Outer Free Surface Research Articles

Thermodynamical interactions in a double porosity model with diffusion and microtemperatures

This manuscript investigates the disruptions occurring in a two-dimensional homogeneous, isotropic, thermoelastic medium with diffusion, double porosity and microtemperatures under Lord and Shulman (LS) theory of generalized thermoelasticity. A mechanical load is applied at the outer free surface of the solid half-space. To procure the exact expressions for various field variables, normal mode analysis is utilized. Numerical computations are performed for a particular material and the acquired results are visualized through graphical representations with the aid of MATLAB software. Comparisons are carried out to elucidate the influences of diffusion parameter, time, double porosity and intensity of load on the resulting quantities. 2010 MSC: 74A15, 80A20.

The effects on heat and oxygen transport of different heat shield and sidewall insulation designs during continuous Czochralski silicon crystal growth

Numerical work has been done to optimize the hot zone for the continuous Czochralski growth of 8-inch diameter silicon crystals using a double-crucible system. Thicker insulation layers on a high-heel-shaped heat shield and the sidewall insulation led to a reduction in the heater power of more than 40%, a decrease in the oxygen content, and a significant flattening of the growth interface. This design also allowed a stronger argon gas flow near the outer free melt surface and the quartz crucible wall, which prevented the generation of an argon gas vortex in this area. Stronger flow of argon gas would assist in moving more SiO gas and dust out of the chamber. However, the reduction in the outer melt temperature compared to the original design could slow down the melting of the silicon granules.

Influence of thermal load on a rotating thermoelastic medium with diffusion and double porosity

In the present work, we have studied the thermodynamical interactions in a two-dimensional thermoelastic medium with diffusion, rotation and double porosity in the context of Green–Lindsay theory. A thermal load is applied at the outer free surface of the medium. The normal mode technique is employed to derive the analytic expressions of the field quantities such as stresses, displacement components, temperature field and mass concentration. Numerical computations are performed with the help of MATLAB software for a specific material for illustrating the results. To the author’s best knowledge, no attempt has been made to investigate the therodynamical interactions in a rotating double porous thermoelastic medium with diffusion under the influence of a thermal load. Comparisons of the physical quantities are shown in figures to study the effects of time, double porosity, rotation, thermal load and diffusion. Some particular cases of interest have also been inferred from the present problem. The theoretical and numerical computations are found to be in close agreement.

Photothermal interactions in a semiconducting fiber‐reinforced elastic medium with temperature‐dependent properties under dual‐phase‐lag model

AbstractThis article highlights the study of photothermoelastic interactions in a semiconducting fiber‐reinforced anisotropic medium with temperature‐dependent properties. The model is studied in the context of the photothermal transport process with dual‐phase‐lag theory of generalized thermoelasticity. The governing equations describe the interactions between elastic and plasma thermal waves. The normal mode analysis is employed to procure the exact expressions of the physical fields under investigation. A mechanical load is applied at the outer free surface of the medium to obtain the complete solution of the displacements, stresses, temperature, and carrier density distributions. Numerical results are obtained and displayed graphically with the help of MATLAB software. Some special cases of interest have been deduced from the present study and comparisons are also made among the different theories of thermoelasticity.

Use of Profilometry‐Based Indentation Plastometry to Study the Effects of Pipe Wall Flattening on Tensile Stress–Strain Curves of Steels

Herein, the flattening and subsequent tensile testing (in the hoop direction) of steel pipes used for transmission of oil and gas are concerned. A particular focus is on the use of a novel indentation plastometry test (PIP), applied to the outer free surface of an as‐received pipe. This allows a stress–strain curve to be obtained from a relatively small volume (a disk of diameter about 1 mm and thickness around 100–200 μm). Whole section and reduced section tensile testing, of as‐received and flattened samples are carried out. Four different pipes are studied. While there are some variations between them, there is a general trend for near‐surface regions of the pipe to be a little harder than the interior, and for flattened pipes to be a little harder than unflattened ones, although these are not dramatic or well‐defined effects. PIP testing also confirms that these pipes exhibit little or no anisotropy. It is in general concluded that PIP‐derived stress–strain curves for testing of the outside of a pipe are likely to be quite close to those obtained by tensile testing of the whole section in the hoop direction, after flattening.

