The governing equations for generalized thermoelasticity of a mixture of an elastic solid and a Newtonian fluid are formulated in the context of Lord-Shulman and Green-Lindsay theories of generalized thermoelasticity. These equations are solved to show the existence of three coupled longitudinal waves and two coupled transverse waves, which are dispersive in nature. Reflection from a thermally insulated stress-free surface is considered for incidence of coupled longitudinal wave. The speeds and reflection coefficients of plane waves are computed numerically for a particular model.

The soil consists of an assemblage of particles with different sizes and shapes which form a skeleton whose voids are filled by water and air or gas. The word “soil,” therefore, implies a mixture of assorted mineral grains with various fluids. The first continuum theory of mixtures was proposed by Truesdell [

Many engineering materials, as well as soils, rocks, granular materials, sand, and underground water mixtures may be modeled more realistically by means of micropolar continua. Eringen [

We consider a binary mixture of an elastic solid and a Newtonian fluid at the same temperature where no chemical reaction takes place between the two species of the mixture. According to the last section given in Eringen [

The use of symbol

By introducing the scalar potentials

Using (

In this section, the plane wave propagation in an infinite thermally conducting mixture of elastic solid and Newtonian fluid is studied. In order to solve (

Equation (

In absence of fluid, (

In absence of thermal effects, the cubic equation (

We consider the half-space of the medium with

Geometry of the problem showing incident and reflected waves.

The appropriate potentials required to satisfy the above boundary conditions are

Using the appropriate potentials given by (

In this section, the complex absolutes of phase speeds and reflection coefficients are computed with the following physical constants at

The densities of solid, fluid, and mixture are related as

Numerical computations of phase speeds and reflection coefficients are restricted to the particular case of Lord-Shulman theory only. The phase speeds of the coupled waves are shown graphically in Figure

Thermal effects on speeds of coupled waves against frequency.

Reflection coefficients are computed for incident CL I wave only. The reflection coefficients of coupled longitudinal waves are shown graphically in Figure

Thermal effects on coefficients of reflected coupled longitudinal waves for incident CL I wave.

Thermal effects on coefficients of reflected coupled transverse waves for incident CL I wave.

The generalized thermoelasticity of a mixture of an elastic solid and a Newtonian fluid is developed in accordance with Lord-Shulman and Green-Lindsay theories. The solutions of governing equations suggest that there will exist three coupled longitudinal waves and two coupled transverse waves in the present model. From numerical results, it is observed that the phase speeds of coupled waves increase with the increase in frequency. The presence of thermal parameters affects the phase speeds of coupled longitudinal waves only. Reflection coefficients of all reflected coupled waves are affected significantly by thermal disturbances in the material.