane waves in elastic media in the context of the linear theory of two-temperature generalized thermoelasticity. The exact dispersion relation solutions for the longitudinal plane wave are determined analytically. Asymptotic expansions of several characterizations of the wave field, like phase velocity, specific loss and penetration depth of the dilatational waves, are obtained for both the high frequency as well as low frequency values. The effects of thermal relaxation parameter on the plane wave is analyzed in details by comparing the theoretical as well as numerical results of the present work with the corresponding results in the context of classical two-temperature thermoelasticity theory as reported earlier.

Damped-Wave Conduction and Relaxation in a Finite Sphere and Cylinder

Damped-Wave Conduction and Relaxation in a Finite Sphere and Cylinder

Further investigations on Rayleigh waves in piezothermoelastic materials

The present paper is devoted to extend the study on propagation of Rayleigh surface waves in homogeneous, transversely isotropic, piezothermoelastic semi-space subjected to stress free, open or closed circuit, thermally insulated/isothermal boundary conditions, in the context of non-classical (generalized) theories of thermoelasticity. Secular equations for surface wave propagation in the considered media are derived from a coupled system of governing partial differential equations of linear generalized piezothermoelasticity. The surface amplitudes, specific loss factor, and surface particle motion are also investigated. The surface particle paths during the motion are found to be elliptical which degenerate into straight lines in case there is no phase difference between horizontal and vertical components of surface displacements. The results in the context of coupled theory of thermoelasticity can be obtained from the present analysis by setting thermal relaxation parameters equal to zero. Finally, in order to illustrate and verify the analytical developments, the numerical solution of secular equations, specific loss factor, eccentricities, and inclination of particle paths with wave normal is carried out for cadmium-selenide (6 mm class) material with the help of Descartes’ algorithm and functional iteration method. The computer simulated results are then presented graphically in order to illustrate and compare them in the context of coupled and generalized theories of thermoelasticity.

Relaxation Effects on Plane Wave Propagation in a Rotating Magneto-Thermo-Viscoelastic Medium

The present work aims at investing the propagation of plane magneto-thermo-viscoelastic waves in a homogeneous viscoelastic medium, which is rotating with a uniform angular velocity. Both the coupled dynamical thermoelasticity theory and the generalized thermoelasticity theory are applied to obtain the analytical solution for the phase velocities and the decay coefficients of the plane wave. The numerical values of the phase velocities and the decay coefficients are also computed for a suitable material and the results are presented in graphs. The effects of rotation and the thermal relaxation parameters on phase velocities and decay coefficients are discussed in details for both high and low frequency wave modes.

Theory of nonradiative decay dynamics in intensely pumped solid-state laser media via laser photothermal diagnostics

A rigorous analytical treatment of nonradiative deexcitation and thermal-conduction transient evolution in solid-state laser media, resulting from intense optical pumping with rectangular pulses from a time-gated laser source, is presented. This situation arises in rate-window photothermal detection from laser rods with bulk and surface absorptions, the latter being due to polishing during the manufacturing of the rod. Numerical simulations of the theory show that the surface nonradiative (optical-to-thermal) energy conversion term is likely to dominate even at absorptances on the order of 1%–2%. Therefore, polishing optimization appears to be necessary in order to minimize laser losses at the surfaces when laser rods are active in a resonator cavity. The present theory also provides physical insights into the very different nature of the bulk- and surface-originating heat-conduction transients, as well as on the profile of the superposition photothermal wave form and its dependence on the optical, thermal, and metastable-state relaxation parameters. As a prelude for input to the photothermal theory, a treatment of the excited-state dynamics of a typical laser manifold pumped by an intense laser beam, away from or near saturation, is developed, and the luminescence and photothermal energy source profiles are calculated analytically.

Formulation and solution of hyperbolic Stefan problem

The interface condition for hyperbolic phase change problems, which includes sensible heat at the interface, is derived as an extension of the interface condition for standard parabolic phase change problems. The enthalpy formulation of the hyperbolic Stefan problem is presented and is used to numerically solve for the temperature distributions and the interface position. MacCormack’s predictor–corrector method is applied to solve the hyperbolic phase change problem and is validated by comparing the limiting case where the thermal relaxation parameter approaches zero to the parabolic phase change problem, in which the relaxation parameter is zero. Solutions with an applied surface temperature greater than the melt temperature are presented for two different Stefan numbers. It is noted that a discontinuity occurs at the phase change interface as well as at the thermal front.

Variable Specific Heat and Thermal Relaxation Parameter in Hyperbolic Heat Conduction

Variable Specific Heat and Thermal Relaxation Parameter in Hyperbolic Heat Conduction