Unsteady boundary layer flow and heat transfer over an exponentially shrinking sheet with suction in a copper-water nanofluid

An analysis of unsteady boundary layer flow and heat transfer over an exponentially shrinking porous sheet filled with a copper-water nanofluid is presented.Water is treated as a base fluid.In the investigation,non-uniform mass suction through the porous sheet is considered.Using Keller-box method the transformed equations are solved numerically.The results of skin friction coefficient,the local Nusselt number as well as the velocity and temperature profiles are presented for different flow parameters.The results showed that the dual non-similar solutions exist only when certain amount of mass suction is applied through the porous sheet for various unsteady parameters and nanoparticle volume fractions.The ranges of suction where dual non-similar solution exists,become larger when values of unsteady parameter as well as nanoparticle volume fraction increase.So,due to unsteadiness of flow dynamics and the presence of nanoparticles in flow field,the requirement of mass suction for existence of solution of boundary layer flow past an exponentially shrinking sheet is less.Furthermore,the velocity boundary layer thickness decreases and thermal boundary layer thickness increases with increasing of nanoparticle volume fraction in both non-similar solutions.Whereas,for stronger mass suction,the velocity boundary layer thickness becomes thinner for the first solution and the effect is opposite in the case of second solution.The temperature inside the boundary layer increases with nanoparticle volume fraction and decreases with mass suction.So,for the unsteadiness and for the presence of nanoparticles,the flow separation is delayed to some extent.

A Simplified Scheme of the Generalized Layered Radiative Transfer Model

In this paper, firstly, a simplified version （SGRTM） of the generalized layered radiative transfer model （GRTM） within the canopy, developed by us, is presented. It reduces the information requirement of inputted sky diffuse radiation, as well as of canopy morphology, and in turn saves computer resources. Results from the SGRTM agree perfectly with those of the GRTM. Secondly, by applying the linear superposition principle of the optics and by using the basic solutions of the GRTM for radiative transfer within the canopy under the condition of assumed zero soil reflectance, two sets of explicit analytical solutions of radiative transfer within the canopy with any soil reflectance magnitude are derived： one for incident diffuse, and the other for direct beam radiation. The explicit analytical solutions need two sets of basic solutions of canopy reflectance and transmittance under zero soil reflectance, run by the model for both diffuse and direct beam radiation. One set of basic solutions is the canopy reflectance αf （written as α1 for direct beam radiation） and transmittance βf （written as β1 for direction beam radiation） with zero soil reflectance for the downward radiation from above the canopy （i.e. sky）, and the other set is the canopy reflectance （αb） and transmittance βb for the upward radiation from below the canopy （i.e., ground）. Under the condition of the same plant architecture in the vertical layers, and the same leaf adaxial and abaxial optical properties in the canopies for the uniform diffuse radiation, the explicit solutions need only one set of basic solutions, because under this condition the two basic solutions are equal, i.e., αf = αb and βf = βb. Using the explicit analytical solutions, the fractions of any kind of incident solar radiation reflected from （defined as surface albedo, or canopy reflectance）, transmitted through （defined as canopy transmittance）, and absorbed by （defined as canopy absorptance） the canopy and other properties pertinent to the radiative transfer within the canopy can be estimated easily on the ground surface below the canopy （soil or snow surface） with any reflectance magnitudes. The simplified transfer model is proven to have a similar accuracy compared to the detailed model, as well as very efficient computing.

Numerical Simulation of the Marangoni Effect with Interphase Mass Transfer Between Two Planar Liquid Layers

The Marangoni effect induced by mass transfer at the interface between two immiscible liquids displays important influence on laboratory and industrial operation of solvent extraction. A systematic numerical study of the two-dimensional Marangoni effect in a two liquid layer system was conducted. The linear relationship of the inter- facial tension versus the solute concentration was incorporated into a mathematical model accounting for liquid flow and mass transfer in both phases. The typical cases analyzed by Sternling ＆ Scriven （AIChE J., 1959） using the linear instability theory were simulated bv the finite difference method and good agreement between the theory and the numerical simulation was observed. The simulation suggests that the Marangoni convection needs certain time to develop sufficiently in strength and scale to enhance the interphase mass transfer, the Marangoni effect is dynamic and transient, and remains at some stabilized level as long as the mass transfer driving force is kept con- stant. When certain level of shear is imposed at the interface as in most cases of practical significance, the Maran- goni effect is suppressed slightly but progressively as the shear is increased gradually. The present two-dimensional simulation of the Marangoni effect provides some insight into the underlying mechanism and also the basis for further theoretical study of the three-dimensional Marangoni effect in the real world and in chemical engineering applications.

