Effect of natural convection on oscillating flow in a pipe with cryogenic temperature difference across the ends

The effect of natural convection on the oscillatory flow in an open-ended pipe driven by a timewise sinusoidally varying pressure at one end and subjected to an ambient-to-cryogenic temperature difference across the ends, is numerically studied. Conjugate effects arising out of the interaction of oscillatory flow with heat conduction in the pipe wall are taken into account by considering a finite thickness wall with an insulated exterior surface. Two cases, namely, one with natural convection acting downwards and the other, with natural convection acting upwards, are considered. The full set of compressible flow equations with axissymmetry are solved using a pressure correction algorithm. Parametric studies are conducted with frequencies in the range 5-15 Hz for an end-to-end temperature difference of 200 and 50 K. Results are obtained for the variation of velocity, temperature. Nusselt number and the phase relationship between mass flow rate and temperature. It is found that the Rayleigh number has a minimal effect on the time averaged Nusselt number and phase angle. However, it does influence the local variation of velocity and Nusselt number over one cycle. The natural convection and pressure amplitude have influence on the energy flow through the gas and solid. (C) 2011 Elsevier Ltd. All rights reserved.

Modeling of terahertz heating effects in realistic tissues

Theterahertz (THz) propagation in real tissues causes heating as with any other electromagnetic radiation propagation. A finite-element (FE) model that provides numerical solutions to the heat conduction equation coupled with realistic models of tissues is employed in this study to compute the temperature raise due to THz propagation. The results indicate that the temperature raise is dependent on the tissue type and is highly localized. The developed FE model was validated through obtaining solutions for the steady-state case and showing that they were in good agreement with the analytical solutions. These types of models can also enable computation of specific absorption rates, which are very critical in planning/setting up experiments involving biological tissues.

Analytical solutions for movement of cold water thermal front in a heterogeneous geothermal reservoir

In the present study an analytical model has been presented to describe the transient temperature distribution and advancement of the thermal front generated due to the reinjection of heat depleted water in a heterogeneous geothermal reservoir. One dimensional heat transport equation in porous media with advection and longitudinal heat conduction has been solved analytically using Laplace transform technique in a semi infinite medium. The heterogeneity of the porous medium is expressed by the spatial variation of the flow velocity and the longitudinal effective thermal conductivity of the medium. A simpler solution is also derived afterwards neglecting the longitudinal conduction depending on the situation where the contribution to the transient heat transport phenomenon in the porous media is negligible. Solution for a homogeneous aquifer with constant values of the rock and fluid parameters is also derived with an aim to compare the results with that of the heterogeneous one. The effect of some of the parameters involved, on the transient heat transport phenomenon is assessed by observing the variation of the results with different magnitudes of those parameters. Results prove the heterogeneity of the medium, the flow velocity and the longitudinal conductivity to have great influence and porosity to have negligible effect on the transient temperature distribution. (C) 2013 Elsevier Inc. All rights reserved.

Approximation of Spatio-Temporal Random Processes Using Tensor Decomposition

A new representation of spatio-temporal random processes is proposed in this work. In practical applications, such processes are used to model velocity fields, temperature distributions, response of vibrating systems, to name a few. Finding an efficient representation for any random process leads to encapsulation of information which makes it more convenient for a practical implementations, for instance, in a computational mechanics problem. For a single-parameter process such as spatial or temporal process, the eigenvalue decomposition of the covariance matrix leads to the well-known Karhunen-Loeve (KL) decomposition. However, for multiparameter processes such as a spatio-temporal process, the covariance function itself can be defined in multiple ways. Here the process is assumed to be measured at a finite set of spatial locations and a finite number of time instants. Then the spatial covariance matrix at different time instants are considered to define the covariance of the process. This set of square, symmetric, positive semi-definite matrices is then represented as a third-order tensor. A suitable decomposition of this tensor can identify the dominant components of the process, and these components are then used to define a closed-form representation of the process. The procedure is analogous to the KL decomposition for a single-parameter process, however, the decompositions and interpretations vary significantly. The tensor decompositions are successfully applied on (i) a heat conduction problem, (ii) a vibration problem, and (iii) a covariance function taken from the literature that was fitted to model a measured wind velocity data. It is observed that the proposed representation provides an efficient approximation to some processes. Furthermore, a comparison with KL decomposition showed that the proposed method is computationally cheaper than the KL, both in terms of computer memory and execution time.

