Abstract: In this study, the free vibration analysis of conical helicoidal rods with two different elliptically oriented cross sections is investigated and the results are compared by the circular cross-section keeping the net area for all cases equal to each other. Problems are solved by using the mixed finite element formulation. Element matrices based on Timoshenko beam theory are employed. The finite element matrices are derived by directly inserting the analytical expressions (arc length, curvature, and torsion) defining helix geometry into the formulation. Helicoidal rod domain is discretized by a two-noded curvilinear element. Each node of the element has 12 DOFs, namely, three translations, three rotations, two shear forces, one axial force, two bending moments and one torque. A parametric study is performed to investigate the influence of elliptical cross sectional geometry and its orientation over the natural frequencies of the conical type helicoidal rod.
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state, the pressure gradient is suddenly withdrawn and the resulting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 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: An attempt has been made to develop a
seminumerical model to study temperature variations in dermal
layers of human limbs. The model has been developed for two
dimensional steady state case. The human limb has been assumed to
have elliptical cross section. The dermal region has been divided
into three natural layers namely epidermis, dermis and subdermal
tissues. The model incorporates the effect of important physiological
parameters like blood mass flow rate, metabolic heat generation, and
thermal conductivity of the tissues. The outer surface of the limb is
exposed to the environment and it is assumed that heat loss takes
place at the outer surface by conduction, convection, radiation, and
evaporation. The temperature of inner core of the limb also varies at
the lower atmospheric temperature. Appropriate boundary conditions
have been framed based on the physical conditions of the problem.
Cubic splines approach has been employed along radial direction and
Fourier series along angular direction to obtain the solution. The
numerical results have been computed for different values of
eccentricity resembling with the elliptic cross section of the human
limbs. The numerical results have been used to obtain the
temperature profile and to study the relationships among the various
physiological parameters.