Effect Of Inclination Angle Research Articles

Investigating the interplay of fracture inclination and rock properties on supercritical CO2-foam flow in porous media

Natural and induced fractures in porous media pose significant challenges in subsurface applications such as carbon storage, hydrocarbon production, and aquifer contamination mitigation. These highly permeable fractures disrupt the natural flow in porous formations, leading to issues including reduced pressure buildup and early fluid breakthrough. To address these challenges, foam injection serves as an effective method for fluid diversion, offering enhanced mobility control in fractured media. However, the foam's performance must be carefully optimized considering factors such as reservoir conditions, in-situ fluid compatibility, rock properties like pore structure, permeability, and mineralogy, as well as fracture roughness, homogeneity, and orientation. This study investigates the effects of inclination angles (0°, 5°, 10°, and 15°) of smooth, saw-cut fractures on the performance of supercritical carbon dioxide foam in three distinct carbonate rocks: Indiana limestone, Fond Du Lac dolomite, and Alabama Silver limestone. These rocks exhibit a wide range of permeabilities, from 0.4 mD to 5.4 D. The findings are compared with previous research on Berea sandstone. It is demonstrated that optimal foam performance is more readily achieved in fractured porous media with higher permeability, larger pore throat sizes, and mineralogically compatible formations. Unlike previous work where studies focused on the individual impact of specific parameters, including a previous study conducted by our group to explore the effect of fracture orientation, the novelty of this paper is that it addresses multiple parameters at the same time and the interconnected roles that they play. This interplay of fracture orientation, rock type, and flow properties is what determines the ideal conditions that must be optimized to achieve the required foam performance.

Experimental study on the dynamic mechanical and progressive fracture behavior of multi-jointed rock mass under repetitive impact loading

The failure of rock masses is often controlled by structural planes, and the study on the dynamic mechanical behavior of multi-jointed rock masses under repetitive dynamic loading is still few. A series of repetitive impact tests on multi-jointed gabbro (MJG) are conducted with the split Hopkinson pressure bar (SHPB) testing apparatus. The effects of repetitive impact and joint inclination angles (α) on the dynamic mechanical behavior of MJG from the perspectives of impact number, stress equilibrium, dynamic mechanical properties, energy evolution, and macro and micro failure modes are deeply investigated. The results show that the joint inclination angle affects the impact resistance of the MJG. Under repetitive impact loadings, the mechanical behavior of the MJG is consistent, with tensile wing cracks initiating from the joint tips and propagating along the loading direction until specimen failure. During this process, cracks propagate along the weakest paths, thereby consuming the energy generated by the impact and preventing the activation of other minor defects. The macroscopic failure of the MJG undergoes four stages: the appearance of white patch, crack coalescence, crack penetration, and fracture, with the final failure mode being splitting. The microscopic formation stage of white patch is divided into microcrack activation and microcrack widening.

CFD-DEM numerical investigation of the effects of water content and inclination angle on interactions between debris flows and slit dam

Debris flows, composed of sediment–water mixtures, can pose significant risks to downstream populations and infrastructure in mountainous regions. Slit dams have been demonstrated as being effective measures for decreasing the destructivity of debris flows. Reliable evaluations of the interactions between debris flows and slit dams are challenging if the complicated component characteristics of debris flows, such as the water content, are not considered. Here, a multi-scale study of debris flows impacting a slit dam is conducted via computational fluid dynamics and discrete element method (CFD-DEM) simulations to understand the influences of the water content (controlled by solid volume fraction in this study) and the channel inclination angle on flow–slit dam interactions. The results indicate that both the initial solid volume fraction and the channel inclination angle have significant effects on the impact kinematics of flow–slit dam interactions and regulation functions of the slit dam: (i) For gentle slopes, the deposition of debris flows is primarily influenced by flume basal friction, and the normalized peak total impact forces have little difference for a given inclination angle, whereas for steep slopes, an overtopping can occur, further result in the increasing of the normalized peak total impact forces with the increase of solid volume fraction. (ii) The run-up height and retention efficiency are also analyzed to provide a scientific reference for optimizing the design of slit dams.