A novel interferometric technique to estimate thermal diffusivity of `optically transparent solid' using `Isothermal surface velocimetry'

One-dimensional transient heat flow is interpreted as a procession of `macro-scale translatory motion of indexed isothermal surfaces'. A new analytical model is proposed by introducing velocity of isothermal surface in Fourier heat diffusion equation. The velocity dependent function is extracted by revisiting `the concept of thermal layer of heat conduction in solid' and `exact solution' to estimate thermal diffusivity. The experimental approach involves establishment of 1 D unsteady heat flow inside the sample through Step-temperature excitation. A novel self-reference interferometer is utilized to separate a `unique isothermal surface' in time-varying temperature field. The translatory motion of the said isothermal surface is recorded using digital camera to estimate its velocity. From the knowledge of thermo-optic coefficient, temperature of the said isothermal surface is predicted. The performance of proposed method is evaluated for Quartz sample and compared with literature.

Effect of ambient pressure and radiation reabsorption of atmosphere on the flame spreading over thermally thin combustibles in microgravity

For the flame spread over thermally thin combustibles in an atmosphere, if the atmosphere cannot emit and absorb the thermal radiation (e.g. for atmosphere Of O-2-N-2), the conductive heat transfer from the flame to the fuel surface dominates the flame spread at lower ambient atmosphere. As the ambient pressure increases, the flame spread rate increases, and the radiant heat transfer from the flame to the fuel surface gradually becomes the dominant driving force for the flame spread. In contrast, if the atmosphere is able to emit and absorb the thermal radiation (e.g. for atmosphere Of O-2-CO2), at lower pressure, the heat transfer from flame to the fuel surface is enhanced by the radiation reabsorption of the atmosphere at the leading edge of the flame, and both conduction and thermal radiation play important roles in the mechanism of flame spread. With the increase in ambient pressure, the oxygen diffuses more quickly from ambient atmosphere into the flame, the chemical reaction in the flame is enhanced, and the flame spread rate increases. When the ambient pressure is greater than a critical value, the thermal radiation from the flame to the solid surface is hampered by the radiation reabsorption of ambient atmosphere with the further increase in ambient pressure. As a result, with the increase in ambient pressure, the flame spread rate decreases and the heat conduction gradually dominates the flame spread over the fuel surface.

The temperature dependence of effective thermal conductivity of open-celled steel alloy foams

The effective thermal conductivity of steel alloy FeCrAlY (Fe-20 wt.% Cr-5 wt.% Al-2 wt.% Y-20 wt.%) foams with a range of pore sizes and porosities was measured between 300 and 800 K, under both vacuum and atmospheric conditions. The results show that the effective thermal conductivity increases rapidly as temperature is increased, particularly in the higher temperature range (500-800 K) where the transport of heat is dominated by thermal radiation. The effective conductivity at temperature 800 K can be three times higher than that at room temperature (300 K). Results obtained under vacuum conditions reveal that the effective conductivity increases with increasing pore size or decreasing porosity. The contribution of natural convection to heat conduction was found to be significant, with the effective thermal conductivity at ambient pressure twice the value of vacuum condition. The results also show that natural convection in metal foams is strongly dependent upon porosity. © 2003 Elsevier B.V. All rights reserved.

Thermal fatigue on pistons induced by shaped high power laser. Part II: Design of spatial intensity distribution via numerical simulation

In the laser induced thermal fatigue simulation test on pistons, the high power laser was transformed from the incident Gaussian beam into a concentric multi-circular pattern with specific intensity ratio. The spatial intensity distribution of the shaped beam, which determines the temperature field in the piston, must be designed before a diffractive optical element (DOE) can be manufactured. In this paper, a reverse method based on finite element model (FEM) was proposed to design the intensity distribution in order to simulate the thermal loadings on pistons. Temperature fields were obtained by solving a transient three-dimensional heat conduction equation with convective boundary conditions at the surfaces of the piston workpiece. The numerical model then was validated by approaching the computational results to the experimental data. During the process, some important parameters including laser absorptivity, convective heat transfer coefficient, thermal conductivity and Biot number were also validated. Then, optimization procedure was processed to find favorable spatial intensity distribution for the shaped beam, with the aid of the validated FEM. The analysis shows that the reverse method incorporated with numerical simulation can reduce design cycle and design expense efficiently. This method can serve as a kind of virtual experimental vehicle as well, which makes the thermal fatigue simulation test more controllable and predictable. (C) 2007 Elsevier Ltd. All rights reserved.

Fractal geometry model for effective thermal conductivity of three-phase porous media

An approximate model, a fractal geometry model, for the effective thermal conductivity of three-phase/unsaturated porous media is proposed based on the thermal-electrical analogy technique and on statistical self-similarity of porous media. The proposed thermal conductivity model is expressed as a function of porosity (related to stage n of Sierpinski carpet), ratio of areas, ratio of component thermal conductivities, and saturation. The recursive algorithm for the thermal conductivity by the proposed model is presented and found to be quite simple. The model predictions are compared with the existing measurements. Good agreement is found between the present model predictions and the existing experimental data. This verifies the validity of the proposed model. (C) 2004 American Institute of Physics.

