Finite Difference Numerical Code Research Articles

Design, optimization and implementation of a solar cell for wood phytosanitary treatment

ABSTRACT A research program was undertaken with the goal of developing dehumidifier solar wood dryers and wood thermal phytosanitary treatment cells. The first step of the program, was dedicated to the development of the numerical tools that would assist in the design and optimization of the dryers. These were based on an approach that combines micro (at the level of the wood board) and macro (at the level of the entire dryer and its solar heating system) modellings, and that uses typical year weather data, to perform the simulations. A finite difference numerical code was employed to predict the time evolution of the wood and air properties during the thermal phytosanitary treatment of wood. These predictions are employed as input to the TRNSYS© software to model the retained solar phytosanitary treatment installation configuration. In this system, the air leaving the treatment cell is recycled. But prior to injecting it back, it is mixed, in the right proportions, with outside air in order to adjust its humidity. The recycled air temperature is then risen to the operating value in an air-water heat exchanger fed from the storage tank of the solar water loop. The latter includes solar evacuated collectors, two pumps, a storage tank and a heat exchanger. The concept technical feasibility was prooved. The sytem optimization showed that, for a cell to be installed in Tunis, a 22 m2 evacuated tube collector and a 1.5 m3 water reservoir are needed for the treatment of 1 m3 wood stack i.e. 0.7 m3 of wood (reduced to 0.42 m3 in the winter season). A prototype of the optimized system was constructed and preliminary experimental tests are presented.

Analysis of the coupled electro-osmotic and mechanical consolidation in clayey soils

Electrokinetic (EK) treatment is a possible attractive way to speed up the consolidation of fine-grained dredged sediments. The effectiveness of this method depends on the complex physical–chemical interaction between soil particles, interstitial fluid and pollutants. This paper presents the experimental laboratory results obtained by inducing mechanical and EK consolidation in a fine-grained dredged material. Then, a finite-difference numerical code implemented by the authors able to solve the large and small strain consolidation equations (Lassec1), including the electro-osmotic flow, is described along with the theoretical simplifications adopted and the calibration procedure required. The experimental results have been numerically simulated, showing the ability of Lassec1 to reproduce the coupled mechanical and electrical consolidation processes, highlighting that under very low stress levels it is necessary to take into account the highly non-linear soil behaviour, and thus the large strain theory is needed to obtain a reliable prediction of the consolidation process. With this aim, special laboratory devices are necessary for a good calibration of the permeability function and of the stress–strain relationship at very low stress levels.

Non-Boussinesq gravity currents and surface waves generated by lock release in a circular-section channel: theoretical and experimental investigation

We present a combined theoretical and experimental study of lock-release inertial gravity currents (GCs) propagating in a horizontal channel of circular cross-section with open-top surface in the non-Boussinesq regime. A two-layer shallow-water (SW) model is developed for a generic shape of the cross-section with open top, and then implemented in a finite difference numerical code for the solution in a circular-cross-section channel of the type used in the experiments. The model predicts propagation with (almost) constant speed for a fairly long distance, accompanied by a depression of the ambient free open-top surface behind the front of the current. Sixteen experiments were conducted with a density ratio $r=0.587{-}0.939$ in full-depth and part-depth release conditions, measuring the front speed and the free-surface time series at four cross-sections. The channel was a circular tube 409 cm long, with a radius of 9.5 cm; the lengths of the locks were 52 and 103.5 cm. Density contrast was obtained by adding sodium chloride and dipotassium phosphate to fresh water. The theoretical values of the front speed and of the depression overestimate the experimental values, but they predict correctly their trend for varying parameters and provide reliable insights into the underlying mechanisms. In particular, we demonstrate that the circular cross-section increases the speed of propagation as compared to the standard rectangular cross-section case (for the same initial height and density ratio). The discrepancies between the SW predictions and the present experiments are of the same order of magnitude as those of previously published results for simpler systems (Boussinesq, rectangular). In addition to the depression, which is a wave bound to, and following the front of, the GC, the system also displays two kinds of free-surface waves, namely the initial bump (its amplitude is of the same order as the depression) and some short-length and low-amplitude waves in the tail of the bump. These free waves propagate with a celerity well predicted by the ‘fast’ eigenvalues of the mathematical model. Comparison is provided with the celerity of a solitary wave. It is expected that discrepancies between theory and experiments can be partly attributed to the presence of these waves. The reported insights and SW prediction method can be applied to a variety of cross-sections of practical interest (triangles, trapezoids, etc.).