Effect of SDBS on interfacial electron transfer at the liquid/liquid interface by thin layer method

The effect of an adsorbed anionic surfactant sodium dodecyl benzene sulfonate （SDBS） on electron transfer （ET） reaction between ferricyanide aqueous solution and decamethylferrocene （DMFc） located on the adjacent organic phase was investigated for the first time by thin layer method. The adsorption of SDBS at the interface resulted in a decay in the cathodic plateau current of bimolecular reaction with increasing concentrations of SDBS in aqueous phase. However, the rate constant of electron transfer （ket） increased monotonically as the SDBS concentrations increased from 0 to 200 p, moFL. The experimental results showed that SDBS formed patches on the interface and influenced the structure of electrical double layer. 2009 Xiao Quan Lu. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved.

Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer

In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.

Numerical Simulation of Heat Transfer Characteristics of Horizontal Ground Heat Exchanger in Frozen Soil Layer

A simplified numerical model of heat transfer characteristics of horizontal ground heat exchanger (GHE) in the frozen soil layer is presented and the steady-state distribution of temperature field is simulated. Numerical results show that the frozen depth mainly depends on the soil′s moisture content and ambient temperature. The heat transfer loss of horizontal GHE tends to grow with the increase of the soil′s moisture content and the decrease of ambient temperature. Backfilled materials with optimal thermal conductivity can reduce the thermal loss effectively in the frozen soil. The applicability of the Chinese national standard “Technical Code for Ground Source Heat Pump (GB 50366-2005)” is verified. For a ground source heat pump project, the feasible layout of horizontal GHE should be determined based on the integration of the soil′s structure, backfilled materials, weather data, and economic analysis.

Analytical solutions to a compressible boundary layer problem with heat transfer

The problem of momentum and heat transfer in a compressible boundary layerbehind a thin expansion wave was solved by the application of the similarity transformation and theshooting technique. Utilizing the analytical expression of a two-point boundary value problem formomentum transfer, the energy boundary layer solution was represented as a function of thedimensionless velocity, and as the parameters of the Prandtl number, the velocity ratio, and thetemperature ratio.

A Two-Layer Model for Superposed Electrified Maxwell Fluids in Presence of Heat Transfer

Based on a modified-Darcy-Maxwell model, two-dimensional, incompressible and heat transfer flow of two bounded layers, through electrified Maxwell fluids in porous media is performed. The driving force for the instability under an electric field, is an electrostatic force exerted on the free charges accumulated at the dividing interface. Normal mode analysis is considered to study the linear stability of the disturbances layers. The solutions of the linearized equations of motion with the boundary conditions lead to an implicit dispersion relation between the growth rate and wave number. These equations are parameterized by Weber number, Reynolds number, Marangoni number, dimensionless conductivities, and dimensionless electric potentials. The case of long waves interfaciaJ stability has been studied. The stability criteria are performed theoreticaily in which stability diagrams are obtained. In the limiting cases, some previously published results can be considered as particular cases of our results. It is found that the Reynolds number plays a destabilizing role in the stability criteria, while the damping influence is observed for the increasing of Marangoni number and Maxwell relaxation time.

Influence of Chemical Reaction and Thermal Radiation on MHD Boundary Layer Flow and Heat Transfer of a Nanofluid over an Exponentially Stretching Sheet

In the present article a numerical analysis has been carried out to study the boundary layer flow behavior and heat transfer characteristics of a nanofluid over an exponential stretching sheet. By assuming the stretching sheet to be impermeable, the effect of chemical reaction, thermal radiation, thermopherosis, Brownian motion and suction parameters in the presence of uniform magnetic field on heat and mass transfer are addressed. The governing system of equations is transformed into coupled nonlinear ordinary differential equations using suitable similarity transformations. The transformed equations are then solved numerically using the well known Runge-Kutta-Fehlberg method of fourth-fifth order. A detailed parametric study is performed to access the influence of the physical parameters on longitudinal velocity, temperature and nanoparticle volume fraction profiles as well as the local skin-friction coefficient, local Nusselt number and the local Sherwood number and the results are presented in both graphical and tabular forms.