Preliminary thermal performance characterization of a flexible separate heat pipe used for the tracking-type photovoltaic/thermal system

In the solar heating field, the separate heat pipe-based photovoltaic/thermal technology can improve the comprehensive utilization efficiency of solar energy and reduce the maintenance difficulty in long-term outdoor operation by preventing freezing and scaling problems. Its promotion and application are of great significance for reducing fossil energy consumption and carbon emissions, and thus have attracted much attention. However, the performance of conventional photovoltaic/thermal modules is limited by their frame shadow due to the insulation demand, which leaves plenty of room for overall efficiency gains. To solve this problem, a novel separate heat pipe-based photovoltaic/thermal system is proposed by introducing a dual-axis tracking method through a flexible separate heat pipe and side-altitude inclination. To preliminarily characterize the thermal performance of the flexible separate heat pipe in dual-axis tracking conditions, an indoor experimental platform of the flexible separate heat pipe using the solar collector and finned-tube heat exchanger in the water tank as the evaporator and condenser was set up. The effects of side inclination angle, altitude angle of the solar collector and solar irradiance on the thermal efficiency, mass flow rate, and thermal resistance of the system are investigated in detail. The experimental results show the system can generally maintain effective heat transfer in side inclination states, with thermal efficiency mostly ranging from 44.68% to 86.12%. The proposed flexible separate heat pipe is qualified for the dual-axis tracking of photovoltaic/thermal system and shows great potential in improving the utilization of solar energy.

Study on silage mixing device of King Grass stalk particles based on DEM simulation and bench test

This study designed a silage mixing device for King Grass stalk particles and optimized the core component, the blender, based on the discrete element method (DEM). Through simulation tests, the effect of different blender forms, blade lengths and blade orientations on the Lacey mixing index (LMI) was studied, and the structural form of the blender was selected as the inclined blade-same-up impeller blender. Based on simulation tests, to verify the reliability of the simulation test and further determine the optimal blade inclination angle and mixing speed of the blender, a mixing experimental bench was built for bench tests. The LMI was compared between simulation and bench tests. At three speeds of 60, 80 and 100 r min- −1, the average relative errors are 2.3%, 2.1% and 1.5%, indicating that the simulation test can simulate actual tests well. The central composite design (CCD) was used to establish a binary quadratic regression model of the effects of blade inclination angle and mixing speed on LMI and mixing energy consumption. Using the NSGA-II algorithm, it was determined that the best inclination angle of the mixing blade is 42° and the best mixing speed is 78 r min−1.

Effect of size factor and tapered angles on the shear behavior and strength of haunched beams reinforced with basalt fiber reinforced polymer rebars: Experimental and analytical study

Haunched beams are beams that exhibit varying effective depth over their span. This study includes an experimental and analytical analysis aimed at investigating the influence of size factor on the shear behavior of tapered beams reinforced with basalt fiber reinforced polymer BFRP bars. The main focus of this study revolves around investigating the effects of both inclination angle and size factor as key variables. In this study, a total of eight simply supported beams were tested. The beams were longitudinally reinforced with a 1% ratio of BFRP reinforcement, and separated into two equal groups. Each group consisted of one straight beam and three haunched beams. The haunched beams had varied tapering angles, namely 4⁰, 7.96⁰, and 11.86⁰. The first group is designated for the allocation of large beams, while the second group is designated for the allocation of small beams, which have a cross-section that is one-fourth the size of the large beams. The test results indicate that an increase in tapered angles leads to an increase in shear strength. Additionally, it was observed that smaller beams exhibited a greater normalized shear strength compared to larger beams with a significant rate as compared with straight beams. Subsequently, two equations were developed using the tested data, whereby one of them represents an optimal equation including a logical safety margin, while the other equation is characterized by a conservative equation, providing a substantial safety margin for predictions.

Analysis of machined surface quality for multi-feature standard parts

Analyzing the machined surface quality of a multi-feature part helps to find out a comprehensive solution for machining quality promotion for complex multi-feature products. It is also significant to detect the machining accuracy and performance of the machine tools. In this paper, the surface of a standard part is adopted to investigate multi-feature part machining application, which has more than 5 types of features, such as plane, bevel, curved, cylindrical, etc. Three groups of finish machining experiments with different parameters are firstly conducted to conclude the effect of features on the machined surfaces. Then, surface roughness and morphology were measured and compared for five features under the same machining parameters to reveal machined quality differences between surfaces. The effects of inclination angle and curvature on the surface quality are also theoretically analyzed. It is found that the contact area between the tool and the part varies with the inclination angle of the bevel, leading to different roughness variations. Between the plane and curved surfaces, the concave surface has the highest roughness, while the convex surface has the lowest. Moreover, the wear of four tools with different machining time is examined. It is shown that, with the increase of machining time, the tool tip wears more severely than the rake and the flank. Furthermore, the correlation between tool wear and surface roughness is also studied by regression analysis, which confirms that the quality difference of some surfaces is related to the tool wear state.

