Non-uniform Temperature Gradient Research Articles

Investigation of Evaporation and Diffusion Phenomena in Porous Media

Many industrial and biological phenomena involve the evaporation of liquids in porous media. In drying processes the evaporation of a liquid meniscus from the solid is the key mechanism in the process and its efficiency. After a first steady stage of evaporation the meniscus becomes unsteady and recedes inside the pore. Diffusion of vapour becomes the controlling mechanism for evaporation in a later stage. In this work an experimental investigation is undertaken to study the various stages of evaporation of different liquids in capillary tubes (pores) of various sizes. The analysis of the data obtained from this investigation reveals some interesting behaviours and emphasizes the role played by vapour diffusion in the case of unsteady interface. The preliminary transient regime allowing the thermal field establishment, is followed by the first stage of evaporation is found to be dominated by thermocapillary effects associated with non-uniform evaporation and temperature gradients. The laste stage is a molecular diffusion-limited mode. The liquid volatility and the effect of the size of the tube (ranging from 200 to 900 μm) are also analysed to show the interaction between the various effects at different scales.

Experimental and Numerical Studies on Flow Uniformity in Interconnects and its Influence on a Single Planar Solid Oxide Fuel Cell

This paper studies experimentally and numerically flow uniformity in various interconnects and its influence to temperature distributions and cell performance of a planar solid oxide fuel cell (SOFC). A transparent hydraulic platform is first established to evaluate the degree of flow uniformity in many different modules of interconnects using the same rib- channels for both the cathode and the anode or using Ni-mesh without rib-channels only for the anode side. This novel setup allows direct imaging and measurements of flow uniformity in both rib-channels and Ni-mesh, so that these experimental data can be used to validate numerical flow data. A three- dimensional numerical model using CFD-RC package with sub- models is then used to simulate various transport phenomena and electrochemical reactions of a single cell with the consideration of different degrees of flow uniformity in interconnects. It is found that previous modules using either single-inlet/single-outlet or double-inlets/single-outlet designs cannot provide uniform velocity distributions in these rib-channels, which can result in serious non-uniform temperature gradients in the cell. We propose a new design, using small guide vanes equally-spaced around the feeder of the double-inlet module on the cathode side and using Ni-mesh on the anode side, which features a highest degree of flow uniformity and least non-uniform temperature gradients in the cell among all different modules studied.

Suppressing stimulated Brillouin scattering in fiber amplifiers using nonuniform fiber and temperature gradient

A nonuniform large mode area fiber having an larger core at most locations to reduce power intensity and having a relatively smaller core at certain locations to reduce bending sensitivity is proposed for suppression of stimulated Brillouin scattering (SBS) in a high power fiber amplifier. A comprehensive model taking into account fiber nonuniformity, profile and temperature gradient shows that the fiber can achieve kilowatt output at a temperature gradient of >250 degrees C. Compared with a conventional large mode area fiber, a total of 7 dB SBS suppression can be achieved using this unique fiber.

Effect of a non-uniform basic temperature gradient on the onset of Bénard-Marangoni convection: Stationary and oscillatory analyses

The qualitative effect of a non-uniform basic temperature gradient on the stationary and oscillatory stability analyses of the onset of Bénard-Marangoni convective in a horizontal fluid layer is investigated numerically using the fourth order Runger-Kutta-Gill's method coupled with the iterative Broyden's method. The effects of crispation at a deformable upper free surface and the conductive effect of non-steady conditions within the fluid layer on onset are discussed. Results show that the effect of crispation (i.e., Crispation number C) is a clearly destabilizing factor, but the conductive effect (i.e., a i * of non-steady conditions within the fluid layer does play a stabilizing state. The system becomes more stable at larger values of the Prandtl number Pr, the Biot number B i and the Bond number B o . We obtain a set of characteristic curves in the ( M C, R)-plane that satisfy the linear relation on the onset of the stationary and oscillatory Bénard-Marangoni convective instability.

Genetic Algorithm Based Resistive Susceptor Design for Uniform Heating During the Induction Bonding Process

In this research work, cut mesh design optimization for the induction bonding process using genetic algorithms (GAs) is investigated to solve the problem of nonuniform heating, which leads to nonuniform temperature fields and temperature gradients exceeding the process window required for bonding. Cut patterns in the metal mesh can redirect the magnetically induced electric currents generated thus changing the temperature distribution. In this work, the heat generation model for determining current and heat generation distribution for a given coil and mesh size, coded as a Mathematica function, was coupled with a simple genetic algorithm. The cost function to be minimized by the GA was the ratio of the maximum heat generation in the mesh to the minimum heat generation. Two studies were performed with the GA-based design optimization: the first with a six sided square mesh and the second using a ten sided square mesh. The best cut mesh designs obtained from the GA were compared with the globally optimal designs, where available, and with the baseline mesh. The GA could not reach the global optima due to the complex nature of the design search space. However, it was determined that the GA was able to reduce the variations in heat generation in the mesh for all cases and delivered significant improvements over the baseline case in reasonable computational time, evaluating less than 2% of the possible cut mesh patterns. Thus the genetic algorithm based design optimization was proven to be a computationally efficient tool in the generation of good cut mesh designs for the induction bonding process.