Mathematical modeling of the dynamics of a hydroelastic system—A hollow cylinder with inhomogeneous initial stresses and compressible fluid

This work attempts to present mathematical modeling of the dynamics of the hydroelastic system consisting of a hollow cylinder with inhomogeneous initial stresses and a compressible barotropic inviscid fluid which filled the interior of the cylinder. The motion of the cylinder is described with the 3D linearized theory of elastic waves in bodies with initial stresses; however, the flow of the fluid is described with the linearized Euler equations for compressible inviscid fluid. Formulations of the boundary conditions on the outer surface of the cylinder and compatibility conditions between the cylinder and fluid on the interior surface of the cylinder are presented. Concrete formulations are made for the axisymmetric case, and general aspects of the solution methods of the formulated problems are considered. Under these considerations, two types of problem are selected: (1) the axisymmetric longitudinal wave propagation and (2) fluid flow profile on the outer free surface of the cylinder—the “circular” radial moving load. Numerical results are presented and discussed for the first type of problem. In particular, it is established that the character of the influence of the inhomogeneous initial stresses on the wave propagation velocity in the hydroelastic system under consideration depends on the dimensionless wavenumber. The perspective of future investigations is also presented and discussed.

Temperature dependent thermal conductivity during photothermal excitation process of semiconductor medium with an internal heat source in gravitational field

In this work, a novel model of semiconducting elastic material is studied during a process of photothermal excitation. The dual phase lag (DPL) for the heat conduction equation is introduced in the context of the variable of the thermal conductivity. The thermal conductivity can be chosen as a linear function of temperature (depend on temperature). The generalized thermoelasticy theory is investigated when an internal heat source is steady with a constant speed in the context of the gravitational field. The harmonic wave technique is used in two-dimensional deformations to obtain the considered physical fields. Some thermal loading subjected to thermal shock and other mechanical forces at the outer free surface of a semi-infinite elastic medium (semiconductor as silicon) are applied. The considered physical fields were illustrated graphically. The influences of some several variables are obtained which based on the DPL (thermal memories) model and the variable thermal conductivity. The results obtained are investigated and are depicted graphically.

Torsional wave dispersion in a bi-layered hollow cylinder with inhomogeneous initial stresses caused by internal and external radial pressures

The present paper studies the influence of the inhomogeneous initial stresses in the bi-layered hollow cylinder and it is assumed that these stresses are caused by the hydrostatic pressures acting on the interior and outer free surfaces of the cylinder. The study is made by utilizing the version of the three-dimensional linearized theory of elastic waves in bodies with initial stresses for which the initial stress-strain state in bodies is determined within the scope of the classical linear theory of elasticity. For the solution to the corresponding eigenvalue problem, the discrete-analytical method is employed. Numerical results are presented and analyzed for concrete selected pairs of materials. According to these results and their analyses, it is established that, unlike homogeneous initial stresses, the influence of the inhomogeneous initial stresses on the torsional wave dispersion has not only quantitative but also qualitative character. For instance, in particular, it is established that as a result of the initial stresses caused by the hydrostatic pressure acting in the interior free surface of the cylinder, the cut-off frequency appears for the fundamental dispersive mode and the values of this frequency increase with the intensity of this pressure.

Generalized photo-thermo-microstretch elastic solid semiconductor medium due to the excitation process

A novel model in the photo-thermoelasticity theory with microstretch properties is studied. The plasma-elastic-thermal plane waves are propagated in a linear isotropic generalized photo-thermo-microstretch elastic semiconductor solid medium. The photothermal excitation occurs in the context of the microinertia of the microelement process during two-dimensional (2D) deformation. The harmonic wave techniques are used to get the solutions for the basic variables. The analytical solution of the main physical fields; carrier intensity, normal displacement components, temperature, stress load force, microstress and tangential coupled stress can be obtained. Some graphics illustrated when using the plasma, thermal and mechanical load boundary conditions are applied at the outer free surface of the elastic medium. Some semiconductor materials, as silicon (Si) and Germanium (Ge), are used to make the numerical simulation and some comparisons in different thermal memories are made. The main physical variables with new parameters are discussed theoretically and shown graphically.