A solution to the upward migration of an intrusion

The evolution of the upward migration of the magma is a nonlinear and unstable problem in mathematics. It is difficult to solve it. And using the numerical method, the solution is relatively tedious and time-consuming. This paper introduces a method of the instantaneous point source to solve the linear and unstable heat conduction equation during the infinite period of time instead of the solution of the nonlinear and unstable heat conduction equation. The results obtained by this method coincide with those by the numerical method, meaning that this method offers a simple way to solve the nonlinear and unstable heat conduction equation.

大洋中脊的形成过程

本文从热传导方程出发,得到了大洋中脊下岩石层温度分布的分析表达式及数值计算结果。结果表明,软流层上涌流动所提供的热源可以使大洋中脊下岩石层逐步融化;岩石层的相对移动速度对大洋中脊岩石层温度场及融化深度影响较大。 

Design of a Self-Adaptive Down-Hole Layered Steam Injector and Its Application

Layered steam injection, widely used in Liaohe Oilfield at Present, is an effective recovery technique to heavy oil reserves. Which makes the steam front-peak push forward uniformly, the amount of steam injection be assigned rationally, and the effect of injection steam be obtained as expected. To maintain a fixed ratio of layered steam injection and solve the problem of nonadjustable hole diameter with the change of layer pressure in the existing injectors, a new method is proposed in this paper to design layered steam injectors based on the dynamic balance theory. According to gas-liquid two-phase flow theory and beat transfer theory, the energy equation and the heat conduction equation in boreholes are developed. By analyzing the energy equilibrium of water-steam passing through the injector hole, we find an expression to describe the relation between the cross-sectional area of injector hole and the layer pressure. With this expression, we provide a new set of calculation methods and write the corresponding computer program to design and calculate the main parameters of a steam injector. The actual measurement data show that the theoretically calculated results are accurate, the software runs reliably, and they provide the design of self-adjustable layered steam injectors with the theoretical foundation.

Design of a Self-Adaptive Down-Hole Layered Steam Injector and Its Application

Layered steam injection, widely used in Liaohe Oilfield at present, is an effective recovery technique to heavy oil reserves. Which makes the steam front-peak push forward uniformly, the amount of steam injection be assigned rationally, and the effect of injection steam be obtained as expected. To maintain a fixed ratio of layered steam injection and solve the problem of nonadjustable hole diameter with the change of layer pressure in the existing injectors, a new method is proposed in this paper to design layered steam injectors based on the dynamic balance theory According to gas-liquid two-phase flow theory and heat transfer theory, the energy equation and the heat conduction equation in boreholes are developed. By analyzing the energy equilibrium of water-steam passing through the injector hole, we find an expression to describe the relation between the cross-sectional area of injector hole and the layer pressure. With this expression, we provide a new set of calculation methods and write the corresponding computer program to design and calculate the main parameters of a steam injector. The actual measurement data show that the theoretically calculated results are accurate, the software runs reliably, and they provide the design of self-adjustable layered steam injectors with the theoretical foundation.

A universal Biot number determining the susceptibility of ceramics to quenching

A universal Biot number of ceramics, which not only determines the susceptibility of the ceramics to quenching but also indicates the duration that the ceramics fail during thermal shock, is theoretically obtained. The present analysis shows that the thermal shock failure of the ceramics with a Biot number greater than this universal value is a very rapid process that just occurs in the initial regime of the heat conduction of the ceramics. This universal Biot number provides a guide to the selection of the ceramics applying to the thermostructural engineering including thermal shock.

On the transport properties of fluid-particle flow

The hydrodynamic forces acting on a solid particle in a viscous, incompressible fluid medium at low Reynolds number flow is investigated mathematically as a prerequisite to the understanding of transport processes in two-phase flow involving solid particles and fluid. Viscous interaction between a small number of spherical particles and continuous solid boundaries as well as fluid interface are analyzed under a “point-force” approximation. Non-spherical and elastic spherical particles in a simple shear flow area are then considered. Non-steady motion of a spherical particle is briefly touched upon to illustrate the transient effect of particle motion.

A macroscopic continuum description of particle-fluid flow is formulated in terms of spatial averages yielding a set of particle continuum and bulk fluid equations. Phenomenological formulas describing the transport processes in a fluid medium are extended to cases where the volume concentration of solid particles is sufficiently high to exert an important influence. Hydrodynamic forces acting on a spherical solid particle in such a system, e.g. drag, torque, rotational coupling force, and viscous collision force between streams of different sized particles moving relative to each other are obtained. Phenomenological constants, such as the shear viscosity coefficient, and the diffusion coefficient of the bulk fluid, are found as a function of the material properties of the constituents of the two-phase system and the volume concentration of solid. For transient heat conduction phenomena, it is found that the introduction of a complex conductivity for the bulk fluid permits a simple mathematical description of this otherwise complicated process. The rate of heat transfer between particle continuum and bulk fluid is also investigated by means of an Oseen-type approximation to the energy equation.