Numerical study of mixing vane spacer grid effect on subchannel mixing in a 5 × 5 rod bundle

Turbulent flow in rod bundle with spacer grid without mixing vanes and with mixing vanes of inclination angles from 10° to 30° was investigated by Reynolds Stress Transportation (RST) model under Reynolds numbers (Re) from 3.96 × 103 to 3.96 × 105. The predicted results were validated by experimental data of lateral velocity field in 5 × 5 rod bundle. The cross-flow velocity was relatively well predicted against experimental data, while lateral Reynolds normal stress was underpredicted near spacer grid and overpredicted far from spacer grid. The mixing vanes in one sub-channel generate high pressure region at the upstream side of mixing vane and low-pressure region at the downstream side of mixing vane, forming secondary flow structures. The lateral velocity increases with inclination angle and Re increasing. The lateral Reynolds stress increases with inclination angle increasing and decreases with Re increasing. The anisotropic turbulent states were studied by Lumley triangle method. The mixing vanes are the main factor dominating the turbulent states in rod bundle. The space grid resistance follows decreasing power function of Re and increases with inclination angle increasing. The secondary flow intensity follows an exponentially decaying function of distance from spacer grid and increases with inclination angle and Re increasing. The turbulent mixing coefficient model is an exponentially decreasing function of the distance from spacer grid, and it increases with inclination angle increasing and decreases with Re increasing. This paper studied the inclination angle and Re effect on the sub-channel mixing in a relatively large range of inclination angle and Re, improving the understandings of the sub-channel mixing phenomena.

Experimental Investigation of the Effect of the Burner Cap Geometry on the Performance of a Domestic Liquefied Petroleum Gas Stove

Abstract Cooking is an important domestic activity that needs energy. Traditionally, solid fuels such as firewood and charcoal have been used. However, the combustion of solid fuels inside households causes internal pollution and harms the health of users and other occupants. Nowadays, gaseous fuels like natural gas (NG) and liquefied petroleum gas (LPG) are the most used for domestic cooking. Considering the limitation of fossil fuel resources, energy conservation issues, environmental problems, and the increase in demand for gaseous fuels, it is necessary to explore ways to improve the thermal efficiency and emission characteristics of existing cooking systems. Although the use of gaseous fuels reduces domestic air pollution, the earliest domestic gas burners have low heat performance with an efficiency value of approximately 40%. Continuous research and development in stove design and analysis has led to a significant improvement in the thermal performance of commercial gas burners, with efficiencies exceeding 60%. This study’s main objective is to improve an LPG domestic stove through the modification of the cap burner geometry. The effects of various inclination angles (between the top and the lateral cap faces) ranging from 0 deg to 90 deg have been experimentally investigated. Results demonstrated that the thermal efficiency of the burner increases with increasing inclination angle. The highest efficiency was obtained at an angle of 75 deg, and beyond this value, the efficiency dropped. Unfortunately, at this angle value, CO emissions were the highest.

Three-dimensional numerical investigation of impact-freezing of tin drops on an incline using a phase field method

Drop impact-freezing on an incline is omnipresent in nature and industrial applications like 3D (three-dimensional) printing, but most current research concentrates on the impact instead of the interaction between impact and freezing. This paper thus developed an OpenMP-paralleled phase field model to probe into the underlying physics in 3D printing conditions. The finite difference solution to the Cahn–Hilliard equation helps track the evolving liquid–gas interface, and the liquid fraction is defined over the whole computational domain to distinguish between solid and fluid. The model was first validated against two experiments, showing agreeable consistency. Then, it was applied to inclined impact without and with phase change. The effect of inclination angles was also examined. It was found that increasing inclination angles can extend contact time, and that solidification cannot retard the gravity-driven fluid flow down the incline at an inclination angle of 45° but can at an inclination angle below 30°. Besides, the retracting speed declines with increased inclination angles.

