Abstract: This paper uses quasi-steady molecular statics model
and diamond tool to carry out simulation temperature rise of nanoscale
orthogonal cutting single-crystal silicon. It further qualitatively
analyzes temperature field of silicon workpiece without considering
heat transfer and considering heat transfer. This paper supposes that
the temperature rise of workpiece is mainly caused by two heat sources:
plastic deformation heat and friction heat. Then, this paper develops a
theoretical model about production of the plastic deformation heat and
friction heat during nanoscale orthogonal cutting. After the increased
temperature produced by these two heat sources are added up, the
acquired total temperature rise at each atom of the workpiece is
substituted in heat transfer finite difference equation to carry out heat
transfer and calculates the temperature field in each step and makes
related analysis.
Abstract: The present paper develops and validates a numerical procedure for the calculation of turbulent combustive flow in converging and diverging ducts and throuh simulation of the heat transfer processes, the amount of production and spread of Nox pollutant has been measured. A marching integration solution procedure employing the TDMA is used to solve the discretized equations. The turbulence model is the Prandtl Mixing Length method. Modeling the combustion process is done by the use of Arrhenius and Eddy Dissipation method. Thermal mechanism has been utilized for modeling the process of forming the nitrogen oxides. Finite difference method and Genmix numerical code are used for numerical solution of equations. Our results indicate the important influence of the limiting diverging angle of diffuser on the coefficient of recovering of pressure. Moreover, due to the intense dependence of Nox pollutant to the maximum temperature in the domain with this feature, the Nox pollutant amount is also in maximum level.
Abstract: Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.
Abstract: Heating is inevitable in any bearing operation. This
leads to not only the thinning of the lubricant but also could lead to a
thermal deformation of the bearing. The present work is an attempt to
analyze the influence of thermal deformation on the thermohydrodynamic
lubrication of infinitely long tilted pad slider rough
bearings. As a consequence of heating the slider is deformed and is
assumed to take a parabolic shape. Also the asperities expand leading
to smaller effective film thickness. Two different types of surface
roughness are considered: longitudinal roughness and transverse
roughness. Christensen-s stochastic approach is used to derive the
Reynolds-type equations. Density and viscosity are considered to be
temperature dependent. The modified Reynolds equation, momentum
equation, continuity equation and energy equation are decoupled and
solved using finite difference method to yield various bearing
characteristics. From the numerical simulations it is observed that the
performance of the bearing is significantly affected by the thermal
distortion of the slider and asperities and even the parallel sliders
seem to carry some load.
Abstract: A numerical study on the heat transfer in the thermal
barrier coatings and the substrates of a parallel-plate enclosure is
carried out. Some of the thermal barrier coatings, such as ceramics, are
semitransparent and are of interest for high-temperature applications
where radiation effects are significant. The radiative transfer equations
and the energy equations are solved by using the discrete ordinates
method and the finite difference method. Illustrative results are
presented for temperature distributions in the coatings and the opaque
walls under various heating conditions. The results show that the
temperature distribution is more uniform in the interior portion of each
coating away from its boundary for the case with a larger average of
varying refractive index and a positive gradient of refractive index
enhances radiative transfer to the substrates.
Abstract: In this paper, growth and collapse of a vapour bubble
generated due to a local energy input inside a rigid cylinder and in
the absence of buoyancy forces is investigated using Boundary
Integral Equation Method and Finite Difference Method .The fluid is
treated as potential flow and Boundary Integral Equation Method is
used to solve Laplace-s equation for velocity potential. Different
ratios of the diameter of the rigid cylinder to the maximum radius of
the bubble are considered. Results show that during the collapse
phase of the bubble inside a vertical rigid cylinder, two liquid micro
jets are developed on the top and bottom sides of the vapour bubble
and are directed inward. It is found that by increasing the ratio of the
cylinder diameter to the maximum radius of the bubble, the rate of
the growth and collapse phases of the bubble increases and the life
time of the bubble decreases.