Effect of a non-uniform temperature gradient on the onset of oscillatory Bénard–Marangoni convection of an electrically conducting liquid in a magnetic field

This study deals theoretically with the effect of a non-uniform basic temperature gradient on the linear stability of the oscillatory Bénard–Marangoni convection in a horizontal layer of a viscous quiescent, electrically conducting fluid in the presence of a uniform vertical magnetic field. The upper surface of a fluid layer is deformably free and the lower surface is rigid. The eigenvalue equations of the perturbed state obtained from the normal mode analysis are solved by using the fourth order Runge–Kutta–Gill’s method with the shooting technique. The results show that the critical Rayleigh number Ra c and the critical Marangoni number − Ma c become larger as the Chandrasekhar number Q or the Biot number Bi of the upper free surface increases, and the Crispation number Cr decreases. When compared with the linear temperature profile, the inverted parabolic temperature profile indicates a reinforcement of stability, while the parabolic temperature profile indicates a diminution of stability in both Rayleigh–Bénard and Bénard–Marangoni convections. In addition, for the piecewise linear temperature profiles, the influences of thermal depth on the critical conditions are also obtained. Comparisons are also made of the critical conditions [− Ma c, a c, q ic] between the present results and published data sets for the linear basic temperature profile case, and the agreement is found out to be generally good.

Effects of nonuniform temperature gradients on the onset of oscillatory Marangoni convection in a magnetic field

This article theoretically studies the onset of oscillatory Marangoni convection in a horizontal layer of an electrically conducting fluid, to which a nonuniform thermal gradient and a uniform magnetic field are applied. The top surface of a fluid layer is deformably free and the bottom is rigid. By means of the linear stability theory and a normal mode analysis, the eigenvalue equations of the perturbed state are solved by using the fourth-order Runge-Kutta-Gill's method with the shooting technique. The computational results are compared with those known from the literature, and the agreement is found out to be generally good. The results indicate that the critical Marangoni number −Ma c increases with increasing the Chandrasekhar number Q, the Prandtl number Pr, or the Biot number Bi of the upper free surface, but decreases with increasing the Crispation number Cr. As compared with the linear temperature profile, the inverted parabolic temperature profile shows higher −Ma c values, while the parabolic temperature profile shows lower −Ma c values. In addition, for the piecewise linear temperature profiles, the influences of thermal depth on the critical Marangoni number are also obtained.

Effects of Magnetic Field and Non-Uniform Basic Temperature Gradient

The effects of a non-uniform temperature gradient and magnetic field on the onset of convection in a horizontal layer of Boussinesq fluid with suspended particles confined between an upper free/adiabatic boundary and a lower rigid/isothermal boundary have been considered. A linear stability analysis is performed. The microrotation is assumed to vanish at the boundaries. The Galerkin technique is used to obtain the Eigen values. The influence of various parameters on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the electrically conducting fluid layer with suspended particles heated from below is more stable compared to the classical electrically conducting fluid without Suspended particles. The critical wave number is found to be insensitive to the changes in the parameters but sensitive to the changes in the Chandrasekhar number.

Effect of non-uniform basic temperature gradient on Rayleigh–Benard–Marangoni convection in ferrofluids

The effect of different basic temperature gradients on the onset of ferroconvection driven by combined surface tension and buoyancy forces is studied. The lower boundary is assumed to be rigid and either conducting or insulating to temperature perturbations while the upper boundary at which the surface tension acts is free insulating and non-deformable. The resulting eigenvalue problem is solved by the Galerkin technique for various basic temperature gradients. The results indicate that the stability of Rayleigh–Benard–Marangoni ferroconvection is significantly affected by basic temperature gradients and the mechanism for suppressing or augmenting the same is discussed in detail. It is shown that the results obtained under the limiting conditions compare well with the existing ones.