Parameter Investigation of Flyash Jet Mill with Superheated Steam

To improve the utilization rate of flyash, refining flyash is an important approach, and steam power grinding with superheated steam is an important equipment to meet the fine particle size requirements of flyash grinding. A 2.4 m height jet mill with four Laval nozzles has been employed here, and FLUENT is adopted to numerically simulate the distribution of fluid velocity and pressure in the flow field within the model. Meanwhile, parameter investigation is also carried out to reveal the effect of nozzle spacing and nozzle inclination angle on fluid filed and average particle velocity distribution. It is found that both spacing and nozzle inclination angle can affect the average particle velocity simultaneously. From the present parameter investigation, it can be concluded that Model 2 (nozzle spacing is 455 mm) with an inclination angle of 4° is the best choice since it can provide largest particle velocity distribution along the vertical direction.

Effects of inclination angle on Rayleigh–Bénard convection under non-Oberbeck–Boussinesq approximation in air

This study employs direct numerical simulations to explore the combined effects of inclination angles (ϕ) and non-Oberbeck–Boussinesq (NOB) conditions on heat transfer and flow patterns in inclined Rayleigh–Bénard convection (RBC). The simulations, conducted in air, classify flow behavior into seven regimes based on roll number and flow state. Heat-transport efficiency is found to be higher in the single-roll state. The study investigates the influence of NOB and inclination on top-bottom symmetry in a fluid-filled cavity, with systematic analysis revealing complex non-monotonic behaviors of the Nusselt number (Nu) and Reynolds number (Re) under different conditions. The effects of ϕ on heat transfer are significant in the modest to moderate range of Rayleigh numbers, becoming less pronounced as these values increase. The study finds that power-law scalings of Nu and Re are sensitive to the inclination angle and robust against NOB effects for ϕ≥40∘. Moreover, in NOB scenarios, the distributions of the local thermal boundary layers (BLs) along the hot and cold walls exhibit a lack of antisymmetry. As a result, there is an obvious deviation between the hot and cold global thermal BLs, which is further influenced by the inclination angle.

A numerical study on the effects of inclination angle and container material on thermal energy storage by phase change material in a thick-walled disc

PurposeThe purpose of this study is to examine the effects of inclination angle on the thermal energy storage capability of a phase change material (PCM) within a disc-shaped container. Different container materials are also tested such as plexiglass and aluminium. This study aims to assess the energy storage capacity, melting behaviour and temperature distributions of PCM with a specific melting range (22°C–26°C) for various governing parameters such as inclination angles, aspect ratios (AR) and temperature differences (ΔT) and compare the melting behaviour and energy storage performance of PCM in aluminium containers to those in plexiglass containers.Design/methodology/approachA finite volume approach was adopted to evaluate the thermal energy storage capability of PCMs. Five inclination angles ranging from 0° to 180° were considered and the energy storage capacity. Also, the melting behaviour of the PCM and temperature distributions of the container with different materials were tested. Two different AR and ΔT values were chosen as parameters to analyse for their effects on the melting performance of the PCM. Conjugate heat transfer problem is solved to see the effects of conduction mode of heat transfer.FindingsThe results of the study indicate that as AR decreases, the effect of the inclination angles on the energy storage capacity of the PCM decreases. For lower ΔT, the difference between the maximum and minimum stored energies was 20.88% for AR = 0.20, whereas it was 6.85% for AR = 0.15. Furthermore, under the same conditions, the PCM stored 8.02% more energy in plexiglass containers than in aluminium containers.Originality/valueThis study contributes to the understanding of the influence of inclination angle, container material, AR and ΔT on the thermal energy storage capabilities of PCM in a novel designed container. The findings highlight the importance of AR in mitigating the effect of the inclination angle on energy storage capacity. Additionally, comparing aluminium and plexiglass containers provides insights into the effect of container material on the melting behaviour and energy storage properties of PCM.