Polydisperse particle-driven gravity currents in non-rectangular cross section channels

We consider a high-Reynolds-number gravity current generated by polydisperse suspension of n types of particles distributed in a fluid of density ρi. Each class of particles in suspension has a different settling velocity. The current propagates along a channel of non-rectangular cross section into an ambient fluid of constant density ρa. The bottom and top of the channel are at z = 0, H, and the cross section is given by the quite general form −f1(z) ≤ y ≤ f2(z) for 0 ≤ z ≤ H. The flow is modeled by the one-layer shallow-water equations obtained for the time-dependent motion. We solve the problem by a finite-difference numerical code to present typical height h, velocity u, and mass fractions of particle (concentrations) (ϕ( j), j = 1, …, n) profiles. The runout length of suspensions in channels of power-law cross sections is analytically predicted using a simplified depth-averaged “box” model. We demonstrate that any degree of polydispersivity adds to the runout length of the currents, relative to that of equivalent monodisperse currents with an average settling velocity. The theoretical predictions are supported by the available experimental data. The present approach is a significant generalization of the particle-driven gravity current problem: on the one hand, now the monodisperse current in non-rectangular channels is a particular case of n = 1. On the other hand, the classical formulation of polydisperse currents for a rectangular channel is now just a particular case, f(z) = const., in the wide domain of cross sections covered by this new model.

Gravitational shock wave inside a steadily accreting spherical charged black hole

We numerically investigate the interior of a four-dimensional, spherically symmetric charged black hole accreting neutral null fluid. Previous study by Marolf and Ori suggested that late infalling observers encounter an effective shock wave as they approach the outgoing portion of the inner horizon. Non-linear perturbations could generate an effective gravitational shock wave, which manifests as a drop of the area coordinate $r$ from inner horizon value $r_{-}$ towards zero in an extremely short proper time duration of the infalling observer. We consider three different scenarios: a) A charged black hole accreting a single (ingoing) null fluid; b) a charged black hole perturbed by two null fluids, ingoing and outgoing; c) a charged black hole perturbed by an ingoing null fluid and a self-gravitating scalar field. While we do not observe any evidence for a gravitational shock in the first case, we detect the shock in the other two, using ingoing timelike and null geodesics. The shock width $\Delta\tau$ decreases rapidly with a fairly good match to a new, generalized exponential law, $\Delta\tau\sim e^{-\intop\kappa_{-} (\widetilde{V}_{f})d\widetilde{V}_{f}}$, where $\widetilde{V}_{f}$ is a specific timing parameter for the ingoing timelike geodesics and $\kappa_{-}(\widetilde{V}_{f})$ is a generalized (Reissner-Nordstr\"om like) surface gravity of the charged black hole at the inner horizon. We also gain new insight into the inner (classical) structure of a charged black hole perturbed by two null fluids, including strong evidence for the existence of a spacelike $r=0$ singularity. We use a finite-difference numerical code with double-null coordinates combined with an adaptive gauge method in order to solve the field equations from the region outside the black hole down to the vicinity of the $r=0$ singularity.