Experimental study on convection heat transfer and air drag in sinter layer

Convection heat transfer coefficient and air pressure drop in sinter layer are important factors for the design of sinter cooling craft. Due to the lack of necessary data, the two parameters are studied by experimental method. The experimental results show that heat conduction of sinter impacts the measurement of convection heat transfer coefficient. Convection heat transfer increases with the increase of air volumetric flow rate. Sinter layer without small particles(sample I) gives higher convection heat transfer coefficient than that with small particles(sample II). Under the considered conditions, volumetric convection heat transfer coefficient is in the range of 400-1800 W/(m3·°C). Air pressure drop in sinter layer increases with the increase of normal superficial velocity, as well as with the rise of air temperature. Additionally, air pressure drop also depends on sinter particle size distribution. In considered experimental conditions, pressure drop in sinter sample II is 2-3 times that in sinter sample I, which resulted from 17% small scale particles in sinter sample II.

Boundary Layer Flow of an Unsteady Dusty Fluid and Heat Transfer Over a Stretching Sheet with Non-Uniform Heat Source/Sink

An analysis has been carried out to study the effect of hydrodynamic laminar boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface in the presence of non-uniform heat source/sink. Heat transfer characteristics are examined for two different kinds of boundary conditions, namely 1) variable wall temperature and 2) variable heat flux. The governing partial differential equations are transformed to system of ordinary differential equations. These equations are solved numerically by applying RKF-45 method. The effects of various physical parameters such as magnetic parameter, dust interaction parameter, number density, Prandtl number, Eckert number, heat source/sink parameter and unsteadiness parameter on velocity and temperature profiles are studied.

Fabrication of seeded substrates for layer transferrable silicon films

The layer transfer process is one of the most promising methods for low-cost and highly-efficient solar cells, in which transferrable mono-crystalline silicon thin wafers or films can be produced directly from gaseous feed-stocks. In this work, we show an approach to preparing seeded substrates for layer-transferrable silicon films. The commercial silicon wafers are used as mother substrates, on which periodically patterned silicon rod arrays are fabricated, and all of the surfaces of the wafers and rods are sheathed by thermal silicon oxide. Thermal evaporated aluminum film is used to fill the gaps between the rods and as the stiff mask, while polymethyl methacrylate （PMMA） and photoresist are used as the soft mask to seal the gap between the filled aluminum and the rods. Under the joint resist of the stiff and soft masks, the oxide on the rod head is selectively removed by wet etching and the seed site is formed on the rod head. The seeded substrate is obtained after the removal of the masks. This joint mask technique will promote the endeavor of the exploration of mechanically stable, unlimitedly reusable substrates for the kerfless technology.

Heat transfer for boundary layers with cross flow

An analysis is presented to study the dual nature of solutions for the forced convective boundary layer flow and heat transfer in a cross flow with viscous dissipation terms in the energy equation. The governing equations are transformed into a set of three self-similar ordinary differential equations by similarity transformations. These equations are solved numerically using the very efficient shooting method. This study reveals that the dual solutions of the transformed similarity equations for velocity and temperature distributions exist for certain values of the moving parameter, Prandtl number, and Eckert numbers. The reverse heat flux is observed for larger Eckert numbers; that is, heat absorption at the wall occurs.

Droplet transfer behavior of the stainless steel coated electrode with double-layer coating

In this paper, the droplet transfer behavior of the stainless steel coated electrode with double layer coating is researched by means of those experimental methods, such as high speed camera, collecting droplet in water, surfacing on the steel plate et al. The results show that the droplet transfer indexes of coated electrode are mainly controlled by the size of droplet, which affects the transfer behavior of droplet. The distribution characteristic of the droplet size of the electrode affects the numerical relationship among droplet transfer indexes. The metallurgical process of the coated electrode with double layer coating is carried out continuously in different zones. The main reason for the coated electrode with double layer coating gaining excellent usability quality is that the droplets realize the 'quasi flux wall guided transfer pattern'.