Study on dynamic characteristics of scraper conveyor under various scraper configurations

This study aims to explore the impact of scraper structure on the stable operation of scraper conveyors. A simulation test is designed to investigate the effect of the scraper's lower inclination angle on the wedge-shaped structure of the scraper. Based on the test results, modifications are made to the scraper's lower inclination angle. Using the DEM-MBD coupling model of the scraper conveyor, simulation analyses are conducted to evaluate the influence of the scraper on the dynamic characteristics of the conveyor before and after the modification. The simulation test results reveal that, when coal materials are stuck, the minimum impact force of coal material on the upper sample is observed at inclination angles of 52.35° and 78.19°. The simulation research indicates that the transportation efficiency of the standard scraper and the single-sided 52.35° and 78.19° modified scraper is similar. The single-sided 78.19° scraper demonstrates the most stable vibration amplitude and centroid variance, with an overall maximum vibration amplitude and variance of 0.76 mm and 0.08, respectively. The z-direction speed fluctuation of the single-sided 78.19° scraper is also the smallest and most stable, with a maximum peak-valley difference and fluctuation variance of 0.17 m/s and 0.0004, respectively. Additionally, the force of the coal on the single-sided 78.19° scraper is the smallest and relatively stable, with a fluctuation range of 510.28∼ 18,557.71 N. Overall, the dynamic operation effect of the single-sided 78.19° scraper is deemed the best after considering all factors. This study provides valuable insights into the influence of scraper structure with different lower inclination angles on the stable operation of scraper conveyors and offers a reference for optimizing scraper structure.

Heat transfer investigation on the thermal energy storage using phase change material in low-carbon building

The use of high-conductivity porous medium is an effective method to enhance the heat transfer rate of phase change material (PCM) in thermal energy storage (TES), reducing the energy consumption of low-carbon buildings. This paper establishes a solid-liquid phase change lattice Boltzmann model of a TES unit and investigates the effects of Rayleigh number, inclination angle, porous array, and porosity. The findings indicate that inserting the porous medium enhances conductive heat transfer and weakens convective heat transfer. When the Rayleigh number is increased from 103 to 104, the liquid fraction increases by 3.0%, while an increase from 104 to 105 only results in a 1.6% increase, suggesting a diminishing effect of increasing the Rayleigh number. Results also show that the inclination angle can be disregarded in this study. Furthermore, increasing the specific surface area enhances conductive heat transfer. However, when the array n is changed to 7, the fastest variation of liquid fraction is obtained among the range from 5 to 9. Increasing the porosity will delay the moment that temperature standard deviation reaches to the maximum, getting the temperature distribution more nonuniform. The findings from this paper are valuable for the design of TES systems in low-carbon buildings. Practical application The porous medium can enhance heat transfer in the phase change process. In the field of low-carbon buildings, porous medium is applied to strengthen the energy storage rate. By investigating the parameters of the Rayleigh numbers, inclination angles, porosities and arrangement of porous medium arrays of the composed energy storage unit, the regularity of the effects on the energy characteristics are obtained, which would provide some valuable practice references for designing these parameters of the energy storage units in the future energy-efficient building sector.

Jeffrey fluid flow past inclined stretchable sheet with magnetic dipole and suction/injection

Jeffrey fluid flow past an inclined stretchable sheet affected by magnetic dipole and suction/injection was investigated. The applicable equations were changed into nonlinear ordinary differential equations by similarity transformations. With the Chebyshev spectral collocation approach, solutions were obtained for fluid velocity and temperature. Considering the prescribed surface temperature (PST) and prescribed heat flux (PHF) heat processes, the effect of inclination angle, the Grashof number, and other parameters on the velocity and temperature of the fluid were documented by graphs and tables. Without the angle of inclination, the solutions from this paper were found to agree with those of the Generic algorithm and Nelder Mead method. The fluid is slower when the plate is inclined at a larger angle and this tends to allow for higher fluid temperature. The ferromagnetic interaction parameter and the ratio of relaxation to retardation time have the same effect on fluid velocity and temperature as the angle of inclination. The suction parameter and Prandtl number amplify the Nusselt number, while, as the suction increases, the skin friction increases for all inclination angles. With these results, engineers in chemical/polymer industries can make appropriate changes that can lead to more quality production.