Numerical study of the gravitational shock wave inside a spherical charged black hole

We numerically investigate the interior of a four-dimensional, asymptotically flat, spherically symmetric charged black hole perturbed by a scalar field $\Phi$. Previous study by Marolf and Ori indicated that late infalling observers will encounter an effective shock wave as they approach the left portion of the inner horizon. This shock manifests itself as a sudden change in the values of various fields, within a tremendously short interval of proper time $\tau$ of the infalling observers. We confirm this prediction numerically for both test and self-gravitating scalar field perturbations. In both cases we demonstrate the effective shock in the scalar field by exploring $\Phi(\tau)$ along a family of infalling timelike geodesics. In the self-gravitating case we also demonstrate the shock in the area coordinate $r$ by exploring $r(\tau)$. We confirm the theoretical prediction concerning the shock sharpening rate, which is exponential in the time of infall into the black hole. In addition we numerically probe the early stages of shock formation. We also employ a family of null (rather than timelike) ingoing geodesics to probe the shock in $r$. We use a finite-difference numerical code with double-null coordinates combined with a recently developed adaptive gauge method in order to solve the (Einstein + scalar) field equations and to evolve the spacetime (and scalar field) $ - $ from the region outside the black hole down to the vicinity of the Cauchy horizon and the spacelike $r=0$ singularity.

Particle-driven gravity currents in non-rectangular cross section channels

We consider a high-Reynolds-number gravity current generated by suspension of heavier particles in fluid of density ρi, propagating along a channel into an ambient fluid of the density ρa. The bottom and top of the channel are at z = 0, H, and the cross section is given by the quite general −f1(z) ≤ y ≤ f2(z) for 0 ≤ z ≤ H. The flow is modeled by the one-layer shallow-water equations obtained for the time-dependent motion which is produced by release from rest of a fixed volume of mixture from a lock. We solve the problem by the finite-difference numerical code to present typical height h(x, t), velocity u(x, t), and volume fraction of particles (concentration) ϕ(x, t) profiles. The methodology is illustrated for flow in typical geometries: power-law (f(z) = zα and f(z) = (H − z)α, where α is positive constant), trapezoidal, and circle. In general, the speed of propagation of the flows driven by suspensions decreases compared with those driven by a reduced gravity in homogeneous currents. However, the details depend on the geometry of the cross section. The runout length of suspensions in channels of power-law cross sections is analytically predicted using a simplified depth-averaged “box” model. The present approach is a significant generalization of the classical gravity current problem. The classical formulation for a rectangular channel is now just a particular case, f(z) = const., in the wide domain of cross sections covered by this new model.

Effects of anisotropy in correlation structure on the stability of an undrained clay slope

Slopes are mainly naturally occurred deposits, so slope stability is highly affected by inherent uncertainty. In this paper, the influence of heterogeneity of undrained shear strength on the performance of a clay slope is investigated. A numerical procedure for a probabilistic slope stability analysis based on a Monte Carlo simulation that considers the spatial variability of the soil properties is presented to assess the influence of randomly distributed undrained shear strength and to compute reliability as a function of safety factor. In the proposed method, commercially available finite difference numerical code FLAC 5.0 is merged with random field theory. The results obtained in this study are useful to understand the effect of undrained shear strength variations in slope stability analysis under different slope conditions and material properties. Coefficient of variation and heterogeneity anisotropy of undrained shear strength were proven to have significant effect on the reliability of safety factor calculations. However, it is shown that anisotropy of the heterogeneity has a dual effect on reliability index depending on the level of safety factor adopted.

Using MODFLOW code to approach transient hydraulic head with a sharp‐interface solution

