Abstract: A theoretical constitutive model describing the stress-strain behavior of rock subjected to different confining pressures is presented. A bounding surface plastic model with hardening effects is proposed which includes the effect of temperature drop. The bounding surface is based on a mapping rule and the temperature effect on rock is controlled by Poisson’s ratio. Validation of the results against available experimental data is also presented. The relation of deviatoric stress and axial strain is illustrated at different temperatures to analyze the effect of temperature decrease in terms of stiffness of the material.
Abstract: Conditions corresponding to the unconditional stability
of convection in a mechanically anisotropic fluid saturated porous
medium of infinite horizontal extent are determined. The medium
is heated from below and its bounding surfaces are subjected to
temperature modulation which consists of a steady part and a
time periodic oscillating part. The Brinkman model is employed
in the momentum equation with the Bousinessq approximation.
The stability region is found for arbitrary values of modulational
frequency and amplitude using the energy method. Higher order
numerical computations are carried out to find critical boundaries
and subcritical instability regions more accurately.
Abstract: Exact solution of an unsteady MHD flow of elasticoviscous
fluid through a porous media in a tube of elliptic cross
section under the influence of magnetic field and constant pressure
gradient has been obtained in this paper. Initially, the flow is
generated by a constant pressure gradient. After attaining the steady
state, the pressure gradient is suddenly withdrawn and the resulting
fluid motion in a tube of elliptical cross section by taking into
account of the porosity factor and magnetic parameter of the
bounding surface is investigated. The problem is solved in two-stages
the first stage is a steady motion in tube under the influence of a
constant pressure gradient, the second stage concern with an unsteady
motion. The problem is solved employing separation of variables
technique. The results are expressed in terms of a non-dimensional
porosity parameter, magnetic parameter and elastico-viscosity
parameter, which depends on the Non-Newtonian coefficient. The
flow parameters are found to be identical with that of Newtonian case
as elastic-viscosity parameter, magnetic parameter tends to zero, and
porosity tends to infinity. The numerical results were simulated in
MATLAB software to analyze the effect of Elastico-viscous
parameter, porosity parameter, and magnetic parameter on velocity
profile. Boundary conditions were satisfied. It is seen that the effect
of elastico-viscosity parameter, porosity parameter and magnetic
parameter of the bounding surface has significant effect on the
velocity parameter.
Abstract: Exact solution of an unsteady MHD flow of elasticoviscous
fluid through a porous media in a tube of spherical cross
section under the influence of magnetic field and constant pressure
gradient has been obtained in this paper. Initially, the flow is
generated by a constant pressure gradient. After attaining the steady
state, the pressure gradient is suddenly withdrawn and the resulting
fluid motion in a tube of spherical cross section by taking into
account of the porosity factor and magnetic parameter of the
bounding surface is investigated. The problem is solved in two-stages
the first stage is a steady motion in tube under the influence of a
constant pressure gradient, the second stage concern with an unsteady
motion. The problem is solved employing separation of variables
technique. The results are expressed in terms of a non-dimensional
porosity parameter (K), magnetic parameter (m) and elasticoviscosity
parameter (β), which depends on the Non-Newtonian
coefficient. The flow parameters are found to be identical with that of
Newtonian case as elastic-viscosity parameter and magnetic
parameter tends to zero and porosity tends to infinity. It is seen that
the effect of elastico-viscosity parameter, porosity parameter and
magnetic parameter of the bounding surface has significant effect on
the velocity parameter.
Abstract: Exact solution of an unsteady flow of elastico-viscous
fluid through a porous media in a tube of ellipsoidal cross section
under the influence of constant pressure gradient has been obtained in
this paper. Initially, the flow is generated by a constant pressure
gradient. After attaining the steady state, the pressure gradient is
suddenly withdrawn and the resulting fluid motion in a tube of
ellipsoidal cross section by taking into account of the porosity factor
of the bounding surface is investigated. The problem is solved in twostages
the first stage is a steady motion in tube under the influence of
a constant pressure gradient, the second stage concern with an
unsteady motion. The problem is solved employing separation of
variables technique. The results are expressed in terms of a nondimensional
porosity parameter (K) and elastico-viscosity parameter
(β), which depends on the Non-Newtonian coefficient. The flow
parameters are found to be identical with that of Newtonian case as
elastic-viscosity parameter tends to zero and porosity tends to
infinity. It is seen that the effect of elastico-viscosity parameter and
the porosity parameter of the bounding surface has significant effect
on the velocity parameter.
Abstract: Exact solution of an unsteady flow of elastico-viscous
fluid through a porous media in a tube of spherical cross section
under the influence of constant pressure gradient has been obtained in
this paper. Initially, the flow is generated by a constant pressure
gradient. After attaining the steady state, the pressure gradient is
suddenly withdrawn and the resulting fluid motion in a tube of
spherical cross section by taking into account of the porosity factor of
the bounding surface is investigated. The problem is solved in twostages
the first stage is a steady motion in tube under the influence of
a constant pressure gradient, the second stage concern with an
unsteady motion. The problem is solved employing separation of
variables technique. The results are expressed in terms of a nondimensional
porosity parameter (K) and elastico-viscosity parameter
(β), which depends on the Non-Newtonian coefficient. The flow
parameters are found to be identical with that of Newtonian case as
elastic-viscosity parameter tends to zero and porosity tends to
infinity. It is seen that the effect of elastico-viscosity parameter,
porosity parameter of the bounding surface has significant effect on
the velocity parameter.
Abstract: Exact solution of an unsteady flow of elastico-viscous
electrically conducting fluid through a porous media in a tube of
elliptical cross section under the influence of constant pressure
gradient and magnetic field has been obtained in this paper. Initially,
the flow is generated by a constant pressure gradient. After attaining
the steady state, the pressure gradient is suddenly withdrawn and the
resulting fluid motion in a tube of elliptical cross section by taking
into account of the transverse magnetic field and porosity factor of
the bounding surface is investigated. The problem is solved in twostages
the first stage is a steady motion in tube under the influence of
a constant pressure gradient, the second stage concern with an
unsteady motion. The problem is solved employing separation of
variables technique. The results are expressed in terms of a nondimensional
porosity parameter (K), magnetic parameter (m) and
elastico-viscosity parameter (β), which depends on the Non-
Newtonian coefficient. The flow parameters are found to be identical
with that of Newtonian case as elastic-viscosity parameter and
magnetic parameter tends to zero and porosity tends to infinity. It is
seen that the effect of elastico-viscosity parameter, magnetic
parameter and the porosity parameter of the bounding surface has
significant effect on the velocity parameter.
Abstract: A new elastic-viscoplastic (EVP) constitutive model is proposed for the analysis of time-dependent behavior of clay. The proposed model is based on the bounding surface plasticity and the concept of viscoplastic consistency framework to establish continuous transition from plasticity to rate dependent viscoplasticity. Unlike the overstress based models, this model will meet the consistency condition in formulating the constitutive equation for EVP model. The procedure of deriving the constitutive relationship is also presented. Simulation results and comparisons with experimental data are then presented to demonstrate the performance of the model.
Abstract: The effect of internal heat generation is applied to the Rayleigh-Benard convection in a horizontal micropolar fluid layer. The bounding surfaces of the liquids are considered to be rigid-free, rigid-rigid and free-free with the combination of isothermal on the spin-vanishing boundaries. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. It is shown that the critical Rayleigh number decreases as the value of internal heat generation increase and hence destabilize the system.