Wave propagation at interface of heat conducting micropolar solid and fluid media
02 Jul 2011-Applied Mathematics and Mechanics-english Edition (Shanghai University Press)-Vol. 32, Iss: 7, pp 881-902
TL;DR: In this paper, the amplitude ratios of various reflected and transmitted plane waves are obtained in a closed form, and it is found that they are a function of the angle of incidence and frequency and are affected by the elastic properties of the media.
Abstract: The present investigation is concerned with the wave propagation at an interface of a micropolar generalized thermoelastic solid half space and a heat conducting micropolar fluid half space. Reflection and transmission phenomena of plane waves are investigated, which impinge obliquely at the plane interface between a micropolar generalized thermoelastic solid half space and a heat conducting micropolar fluid half space. The incident wave is assumed to be striking at the interface after propagating through the micropolar generalized thermoelastic solid. The amplitude ratios of various reflected and transmitted waves are obtained in a closed form. It is found that they are a function of the angle of incidence and frequency and are affected by the elastic properties of the media. Micropolarity and thermal relaxation effects are shown on the amplitude ratios for a specific model. The results of some earlier literatures are also deduced from the present investigation.
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TL;DR: In this article, the reflection and transmission coefficients of a longitudinal displacement wave, thermal wave, and two coupled transverse displacement and microrotational waves are derived for different incident waves, and amplitude ratios for different reflected and transmitted waves vs the angle of incidence are calculated numerically for various thermoelasticity models.
Abstract: The present investigation is concerned with the reflection and transmission of plane waves at an interface between two micropolar thermoelastic half-spaces with different micropolarity and thermoelastic properties. The three-phaselag theory of thermoelasticity developed by Roychoudhuri is used to study the phenomena mentioned. The reflection and transmission coefficients of a longitudinal displacement wave, thermal wave, and two coupled transverse displacement and microrotational waves are derived for different incident waves. The amplitude ratios for different reflected and transmitted waves vs. the angle of incidence are calculated numerically for various thermoelasticity models. Their graphical representations are given.
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TL;DR: In this article, a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of heat flow.
Abstract: In this work a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of the heat flow. The theory takes into account the coupling effect between temperature and strain rate, but the resulting coupled equations are both hyperbolic. Thus, the paradox of an infinite velocity of propagation, inherent in the existing coupled theory of thermoelasticity, is eliminated. A solution is obtained using the generalized theory which compares favourably with a known solution obtained using the conventional coupled theory.
3,266 citations
"Wave propagation at interface of he..." refers background in this paper
...The first one was proposed by Lord and Shulman [ 19 ] , who obtained a wave-type heat equation by postulating a new law of heat conduction to replace the classical Fourier’s law....
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...Following Eringen [17] , Lord and Shulman [ 19 ] , and Green and Lindsay [22] , the field equations for an isotropic and homogeneous micropolar elastic medium in the context of the generalized theory of thermoelasticity, without body forces, body couples, and heat sources, can be given by Wave propagation at interface of heat conducting micropolar solid and fluid media 883...
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TL;DR: In this article, a unified treatment of thermoelasticity by application and further developments of the methods of irreversible thermodynamics is presented, along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement.
Abstract: A unified treatment is presented of thermoelasticity by application and further developments of the methods of irreversible thermodynamics. The concept of generalized free energy introduced in a previous publication plays the role of a ``thermoelastic potential'' and is used along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement. The general laws of thermoelasticity are formulated in a variational form along with a minimum entropy production principle. This leads to equations of the Lagrangian type, and the concept of thermal force is introduced by means of a virtual work definition. Heat conduction problems can then be formulated by the methods of matrix algebra and mechanics. This also leads to the very general property that the entropy density obeys a diffusion‐type law. General solutions of the equations of thermoelasticity are also given using the Papkovitch‐Boussinesq potentials. Examples are presented and it is shown how the generalized coordinate method may be used to calculate the thermoelastic internal damping of elastic bodies.
2,287 citations
TL;DR: In this paper, the authors derived equations of motion, constitutive equations and boundary conditions for a class of fluids named micropolar fluids, which respond to micro-rotational motions and spin inertia and therefore can support couple stress and distributed body couples.
Abstract: : Equations of motion, constitutive equations and boundary conditions are derived for a class of fluids named micropolar fluids. These fluids respond to micro-rotational motions and spin inertia and therefore can support couple stress and distributed body couples. Thermodynamical restrictions are studied in detail and field equations are obtained for the density, velocity vector and micro-rotation vector. The system is solved for a channel flow exhibiting certain interesting phenomena.
2,256 citations
TL;DR: In this paper, the formulation of the basic field equations, boundary conditions and constitutive equations of simple micro-elastic solids is discussed. And explicit expressions of constitutive expressions of several simple micro elastic solids are given and applied to some special problems.
1,309 citations
01 Sep 1965
TL;DR: In this article, a special class of micro-elastic materials called Micropolar Solids are presented for couple stress and distributed body couples, and the couple stress theory is shown to emanate as a spacial case of the present theory.
Abstract: : Equations of motion, constitutive equations and boundary conditions are presented for a special class of micro-elastic materials called Micropolar Solids. These solids respond to micro-rotational motions and spin inertia and can support couple stress and distributed body couples. The couple stress theory is shown to emanate as a spacial case of the present theory when the motion is constrained so that micro- and macro-rotations coincide. Several energy and uniqueness theorems are given.
929 citations