AbstractSaltwater intrusion problems have been usually tackled through analytical models because of its simplicity, easy implementation and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, which neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. This paper provides insight into the validity of a sharp‐interface approximation defined from a steady state solution when applied to transient seawater intrusion problems. The validation tests have been performed on a 3D unconfined synthetic aquifer, which include spatial and temporal distribution of recharge and pumping wells. Using a change of variable, the governing equation of the steady state sharp‐interface problem can be written with the same structure of the steady confined groundwater flow equation as a function of a single potential variable (ϕ). We propose to approach also the transient problem solving a single potential equation (using also the ϕ variable) with the same structure of the confined groundwater flow equation. It will allow solving the problem by using the classical MODFLOW code. We have used the parameter estimation model PEST to calibrate the parameters of the transient sharp‐interface equation. We show how after the calibration process, the sharp‐interface approach may provide accurate enough results when applied to transient problems and improve the steady state results, thus avoiding the need of implementing a density‐dependent model and reducing the computational cost. This has been proved by comparing results with those obtained using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. The comparison was performed in terms of piezometric heads, seawater penetration, transition zone width and critical pumping rates. Copyright © 2014 John Wiley & Sons, Ltd.

지압형 앵커의 지압력 산정에 관한 실험적 연구

일반적인 영구앵커(마찰형 앵커)는 정착장에서 지반과 그라우트의 마찰력으로 인발에 저항하는 구조이지만, 지압형 앵커는 확공부에서 발생하는 지압력으로 인발에 저항하여 지반변형을 억제하는 방식이다. 본 연구는 확공을 이용한 지압형 앵커 활용 시 합리적인 지압력 산정을 위해 수행되었으며, 지압력 산정 시 도해법, 실내실험, 수치해석적 방법을 수행하고 그 결과를 지반의 일축압축강도와 비교, 분석하였다. 도해법에서는 앵커의 지압력을 천공경(<TEX>$r_i$</TEX>), 확장되는 천공경(<TEX>$r_e$</TEX>), 일축압축강도(<TEX>${\sigma}_c$</TEX>)의 함수로 정의하였다. 실내실험을 통한 연구에서는 실내 모형을 제작하여 앵커 인장시험을 수행하여 지압력을 확인하였고, Flac 3D를 이용한 3차원 유한차분해석을 통해 지반조건별 지압력을 확인하였다. 실내실험 및 수치해석에서 도출된 지압력은 회귀분석을 통해 지압력 산정식을 제시하였다. 지압력은 실내실험에서 일축압축강도 대비 약 28.5배로 가장 큰 결과를 나타내었는데, 이는 순수 지압력 뿐만 아니라 앵커체 확장에 따른 주면마찰저항력이 함께 작용했기 때문인 것으로 판단된다. 도해법과 수치해석에서 확인된 지압력은 일축압축강도의 13.3배, 9.9배로 확인되었으며, 향후 현장실험을 통한 지압력 산정결과와 비교, 분석하여 산정식에 대한 신뢰성 향상이 필요하다. An almost permanent anchor (friction type) is resistant to ground deformation due to the friction between the soil and grout at a fixed length from the anchor body. The purpose of this study is to calculate the force of bearing resistance for a bearing anchor in enlarged boreholes. We conducted analytical and numerical analyses, along with laboratory testing, to find the quantities of bearing resistance prior to grouting in EBA (Enlarged Bearing Anchor) construction. The force of bearing resistance from the analytical method was defined as a function of general borehole diameter, expanded borehole diameter, and soil unconfined compressive strength. We also employed the Flac 3D finite difference numerical modeling code to analyze the bearing resistance of the soil conditions. We then created a laboratory experimental model to measure bearing resistance and carried out a pull-out test. The results of these three analyses are presented here, and a regression analysis was performed between bearing resistance and uniaxial compression strength. The laboratory results yield the strongest bearing resistance, with reinforcement 28.5 times greater than the uniaxial compression strength; the analytical and numerical analyses yielded values of 13.3 and 9.9, respectively. This results means that bearing resistance of laboratory test appears to be affected by skin friction resistance. To improve the reliability of these results, a comparison field study is needed to verify which results (analytical, numerical, or laboratory) best represent field observations.