Effects of Throughflow and Internal Heat Generation on Convective Instabilities in an Anisotropic Porous Layer

CConvective instabilities caused by a nonuniform temperature gradient due to vertical throughflow and internal heat generation were investigated in an anisotropic porous layer. The boundaries are taken to be either impermeable or porous and are perfect conductors of heat. The Forchheimer-extended Darcy model is used to describe the flow in the porous medium. The resulting eigenvalue problem is solved numerically by the Galerkin method with a modified external Rayleigh number as the eigenvalue. Both anisotropic parameters (i.e., effective thermal diffusivity, η, and permeability, ξ) appear through their ratio η/ξ only. We found that an increase in η/ξ increases the stability of the system. Furthermore, we observed that in the absence of internal heat generation, throughflow stabilizes when the boundaries are symmetric and destabilizes when they are asymmetric. However, if an internal heat source exists, throughflow destabilizes the system irrespective of the boundary types considered. A more precise control of the buoyancy-driven instability may be achieved by tuning the anisotropy parameters and internal heat source strength. Copyright © 2002 by Begell House, Inc.

A constraint on the shear stress at the Pacific‐Australian plate boundary from heat flow and seismicity at the Kermadec forearc

New heat flow measurements and relocated hypocenters that constrain the subduction geometry of the Pacific plate at the Kermadec trench yield an estimate of shear stress on the thrust fault. With the exception of a few relatively high values (>60 mW m−2) on the upper forearc region near the active volcanic ridge, most of the 64 heat flow values along two profiles across the forearc range from 20 to 40 mW m−2. Corrections for bottom water temperature variations that caused nonuniform temperature gradients were required for most measurements. The means of the most reliable values for the northern and southern profiles are 28.9±5.8 mW m−2 (n = 33) and 28.9±7.2 mW m−2 (n = 19), respectively, and the measurements show no apparent systematic variation along the profiles over the range ∼50 to 150 km distance from the trench. The means of the 10 values at each of two sites on the Pacific plate seaward of the profiles are 57.2±6.3 and 60.2±6.6 mW m−2. Redeterminations of focal depths and fault plane solutions of earthquakes in the vicinity of the heat flow profiles indicate thrust faulting on a plane dipping 17°±2°. Calculated values of heat flow for a two‐dimensional analytical approximation to conduction through the upper plate, diffusion into the downgoing slab, and advection by that slab are consistent with either a uniform stress of ∼40±17 MPa along the thrust fault or stress increasing linearly at ∼0.5±0.2 MPa km−1 with distance from the trench axis. The comparable scatter in the heat flow measurements about those calculated from these simple stress distributions does not show one to be a better approximation than the other.

Rayleigh‐Benard convection in a viscoelastic fluid‐filled high‐porosity medium with nonuniform basic temperature gradient

The qualitative effect of nonuniform temperature gradient on the linear stability analysis of the Rayleigh‐Benard convection problem in a Boussinesquian, viscoelastic fluid‐filled, high‐porosity medium is studied numerically using the single‐term Galerkin technique. The eigenvalue is obtained for free‐free, free‐rigid, and rigid‐rigid boundary combinations with isothermal temperature conditions. Thermodynamics and also the present stability analysis dictates the strain retardation time to be less than the stress relaxation time for convection to set in as oscillatory motions in a high‐porosity medium. Furthermore, the analysis predicts the critical eigenvalue for the viscoelastic problem to be less than that of the corresponding Newtonian fluid problem.

Convection in a Horizontal Layer in a Rotating Heat Field

An asymptotic laminar-convection pattern in a plane horizontal liquid layer with a radially nonuniform temperature gradient on its boundaries is investigated. The problem arises in applications connected with modified Czochralski crystal growth technology using the heat field rotation method. An analytical model of the flow is compared with the results of experiments, specially carried out using model fluids and a technological melt. The conditions of adequacy of the model are analyzed and the restrictions on the parameter values and fluid thermophysical properties that ensure the validity of the model are found. The range of variation of the heat field rotation velocity for which the mixing of the melt in the crucible is maximum is determined.

Effect of non-uniform basic temperature gradient on the onset of Marangoni convection in a fluid with suspended particles

The effect of a non-uniform basic temperature gradient on the onset of convection driven by surface tension in a horizontal layer of a Boussinesq fluid with suspended particles confined between an upper free, constant heat flux boundary and a lower rigid isothermal boundary is considered. The microrotation is assumed to vanish at the boundaries. A linear stability analysis is performed. The Rayleigh–Ritz technique is used to obtain the eigenvalues. The influence of various parameters on the onset of convection has been analyzed. Six different non-uniform basic state temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the fluid layer with suspended particles heated from below is more stable compared to the classical fluid layer without suspended particles. The problem has possible applications in microgravity situations.