Response of Mechanical Ramp Type of Semiconductor Magneto-Rotator Medium with Variable Thermal Conductivity during Photo-Excitation Microelement Processes

The effect of external magnetic field during microelement processes is used to discuss the excited semiconductor medium in generalized thermoelasticity theory. The thermal conductivity which depends on the temperature is investigated in the context of the photothermal theory to obtain the main variables for a rotator elastic semiconductor medium. In this case the thermal conductivity is variable. The elastic-plasma-thermal waves in two-dimension (2D) deformation have been constructed. Fourier and Laplace integral transformations are used to solve the main governing equations under the effect of microtemperature vector field. Analytical solutions of the main physical field quantities are obtained under these transformations to get the solutions in the physical domain. The mechanical ramp type condition and some other thermal-elastic-plasma conditions are applied on the outer free surface of the medium. To obtain complete solutions for the basic physical quantities, numerical inversion methods of Fourier and Laplace transformations are used in space-time physical domain. Some comparisons are made for some several parameters that they represent graphically and discussed.

Electromagnetic Hall current effect and fractional heat order for microtemperature photo-excited semiconductor medium with laser pulses

In this paper, the elastic semiconductor medium is exposed to outer laser pulses. The laser pulses cause vibrations in the inner structure of the medium with the time fractional heat order. Under the influence of strong external magnetic field, the effect of Hall current is appeared in this case the interaction between the strong magnetic field and microstructure (microelements) of the elastic medium is studied. The microtemperature states is generated due to photo-excited electrons in context of photothermal transport process. The one-dimensional (1D) deformation is used to describe the overlapping process between elastic-magneto-plasma-thermal distribution waves in case of semiconductor elastic rod. The governing equations are solved in Laplace integral transform domain in microelements field. Some external loads are applied at the outer free surface of the medium to obtain the physical quantities under investigation. To obtain the complete solutions of the physical quantities the numerical inversion technique of Laplace transform is used. The Hall current, fractional parameters and micro-temperature effect are presented graphically and discussed theoretically under the effect of laser pulses.

The Movement of a Rectangular Cylinder in a Liquid at Short Times after Impact with Formation of a Cavity

Under consideration is some dynamical mixed problem concerning some separated impact and subsequent motion with constant velocity of a rectangular cylinder in an ideal incompressible heavy liquid. The specificity of this problem is that an attached cavity forms after impact and a new internal free boundary of the liquid appears. The shape of the cavity and the configuration of the outer free surface are unknown in advance and are to be determined during solution of the problem. Studying the problem is carried out at short times with consideration of the dynamics of the points of separation of the internal free boundary of the liquid. Location of the separation points at every time is defined from the Kutta–Zhukovsky condition. The influence is studied of the physical and geometric parameters of the problem on the shape of free boundaries of the liquid at short times. The asymptotic analysis is carried out of the internal free boundary of liquid near the separation points.

Electromagnetic and Thomson effects during photothermal transport process of a rotator semiconductor medium under hydrostatic initial stress

The effect of rotation and hydrostatic initial stresses during electromagnetic field which is fallen on the outer surface of semiconductor medium is studied. The Thomson influence in context of photo thermal excitation process is investigated. The thermoelectricity theory is applied explain the waves behavior in the elastic semiconductor homogenous, isotropic medium. The governing equations describe the overlapping between plasma, electro-magnetic and elastic waves in two dimensional deformations when the medium is in rotation. The induced electric current is studied only when the charge density is a function of time. The normal mode analysis is a mathematical method which is used to get the physical fields distributions under investigation. The mechanical forces, electromagnetic effects thermal loads and plasma diffusion recombination process are taken at the outer free surface of the medium to obtain the complete solutions. All distributions of waves of physical quantities are represented graphically and discussed under the influence of rotation, initial stresses and Thomson parameter.