Magnetohydrodynamic equilibria in barotropic stars

AbstractAlthough barotropic matter does not constitute a realistic model for magnetic stars on short timescales, it would be interesting to confirm a recent conjecture that states that magnetized stars with a barotropic equation of state would be dynamically unstable (Reisenegger 2009). In this work we construct a set of barotropic equilibria, which can eventually be tested using a stability criterion. A general description of the ideal MHD equations governing these equilibria is summarized, allowing for both poloidal and toroidal magnetic field components. A new finite-difference numerical code is developed in order to solve the so-called Grad-Shafranov equation describing the equilibrium of these configurations, and some properties of the equilibria obtained are briefly discussed.

Discussion about the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers

AbstractAnalytical models have been exhaustively used to study simple seawater intrusion problems and the sustainable management of groundwater resources in coastal aquifers because of its simplicity, easy implementation, and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, and their governing equations are expressed in terms of a single potential theory to calculate critical pumping rates in a coastal pumping scenario. The Ghyben–Herzberg approach neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. Therefore, the results of the analytical solutions may be inaccurate and unacceptable for some real‐complex case studies. This paper provides insight into the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers, i.e. when they can be applied to obtain accurate enough results. For that purpose, this work compares sharp‐interface solutions, based on the Ghyben–Herzberg approach, with numerical three‐dimensional variable‐density flow simulations for a set of heterogeneous groundwater flow and mass transport parameters, and different scenarios of spatially distributed recharge values and spatial wells placement. The numerical experiment has been carried out in a 3D unconfined synthetic aquifer using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. This paper finds under which situations the sharp‐interface solution gives good predictions in terms of seawater penetration, transition zone width and critical pumping rates. Additionally, the simulation runs indicate to which parameters and scenarios the results are more sensitive. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Gravity currents in non-rectangular cross-section channels: Analytical and numerical solutions of the one-layer shallow-water model for high-Reynolds-number propagation

We consider the propagation of a high-Reynolds-number gravity current at the bottom of a horizontal channel along the horizontal coordinate x. The bottom and top of the channel are at z = 0, H, and the cross-section is given by the general −f1(z) ⩽ y ⩽ f2(z) for 0 ⩽ z ⩽ H. We use a one-layer, Boussinesq, shallow-water formulation to solve the time-dependent motion produced by release from rest of a fixed volume of fluid from a lock. The dependent variables are the position of the horizontal interface, h(x, t), and the speed (averaged over the area of the current), u(x, t). The non-rectangular cross-section geometry enters the formulation via f(h) and integrals of f(z) and zf(z), where f(z) = f1(z) + f2(z) is the width of the channel. For a given geometry f(z), the only input parameter in the lock-release problem is the height ratio H/h0 of ambient to lock. In general, the solution is obtained by a finite-difference numerical code. Analytical results are derived for the initial dam-break slumping motion, and for the long-time self-similar phase. The model is illustrated for various cross-section shapes: power-law (f(z) = bzα, where b, α are positive constants), trapezoidal, V-shaped valley, and circle-segment. In addition to the quantitative results, the qualitative similarities and differences between the classical rectangular and the general non-rectangular channel have been elucidated: in the first case there is always an initial “slumping” stage of propagation with speed uN = const., followed by a stage of decreasing speed, then a phase of self-similar behavior during which uN decreases like time to some power. In the non-rectangular cross-section channel, the first two stages appear, but the self-similar phase is attained only when the cross-section shape is given by a power-law. When the cross-section of the channel expands upwards, the speed of propagation is larger, and the decay of speed after the slumping stage is weaker, than in the classical rectangular counterpart. The theoretical results are in good agreement with previously published experimental data, but a sharp comparison is not feasible because the experiments were performed in full-depth-lock configurations where the one-layer model is not expected to be accurate.

