Continuum mechanics studies the foundations of deformable body mechanics from a mathematical perspective. It also acts as a base upon which other applied areas such as solid mechanics and fluid mechanics are developed. This book discusses some important topics, which have come into prominence in the latter half of the twentieth century, such as material symmetry, frame-indifference and thermomechanics. The study begins with the necessary mathematical background in the form of an introduction to tensor analysis followed by a discussion on kinematics, which deals with purely geometrical notions such as strain and rate of deformation. Moving on to derivation of the governing equations, the book also presents applications in the areas of linear and nonlinear elasticity. In addition, the volume also provides a mathematical explanation to the axioms and laws of deformable body mechanics, and its various applications in the field of solid mechanics.

Continuum Mechanics : Foundations and Applications of Mechanics

One-dimensional unsteady isothermal and adiabatic flow behind a strong exponential shock wave propagating in a rotational axisymmetric mixture of non-ideal gas and small solid particles, which has variable azimuthal and axial fluid velocities, is analyzed. The shock wave is driven out by a piston moving with time according to exponential law. The azimuthal and axial components of the fluid velocity in the ambient medium are assumed to be varying and obeying exponential laws. In the present work, small solid particles are considered as pseudo-fluid with the assumption that the equilibrium flow-conditions are maintained in the flow-field, and the viscous-stress and heat conduction of the mixture are negligible. Solutions are obtained in both the cases, when the flow between the shock and the piston is isothermal or adiabatic by taking into account the components of vorticity vector and compressibility. It is found that the assumption of zero temperature gradient brings a profound change in the density, axial component of vorticity vector and compressibility distributions as compared to that of the adiabatic case. To investigate the behavior of the flow variables and the influence on the shock wave propagation by the parameter of non-idealness of the gas $$ \,\overline{b} $$
 in the mixture as well as by the mass concentration of solid particles in the mixture $$ K_{p} $$
 and by the ratio of the density of solid particles to the initial density of the gas $$ G_{1} $$
 are worked out in detail. It is interesting to note that the shock strength increases with an increase in $$ G_{1} $$
 ; whereas it decreases with an increase in $$ \,\overline{b} $$
 . Also, a comparison between the solutions in the cases of isothermal and adiabatic flows is made.

Propagation of exponential shock wave in an axisymmetric rotating non-ideal dusty gas

A self-similar model for one-dimensional unsteady adiabatic flows behind a cylindrical shock wave driven out by a piston moving with time according to an exponential law in non-ideal gas in the presence of conductive and radiative heat fluxes is discussed in a rotating atmosphere The ambient medium is assumed to have axial, azimuthal and radial component of fluid velocities The axial and azimuthal component of fluid velocity in the ambient medium is assumed to be varying according to exponential laws The initial density and angular velocity of the ambient medium are taken to be constant for the existence of the similarity solutions It is shown that increase in the parameter of non-idealness of the gas and the conductive or radiative heat transfer parameters have decaying effect on the shock wave It is obtained that the parameter of non-idealness of the gas and heat transfer parameters have same effects on shock strength, density, pressure, axial and azimuthal component of fluid velocity and vorticity vector

Flow Behind an Exponential Shock Wave in a Rotational Axisymmetric Non-ideal Gas with Conduction and Radiation Heat Flux

The propagation of cylindrical shock wave in rotational axisymmetric non-ideal gas with conductive and radiative heat fluxes as well as axial magnetic field is investigated. The magnetic field, azimuthal fluid velocity and axial fluid velocity are assumed to be varying according to exponential law with distance from the axis of symmetry in the undisturbed medium. The similarity method has been performed to obtain the class of self-similar solutions. Distributions of gas-dynamical quantities are discussed.

Unsteady Flow Behind an MHD Exponential Shock Wave in a Rotational Axisymmetric Non-ideal Gas with Conductive and Radiative Heat Fluxes

In the present paper, we investigated the propagation of exponential cylindrical shock wave in the presence of radiative as well as conductive heat fluxes under the influence of gravitational field. The medium is assumed to be non-ideal gas rotating about the axis of symmetry. The ambient medium has variable azimuthal as well as axial components of fluid velocity. It is manifested that the non-idealness parameter of the gas has decaying effect on the shock wave; however, presence of gravitational field has reverse effect on the shock strength.

Similarity Solution for the Flow Behind an Exponential Shock Wave in a Rotational Axisymmetric Non-ideal Gas Under the Influence of Gravitational Field with Conductive and Radiative Heat Fluxes

A.K. Kandya

Papers

Axial eigenfunctions for the axisymmetric problem of an elastic circular cylinder