Zero-Magnetic-Field Oscillation of Spin Transfer Nano-Oscillator with a Second-Order-Perpendicular-Anisotropy Free Layer

The zero-magnetic-field oscillation behavior of spin torque nano-oscillator （STNO） with a perpendicularly mag- netized free layer with second-order uniaxial anisotropy is studied theoretically based on the Landau-Lifshitz- Cilbert-Slonczewski equation. It is demonstrated numerically that the second-order uniaxial anisotropy plays a significant role in the occurrence of a zero-magnetic-field steady-state precession, which can be understood in terms of the energy balance between the energy accumulation due to the spin torque and the energy dissipation due to the Gilbert damping. In particular, a relatively large zero-magnetic-field-oscillation current region, in which the corresponding microwave frequency is increased while the threshold current still maintains an almost constant value, can be obtained by modulating the second-order uniaxial anisotropy of the free layer. These results suggest a tunable zero-magnetic-field STNO, and it may be a promising configuration for STNO＇s applications in future wireless communications.

Boundary Layer Stagnation-Point Slip Flow and Heat Transfer towards a Shrinking/Stretching Cylinder over a Permeable Surface

In this paper, the boundary layer stagnation-point slip flow and heat transfer towards a shrinking/stretching cylinder over a permeable surface is considered. The governing equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into self-similar ordinary differential equations before they are solved numerically using the shooting method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the velocity slip parameter (α), the thermal slip parameter (β), the curvature parameter (γ) and the velocity ratio parameter (c/a). The physical quantities of interest are the skin friction coefficient and the local Nusselt number measured by f’’(0) and –θ’(0), respectively. The numerical results show that the velocity slip parameter α increases the heat transfer rate at the surface, while the thermal slip parameter β decreases it. On the other hand, increasing the velocity slip parameter α causes the decrease in the flow velocity. Further, it is found that the solutions for a shrinking cylinder (c/ac/a>0) case. Finally, it is also found that the values of f’’(0) and –θ’(0) increase as the curvature parameter γ increases.

Experimental Study of Heat Transfer in a Real Scale Building Incorporating PCM in the Air Layer of the Vertical Walls

The purpose of this paper is to study the energy efficiency of a local living space exposed to solar radiation in the subtropical climate of Casablanca. The study was mainly focused on the contribution of a phase change material (PCM), inserted into a 7-cm thick air layer of a double brick wall, in two different locations. We note that the experimental study was conducted using two real-scale test cavities, located in the Faculty of Science Ain Chock-Casablanca. Two PCM mounting methods were used for the south and west walls, in order to test its energy efficiency as a storage and retrieval means of the solar flux coming from the outside. In the case of the southern wall, the PCM is put directly on the internal side of the outside part of the double wall (Case 1). For the west wall, the PCM is placed 1.2 cm away from the internal side of the outer part of the double wall (Case 2). The first result shows that the PCM placed to the wall allows storing the solar heat during the day and releasing it to the outside of the building at night. While in the second case, the PCM keeps the heat stored day and night.

Predicting Mass Transfer Extraction with Steam Flow, Applying Boundary-Layer Concepts

Theory and concepts of boundary layer mass transfer is applied to correlate experimental data on extraction of essential oils from vegetable leaves and stems, using steam. From these theory, concepts and experimental data with seven systems, two correlations are developed to predict the Sherwood number and mass transfer coefficient as function of Reynolds and Schmidt numbers. From these equations, the molar flux, the amount of solute extracted, and the yield of extraction is predicted. A steam of higher temperature normally improves the mass transfer and the yield. A method to estimate the enhancement for temperature increase is proposed. The correlations developed are applied to a case with industrial size that was no part of the data for correlation generation. Theory may be applied for industrial applications.

Effects of Hall Current on MHD Boundary Layer Second-Order Viscoelastic Fluid Flow Induced by a Continuous Surface with Heat Transfer

Effects of Hall current on heat transfer and magnetohydrodynamic (MHD) boundary layer flow induced by a continuous surface in a parallel free stream of a second-order viscoelastic fluid are studied for uniform suction/injection by taking viscous dissipation into account. Complex nonsimilar solutions to the stream function and temperature are developed by means of an elegant technique, known as homotopy analysis method (HAM). Convergence of the solutions is ensured with the help of -curves. Graphical and tabular results for the effects of Hall current reveal that it has a significant influence on: complex velocity, complex temperature, magnitude of the shear stress at the surface, magnitude of the rate of heat transfer at the surface and on boundary layer thickness.

Effects of Solid Matrix and Porosity of Porous Medium on Heat Transfer of Marangoni Boundary Layer Flow Saturated with Power-Law Nanofluids

The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.