Influence of Spatially Variable Geotechnical Properties of MSW on Stability of Landfill Slopes

AbstractProbabilistic slope stability analysis of the municipal solid waste (MSW) landfill slope (height = 30 m and 1V∶3H) with due consideration to the spatial variation of geotechnical properties of MSW (single depth layer versus multilayered depth) is performed. The published data on geotechnical properties of MSW is used to define statistics of spatial variation of geotechnical parameters. Random field theory combined with finite difference numerical code, fast Lagrangian analysis of continua (FLAC) is used. Two-dimensional non-Gaussian homogeneous random field is generated by Cholesky decomposition technique. Monte Carlo simulations are performed to determine the statistics of the stability of the MSW landfill slope, evaluated in terms of factor of safety, and information is utilized to assess the performance in probabilistic framework, i.e., reliability index (β). The results of the analysis are compared and discussed in the light of conventional factor of safety approach, in which the geotechnical ...

Understanding Etna flank instability through numerical models

As many active volcanoes, Mount Etna shows clear evidence of flank instability, and different mechanisms were suggested to explain this flank dynamics, based on the recorded deformation pattern and character. Shallow and deep deformations, mainly associated with both eruptive and seismic events, are concentrated along recognised fracture and fault systems, mobilising the eastern and south-eastern flank of the volcano. Several interacting causes were postulated to control the phenomenon, including gravity force, magma ascent along the feeding system, and a very complex local and/or regional tectonic activity. Nevertheless, the complexity of such dynamics is still an open subject of research and being the volcano flanks heavily urbanised, the comprehension of the gravitative dynamics is a major issue for public safety and civil protection. The present research explores the effects of the main geological features (in particular the role of the subetnean clays, interposed between the Apennine–Maghrebian flysch and the volcanic products) and the role of weakness zones, identified by fracture and fault systems, on the slope instability process. The effects of magma intrusions are also investigated. The problem is addressed by integrating field data, laboratory tests and numerical modelling. A bi- and tri-dimensional stress–strain analysis was performed by a finite difference numerical code (FLAC and FLAC3D), mainly aimed at evaluating the relationship among geological features, volcano-tectonic structures and magmatic activity in controlling the deformation processes. The analyses are well supported by dedicated structural–mechanical field surveys, which allowed to estimate the rock mass strength and deformability parameters. To take into account the uncertainties which inevitably occur in a so complicated model, many efforts were done in performing a sensitivity analysis along a WNW–ESE section crossing the volcano summit and the Valle del Bove depression. This was mainly devoted to evaluate the effect of topography, geometry and rheological behaviour of the structural units. The 3D numerical model, extended 40×60km, was implemented to simulate the volcano deformation pattern. First, the role of the Pleistocene subetnean clays was investigated, then, two “structural weakness zones” – the Pernicana Fault system and the NE rift – were introduced and their effects on the flank instability evaluated. Two extreme hydrogeological conditions, drained and undrained, were analysed. The results are expressed in terms of stress–strain field, displacement pattern, plasticity states and shear strain increments. Two main instability mechanisms were identified: one at shallow depth, with the sliding surface located inside the subetnean Quaternary clay, and another deep-seated mechanism with a not continuous and less evident sliding surface, developed inside the Apennine–Maghrebian Chain flysch, bordered by active structures. Both mechanisms contribute to explain the present deformation pattern and some of the main structures of the Etna flank. The effect of magma pressure exerted on the active dyke walls during eruptions was then simulated and relations between magmatic activity and flank instability were preliminarily investigated.

Deflection and buckling of buried flexible pipe-soil system in a spatially variable soil profile

Response of buried flexible pipe-soil system is studied, through numerical analysis, with respect to deflection and buckling in a spatially varying soil media. In numerical modeling procedure, soil parameters are modeled as two-dimensional non-Gaussian homogeneous random field using Cholesky decomposition technique. Numerical analysis is performed using random field theory combined with finite difference numerical code FLAC 5.0 (2D). Monte Carlo simulations are performed to obtain the statistics, i.e., mean and variance of deflection and circumferential (buckling) stresses of buried flexible pipe-soil system in a spatially varying soil media. Results are compared and discussed in the light of available analytical solutions as well as conventional numerical procedures in which soil parameters are considered as uniformly constant. The statistical information obtained from Monte Carlo simulations is further utilized for the reliability analysis of buried flexible pipe-soil system with respect to deflection and buckling. The results of the reliability analysis clearly demonstrate the influence of extent of variation and spatial correlation structure of soil parameters on the performance assessment of buried flexible pipe-soil systems, which is not well captured in conventional procedures.