Internal Photoemission Metrology of Inhomogeneous Interface Barriers

Interfaces of heterogeneous solids, ranging from polycrystalline materials to composites, are frequently encountered in nanotechnology. Electron transport in these materials and across their interfaces critically depends on the energy barriers electrons encounter on their way. Because of electrode structural heterogeneity, the barriers may exhibit significant spatial variations resulting in a broad distribution of barrier heights and built‐in potentials. Quantification of the distributed interface barriers represents a formidable experimental challenge since direct association of interface properties with those of an outer free surface is generally inaccurate. Here we present a methodology enabling quantification of electron barriers at interfaces of semiconductors and metals with insulators using the electric field‐dependent internal photo‐emission (IPE) of electrons. It is shown that practically relevant interfaces may contain “patches” with differences in barrier height (or the effective work function) of up to 1 eV, which makes the electrode heterogeneity a crucial factor in designing electron devices suitable for low‐voltage operation.

The axisymmetric oscillations of a cylindrical bubble in a liquid bounded volume with free deformable interface

The eigen axisymmetric oscillations of a cylindrical gas bubble surrounded by an incompressible fluid with free deformable interface are considered. The bubble has an equilibrium cylindrical shape and is bounded axially by two parallel solid surfaces. Dynamics of contact lines is taken into account by an effective boundary condition: velocity of the contact line is assumed to be proportional to contact angle deviation from the equilibrium value. The equilibrium contact angle is right. Eigen frequency decreases with liquid outer free surface radius decreasing and increases with the radius-to-height ratio increasing. It’s found that the eigen frequency can vanish in some wetting parameter interval for the volume mode of natural oscillations (which describes the radial compression of the bubble). The length of this interval increases with increasing ratio of the equilibrium bubble radius to the height. The eigen frequencies of other modes decrease with increasing Hocking’s constant. The lowest natural frequency is observed for the freely sliding bubble.

Crack tip flipping under mode I tearing: Investigated by X-ray tomography

The fracture surface morphology that results from mode I tearing of ductile plate metals depends heavily on both the elastic-plastic material properties and the microstructure. Severe tunneling of the advancing crack tip (resulting in cup-cup, or bath-tub like fracture surfaces) can take place in a range of materials, often of low strength, while tearing of high strength metals typically progress by the shear band failure mechanism (slanting). In reality, however, most fracture surfaces display a mixture of morphologies. For example, slant crack propagation can be accompanied by large shear lips near the outer free plate surface or a complete shear band switch - seemingly distributed randomly on the fracture surface. The occasionally observed shear band switch of mode I slant cracks, related to ductile plate tearing, is far from random as the crack can flip systematically from one side to the other in roughly 45° shear bands. This "flipping" action of a slanted crack remains to be fully understood, and the present study serves to share details on the phenomenon by exploiting X-ray tomography scanning to access the plate interior and the very crack tip. Throughout, the focus is on a crack tip where the flip is underway. Extensive growth of single edge cracks under mode I loading is achieved in a purpose build test set-up. Here, considering a 4mm plate of normal strength / high strain hardening steel which has been found to display successive flipping of the slant crack face. While undergoing a shear band switch, such that the flipping mechanism is active, the plate tearing test is interrupted and the crack tip extracted for further investigation. The conducted X-ray tomography scans reveal the failure process ahead of the advancing crack tip to resemble the ductile slant crack growth governed by local thinning and moderate crack tip tunneling. However, small shear lips form at the outer free plate surface, well behind the 45° slant (tunneling) crack tip, as the flipping action engages. Upon further loading, the shear lips subsequently grow to form a set of secondary crack fronts at an angle to the primary tunneling slant crack. Eventually, these secondary crack fronts catch up on the primary slant crack front and overtake the growth to complete the shear band switch. Once the crack slants, an out-of-plane action occurs due to the loss of symmetry in the system. It is this out-of-plane action which is believed to set-off the flipping mechanism.