Abstract: Simultaneous transient conduction and radiation heat
transfer with heat generation is investigated. Analysis is carried out
for both steady and unsteady situations. two-dimensional gray
cylindrical enclosure with an absorbing, emitting, and isotropically
scattering medium is considered. Enclosure boundaries are assumed
at specified temperatures. The heat generation rate is considered
uniform and constant throughout the medium. The lattice Boltzmann
method (LBM) was used to solve the energy equation of a transient
conduction-radiation heat transfer problem. The control volume finite
element method (CVFEM) was used to compute the radiative
information. To study the compatibility of the LBM for the energy
equation and the CVFEM for the radiative transfer equation, transient
conduction and radiation heat transfer problems in 2-D cylindrical
geometries were considered. In order to establish the suitability of the
LBM, the energy equation of the present problem was also solved
using the the finite difference method (FDM) of the computational
fluid dynamics. The CVFEM used in the radiative heat transfer was
employed to compute the radiative information required for the
solution of the energy equation using the LBM or the FDM (of the
CFD). To study the compatibility and suitability of the LBM for the
solution of energy equation and the CVFEM for the radiative
information, results were analyzed for the effects of various
parameters such as the boundary emissivity. The results of the LBMCVFEM
combination were found to be in excellent agreement with
the FDM-CVFEM combination. The number of iterations and the
steady state temperature in both of the combinations were found
comparable. Results are found for situations with and without heat
generation. Heat generation is found to have significant bearing on
temperature distribution.
Abstract: The temperature distribution and the heat transfer
rates through a multi-layer door of a furnace were investigated. The
inside of the door was in contact with hot air and the other side of the
door was in contact with room air. Radiation heat transfer from the
walls of the furnace to the door and the door to the surrounding area
was included in the problem. This work is a two dimensional steady
state problem. The Churchill and Chu correlation was used to find
local convection heat transfer coefficients at the surfaces of the
furnace door. The thermophysical properties of air were the functions
of the temperatures. Polynomial curve fitting for the fluid properties
were carried out. Finite difference method was used to discretize for
conduction heat transfer within the furnace door. The Gauss-Seidel
Iteration was employed to compute the temperature distribution in
the door.
The temperature distribution in the horizontal mid plane of the
furnace door in a two dimensional problem agrees with the one
dimensional problem. The local convection heat transfer coefficients
at the inside and outside surfaces of the furnace door are exhibited.
Abstract: In this paper we use quintic non-polynomial
spline functions to develop numerical methods for approximation
to the solution of a system of fourth-order boundaryvalue
problems associated with obstacle, unilateral and contact
problems. The convergence analysis of the methods has been
discussed and shown that the given approximations are better
than collocation and finite difference methods. Numerical
examples are presented to illustrate the applications of these
methods, and to compare the computed results with other
known methods.
Abstract: Based on Rayleigh beam theory, the sub-impacts of a
free-free beam struck horizontally by a round-nosed rigid mass is
simulated by the finite difference method and the impact-separation
conditions. In order to obtain the sub-impact force, a uniaxial
compression elastic-plastic contact model is employed to analyze the
local deformation field on contact zone. It is found that the horizontal
impact is a complicated process including the elastic plastic
sub-impacts in sequence. There are two sub-zones of sub-impact. In
addition, it found that the elastic energy of the free-free beam is more
suitable for the Poisson collision hypothesis to explain compression
and recovery processes.
Abstract: This paper deals with a numerical analysis of the
transient response of composite beams with strain rate dependent
mechanical properties by use of a finite difference method. The
equations of motion based on Timoshenko beam theory are derived.
The geometric nonlinearity effects are taken into account with von
Kármán large deflection theory. The finite difference method in
conjunction with Newmark average acceleration method is applied to
solve the differential equations. A modified progressive damage
model which accounts for strain rate effects is developed based on
the material property degradation rules and modified Hashin-type
failure criteria and added to the finite difference model. The
components of the model are implemented into a computer code in
Mathematica 6. Glass/epoxy laminated composite beams with
constant and strain rate dependent mechanical properties under
dynamic load are analyzed. Effects of strain rate on dynamic
response of the beam for various stacking sequences, load and
boundary conditions are investigated.