Analysis of angular distortion in weldments using laminated plate theory

The problems of distortion and residual stresses in and around a welded joint are of major concern in heavy industry. In the present work, a formula for weld induced angular distortion, in terms of weld parameters such as heat input and plate thickness, is developed analytically using an infinite laminated plate theory to consider an elliptical cylindrical inclusion with an eigenstrain. The source of angular distortion in weldments is the plastic strains that are caused by non-uniform temperature gradient. The distributions of the plastic strain corresponding to the eigenstrain are determined using Rosenthal's solution, which describes temperature distributions. Comparison of the calculated results with the experimental data shows the accuracy and validity of the proposed method.

The effect of a nonuniform basic temperature gradient on the convective instability of a fluid-saturated porous layer with general velocity and thermal conditions

The effects of a nonuniform basic temperature gradient and bounding permeable walls on Rayleigh-Benard convection in a sparsely packed porous medium are investigated using the single term Galerkin method. The nature of the boundaries dictates general boundary conditions on velocity and temperature. The classical results of free-free, rigid-free and rigid-rigid boundaries with isothermal or adiabatic boundaries are recovered as limiting cases of the present study. The multi-layer porous media problem has practical implications in situations where fluids are used as a working medium and porous media are used as dampers.

Boundary and inertia effects on convection in porous media with throughflow

The effects of a nonuniform temperature gradient and inertia arising due to throughflow on the onset of convection in a porous layer for different types of boundaries are investigated. Closed form solutions are obtained for the boundaries which are insulating to temperature perturbations, and for the conducting boundaries solutions are obtained using Galerkin technique. It is found that when the two boundaries are of the same type, the effect of throughflow is to stabilize the system irrespective of its direction. However, when the lower and upper boundaries are of different types, a small amount of throughflow in one particular direction destabilizes the system depending upon the values of the Prandtl number and the porous parameter. The standard results available are obtained as limiting cases.

Multilateration with the wide-angle airborne laser ranging system: positioning precision and atmospheric effects

Numerical simulations based on previously validated models for the wide-angle airborne laser ranging system are used here for assessing the precision in coordinate estimates of ground-based cube-corner retroreflectors (CCR's). It is shown that the precision can be optimized to first order as a function of instrument performance, number of laser shots (LS's), and network size. Laser beam divergence, aircraft altitude, and CCR density are only second-order parameters, provided that the number of echoes per LS is greater than 20. Thus precision in the vertical is approximately 1 mm, with a signal-to-noise ratio of 50 at nadir, a 10-km altitude, a 20 degrees beam divergence, and approximately 5 x 10(3) measurements. Scintillation and fair-weather cumulus clouds usually have negligible influence on the estimates. Laser biases and path delay are compensated for by adjustment of aircraft offsets. The predominant atmospheric effect is with mesoscale nonuniform horizontal temperature gradients, which might lead to biases near 0.5 mm.

Effect of a non-uniform basic temperature gradient on Rayleigh–Benard convection in a micropolar fluid

The qualitative effect of a non-uniform basic temperature gradient on the linear stability analysis of the Rayleigh–Benard convection in an Eringen's micropolar fluid is studied numerically using a single-term Galerkin technique. The eigenvalue is obtained for free–free, rigid–free, and rigid–rigid velocity boundary combinations with isothermal and adiabatic temperature conditions on the spin-vanishing boundaries. The eigenvalues are also obtained for lower rigid isothermal and upper free adiabatic boundaries with vanishing spin. The influence of various micropolar fluid parameters on the onset of stationary convection has been analysed. Six different basic temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the Rayleigh number obtained is lower than that of the corresponding Newtonian fluid problem. Some important mechanisms of advancing or delaying convection are discussed.

A model for microwave processing of compositionally changing ceramic systems

A finite-difference model was used to simulate the temperature and composition distributions produced inside a specimen heated with microwave energy during a process involving a change in composition. The dielectric properties of the specimen change with composition, resulting in nonuniform microwave power absorption and steady-state temperature gradients. When the specimen becomes less lossy as it reacts, or if the changes in the microwave heating properties are gradual, the reaction proceeds relatively uniformly and the volumetric microwave heating creates an inside-out reaction profile leading to increased conversions for processes such as reaction bonding and chemical vapor infiltration (CVI). If the specimen becomes more lossy as it reacts, then the reaction proceeds nonuniformly with rapid reaction rates in the hottest parts of the specimen and little or no reaction in the cooler areas. The process may then occur as a reaction front which moves along the specimen, as with combustion synthesis. This type of processing has potential advantages and disadvantages depending on the system.