Two-dimensional refractive index and birefringence profiles of a graded index bent optical fibre

Abstract A theory to recover refractive index profile of the bent graded index (GRIN) optical fibre, in core region, is proposed. This theory is applied to the bent GRIN optical fibre when it is located orthogonal in the light path of the object arm in digital holographic phase shifting interferometer; like Mach–Zehnder interferometer. In the experiment, the fibre is bent with two different bending radii and fixed on a microscope slide keeping it immersed in matching liquid. The produced phase shifted holograms, with the presence of the fibre, are recorded using an attached CCD camera. Two different processes controlling the index profile shape of the bent GRIN optical fibre are assumed. In the first process, a linear index variation is evolved from stresses in the direction of the bent radius. In the second one, there is a release of these stresses near the fibre surface, which depends on the fibre’s radius. This will affect the outer free surface of the cladding. Based on these assumptions, we are able to construct the index profile in two dimensions normal to the optical axis. We propose two functions to describe the refractive index profiles in cladding and the core regions of the bent GRIN optical fibre. The recorded phase shifted holograms are combined, reconstructed and analyzed to get the phase map of the bent GRIN optical fibre. Comparing the extracted optical phase differences with the calculated ones, a good agreement between them is found. This means that the used two dimensional proposed functions, which are describing cladding and the core indices profiles, are the most proper in this situation. Thus, we are able to determine a realistic induced birefringence profile inside the fibre which is generated by a bending operation, not only in the cladding but also in graded index core region as well.

Characteristic Features of Boiling and Vaporization of Heterogeneous Liquid Drops in High-Temperature Gaseous Medium

The effect of radiative heat flux on the conditions of heating and phase transformation of heterogeneous water drops in a stream of high-temperature gases corresponding to a group of modern chemical and energy technologies, especially thermal purification of water, is determined with reference to opaque graphite inclusion–water system. It is demonstrated that heterogeneous water drops can not only vaporize from the outer (free) surface, but also boil at the inner interfaces and even burst. The time of occurrence (complete vaporization) of a heterogeneous drop at identical temperatures in combustion products and in air is compared.

The translational oscillations of a cylindrical bubble in a bounded volume of a liquid with free deformable interface

We consider the eigen and forced translation oscillations of a cylindrical gas bubble surrounded by an incompressible fluid with free deformable interface. The bubble has an equilibrium cylindrical shape and is bounded axially by two parallel solid surfaces. Dynamics of contact lines is taken into account by an effective boundary condition: velocity of the contact line is assumed to be proportional to contact angle deviation from the equilibrium value. The equilibrium contact angle is right. Eigen frequency decreases with liquid outer free surface radius decreasing and increases with the radius-to-height ratio increasing. We found that the main translational frequency of eigen oscillation vanishes at a certain value of the Hocking parameter (the so-called wetting parameter). The eigen frequencies of the bubble are higher than the eigen frequencies of fluid volume.

Heat and mass transfer enhancement in a cross-flow elliptical hollow fiber membrane contactor used for liquid desiccant air dehumidification

To improve the performances of a hollow fiber membrane contactor (HFMC) employed for liquid desiccant air dehumidification, an elliptical hollow fiber membrane contactor (EHFMC) is proposed. The contactor is assembled by a collection of elliptical hollow fibers populated in a shell. The liquid desiccant and the processing air streams flow inside and across the elliptical fibers, respectively. They are in a cross-flow configuration. The momentum and the conjugate heat and mass transports in the EHFMC are investigated based on Happel's free surface model. In this approach, a single elliptical fiber, an air stream across the fiber, and a liquid desiccant stream inside the fiber are selected as the calculating element. The air stream in the element is encompassed by a hypothetical outer free surface with an elliptical shape. The equations governing the momentum, heat and mass transports in the air and the solution streams are established and solved together with the conjugate heat and mass transfer boundary conditions. The fundamental data of the friction factor, Nusselt and Sherwood numbers in the element are then numerically calculated, experimentally validated, and analyzed. These basic data are compared with those obtained in the HFMC.