Dynamic Numerical Analysis of Antimoisture-Damage Mechanism of Permeable Pavement Base

As a permeable base material of pavement, the large stone porous asphalt mixture (LSPM) is used widely in China to lessen the moisture damage of the asphalt pavement. However, the dynamics mechanism of the inhibitory effect of permeable base on moisture damage is not clear yet. The dynamic fluid-solid coupling analysis of the saturated pavement with LSPM base course, considering the asphalt mixtures as the porous medium, was performed using the finite difference numerical code FLAC3D. Numerical results revealed that the positive and negative dynamic pore pressure alternated in the pavement with the approaching and leaving of the wheel loads. The phenomenon of water pumping out of and sucking into the pavement under the moving loads was proved. The flow of fluid in pavement can be regarded as the laminar flow. The presence of the LSPM base course greatly decreased the dynamic pore pressure and the scouring force in the surface course because of the large permeability coefficient of the LSPM. The location o...

Numerical Simulation of Laminar Heat Transfer in Aluminium Circular Tube With Internal Longitudinal Fins

This paper presents a numerical simulation of laminar heat transfer in circular tube flows with internal longitudinal fins using finite difference numerical code. Three types of fin models with three different half included angle are considered. Two types of fluids (coolants), namely, water and engine oil, have been considered. Aluminium is considered as tube/fin materials. The variation of thermal conductivity of the tube materials, fluids and viscosity of the fluids with the temperature are taken into account in the solution procedure. The outer surface of the tube is exposed to constant heat flux. Steady, laminar flow and heat transfer is assumed. Reynolds numbers equal to 1,500 are used in this study. The flow is assumed to be fully developed locally, but thermally undeveloped. The governing equations are discretized using finite difference scheme. The momentum equation for the fluid and the energy equations for the fluid and the tube wall are solved simultaneously and iteratively.

Groundwater overdraft and the impact of artificial recharge on groundwater quality in a cone of depression, Jining, China

Groundwater overdraft has led to cone of depression formation in Jining City, China. This paper investigates spatial groundwater overdraft severity by an index and Geographic Information System (GIS) method, and impact of artificial recharge on groundwater quality, by a 3-D groundwater flow finite difference numerical model code MODFLOW, and a solute transport model code MT3D. Hydrogeological and anthropogenic factors were evaluated. Groundwater concentration of chloride ions and total hardness (THD) as a result of artificial recharge were evaluated. The hydro-geochemical formation of the aquifer and recharge water quality greatly impact the groundwater quality. The recharge water must be within high groundwater quality standards.

Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis

In recent years, spatial variability modeling of soil parameters using random field theory has gained distinct importance in geotechnical analysis. In the present study, commercially available finite difference numerical code FLAC 5.0 is used for modeling the permeability parameter as spatially correlated log-normally distributed random variable and its influence on the steady state seepage flow and on the slope stability analysis are studied. Considering the case of a 5.0 m high cohesive–frictional soil slope of 30°, a range of coefficients of variation ( CoV%) from 60 to 90% in the permeability values, and taking different values of correlation distance in the range of 0.5–15 m, parametric studies, using Monte Carlo simulations, are performed to study the following three aspects, i.e., (i) effect of stochastic soil permeability on the statistics of seepage flow in comparison to the analytic (Dupuit′s) solution available for the uniformly constant permeability property; (ii) strain and deformation pattern, and (iii) stability of the given slope assessed in terms of factor of safety (FS). The results obtained in this study are useful to understand the role of permeability variations in slope stability analysis under different slope conditions and material properties.