Numerical simulation study of enhanced convective heat transfer in the tube based on winglet vortex generator

In order to enhance the heat transfer effect and improve the energy utilization efficiency of the circular tube under turbulent flow, rhombic and triangular winglet vortex generators are proposed on the basis of rectangular winglet vortex generator. The effects of three vortex generators on flow and heat transfer in the tube are investigated by numerical simulations. The results indicate that, the rectangular and triangular winglets generate two pairs of longitudinal vortices and the triangular winglets generate four pairs of longitudinal vortices due to additional shrink-age regions. The multiple longitudinal vortices increase the mixing between the fluids, raise the temperature in the central region of the tube, and enhance the heat transfer effect. Furthermore, the triangular winglet enhanced tube has the largest direct flow area and the least effect on resistance. The triangular winglet enhanced tube had the best comprehensive performance, followed by the rhombic winglet enhanced tube, and finally, the rectangular winglet enhanced tube. The performance evaluation criterion reached 1.04-1.13, 1.05-1.15, and 1.08-1.21 for the three enhanced tubes in the given flow rate interval. In addition, the effect of inclination angle on the triangular winglet enhanced tube was further investigated, and the results show that the best comprehensive performance of enhanced heat transfer is achieved at an inclination angle of 45?, with a maximum performance evaluation criterion of 1.25.

Numerical simulation study of enhanced convective heat transfer in the tube based on winglet vortex generator

In order to enhance the heat transfer effect and improve the energy utilization efficiency of the circular tube under turbulent flow, rhombic and triangular winglet vortex generators are proposed on the basis of rectangular winglet vortex generator. The effects of three vortex generators on flow and heat transfer in the tube are investigated by numerical simulations. The results indicate that, the rectangular and triangular winglets generate two pairs of longitudinal vortices and the triangular winglets generate four pairs of longitudinal vortices due to additional shrinkage regions. The multiple longitudinal vortices increase the mixing between the fluids, raise the temperature in the central region of the tube, and enhance the heat transfer effect. Furthermore, the triangular winglet enhanced tube has the largest direct flow area and the least effect on resistance. The triangular winglet enhanced tube had the best comprehensive performance, followed by the rhombic winglet enhanced tube, and finally, the rectangular winglet enhanced tube. The performance evaluation criterion (PEC) reached 1.04-1.13, 1.05-1.15, and 1.08-1.21 for the three enhanced tubes in the given flow rate interval. In addition, the effect of inclination angle on the triangular winglet enhanced tube was further investigated, and the results show that the best comprehensive performance of enhanced heat transfer is achieved at an inclination angle of 45?, with a maximum PEC of 1.25.

THERMO-FLUID PERFORMANCE COMPARISON OF AN IN-LINE PERFORATED BAFFLE WITH OPPOSITELY ORIENTED RECTANGULAR-WING STRUCTURE IN TURBULENT HEAT EXCHANGER

This research study examined the effects of a novel swirl airflow design on the rate of heat transfer in a tubular heat exchanger with axial flow. The novel design consisted of 16 rectangular air deflectors placed in opposite directions, positioned at varying angles of inclination. These deflectors were embedded on circular perforated baffle plates, which were spaced equidistantly apart at different pitch ratios. Hot water was supplied to heat exchanger tubes whose arrangement remained constant throughout the experiment, while atmospheric air is flown over tube bundle at Reynolds number that ranged from 16 × 10<sup>3</sup> to 3 × 10<sup>4</sup> . The effect of pitch ratio and inclination angle on the thermal enhancement factor was experimentally analyzed. The findings demonstrated that using an opposite-oriented deflector baffle plate with an inclination angle of 30 deg and a pitch ratio of 1 resulted in an average improvement of 1.17 in the thermal enhancement factor compared to a heat exchanger without a baffle plate, tested under similar conditions.

Thermal contact conductance model of rough surfaces with inclination based on three-dimensional fractal theory

PurposeThe purpose of this study is to establish a thermal contact conductance model of rough surfaces with inclination based on three-dimensional fractal theory.Design/methodology/approachThe effects of contact load, inclination angle, fractal dimensional and fractal roughness on thermal contact conductance of rough surfaces were studied using numerical simulation.FindingsThe results show that the thermal contact conductance of the rough surface increases with the increase of contact load and fractal dimension and decreases with the increase of fractal roughness and inclination angle. The inclination angle of the rough surface has an important influence on the thermal contact conductance of the rough, and it is a factor that cannot be ignored in the study of the thermal contact conductance of rough surfaces.Originality/valueA thermal contact conductance model of rough surfaces with inclination based on three-dimensional fractal theory was established in this study. The achievements of this study provide some theoretical basis for the investigation of the thermal contact conductance of rough surfaces.