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International Journal of Minerals,Metallurgy and Materials 2011年第4期18卷 502-507页

作者： Kartini Ahmad Roslinda Nazar Ioan Pop Centre for Foundation Studies International Islamic University Malaysia46350 Petaling JayaSelangorMalaysia School of Mathematical Sciences Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia43600 UKM BangiSelangorMalaysia Faculty of Mathematics University of ClujR-3400 ClujCP 253Romania

The steady laminar mixed convection boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretched vertical surface with prescribed skin friction were *** governing partial differential equations were transformed into a system of ordinary differential equations,which were then solved numerically using the shooting *** for the stretching velocity,the local Nusselt number,the temperature,and the velocity profiles are presented for various values of the mixed convection parameter λ and material parameter K when the Prandtl number is equal to *** assisting（heated plate） and opposing（cooled plate） flow regions are *** is found that dual solutions exist for both assisting and opposing flows.

关键词： boundary layer flow dual solutions micropolar fluids mixed convection skin friction

Influences of the Exhaust flow on the boundary layer flow on the Wafer Surface in Spin Coating System

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Journal of Thermal Science 2005年第2期14卷 130-135页

作者： Seiichi KIMURA Mizue MUNEKATA Hiroaki KURISHIMA Kazuyoshi MATSUZAKI Hideki OHBA Graduate School of Science and Technology Kumamoto University Mechanical Engineering and Materials Science Kumamoto UniversityTokyo Electron Kyushu LTDTokyo Electron AT LTDMechanical Engineering and Materials Science Kumamoto University

Recently, development of high technology has been required for the formation of thin uniform film in manufacturing processes of semiconductor as the semiconductor become more sophisticated. Spin coating is usually used for spreading photoresist on a wafer surface. However, since rotating speed of the disk is very high in spin coating, the dropped resist scatters outward and reattaches to the film surface. So, the scattered resist is removed by the exhaust flow generated at the gap between the wafer edge and the catch cup. It is seriously concerned that the stripes called Ekman spiral vortices appears on the disk in the case of high rotating speed and the film thickness increases near the wafer edge in the case of low rotating speed, because it prevent the formation of uniform film. The purpose of this study is to make clear the generation mechanism of Ekman spiral vortices and the influence of exhaust flow on it Moreover the influence of the catch cup geometry on the wafer surface boundary layer flow is investigated.

关键词： rotating disk flow spin coating boundary layer flow hot-wire measurement

Numerical Investigation on Inviscid Instability of Streaky Structures in Incompressible boundary layer flow

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Chinese Physics Letters 2010年第8期27卷 110-113页

作者：刘建新罗纪生 Department of Mechanics Tianjin University T~anjin 300072

Numerical investigation is made on the effect of streaky structures in transition by inviscid linear disturbance equation with temporal mode. Several disturbances with different streamwise wave numbers were induced, and the evolutions with time step were received. It suggests that the exponential growth and periodic variation of the waves are in existence. As the streamwise wave number increases, the disturbance growth rate begins by increasing, reaches a maximum at around α=0.4 with a disturbance frequency of 0.2186 ＋ 0.001457i, and then decreases. Furthermore, the eigenfunctions of pressure disturbance are plotted.

关键词： Growth Streaky Structures boundary layer flow

Effect of Catch Cup Geometry on 3D boundary layer flow over the Wafer Surface in a Spin Coating

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Journal of Thermal Science 2008年第1期17卷 56-60页

作者： Mizue MUNEKATA Seiichi KIMURA Hiroaki KURISHIMA Jinsuke TANAKA Sohei YAMAMOTO Hiroyuki YOSHIKAWA Kazuyoshi MATSUZAKI Hideki OHBA Department of Mechanical System Engineering 2-39-1 KurokamiKumamoto860-8555 Japan Assistant Professor Graduate School of Science and Technology Kumamoto University2-39-1 KurokamiKumamoto860-8555 Japan Tokyo Electron Kyushu LTD. 1-1 FukuharaKoushi-shiKumamoto861-1116 Japan Department of Mechanical System Engineering 2-39-1 KurokamiKumamoto860-8555 Japan Tokyo Electron LTD. 650 MitsuzawaHosaka-choNirasaki-shiYamanashi407-0192 Japan

Recently, development of high technology has been required for the formation of thin uniform film in manufacturing processes of semiconductor as the semiconductor instruments become more sophisticated. Spin coating is usually used for spreading photoresist on a wafer surface. However, since rotating speed of the disk is very high in spin coating, the dropped photoresist scarers outward and reattaches on the film surface. A catch cup is set up outside the wafer in spin coating, and scattered photoresist mist is removed from the wafer edge by the exhaust flow generated at the gap between the wafer edge and the catch cup. In the dry process of a spin coating, it is a serious concern that the film thickness increases near the wafer edge in the case of low rotating speed. The purpose of this study is to make clear the effect of the catch cup geometry on the 3D boundary layer flow over the wafer surface and the drying rate of liquid film.

关键词： Rotating disk Spin coating boundary layer flow Laser Doppler velocimeter Infrared camera

Dual solutions in boundary layer flow of Maxwell fluid over a porous shrinking sheet

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Chinese Physics B 2014年第12期23卷 289-292页

作者： Krishnendu Bhattacharyya Tasawar Hayat Ahmed Alsaedi Department of Mathematics The University of Burdwan Department of Mathematics Quaid-I-Azam University Department of Mathematics Faculty of Science King Abdulaziz University

An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarity transformations, the governing partial differential equations（PDEs） are converted into a nonlinear self-similar ordinary differential equation（ODE）. For the numerical solution of transformed self-similar ODE, the shooting method is applied. The study reveals that the steady flow of Maxwell fluid is possible with a smaller amount of imposed mass suction compared with the viscous fluid flow. Dual solutions for the velocity distribution are obtained. Also, the increase of Deborah number reduces the boundary layer thickness for both solutions.

关键词： dual solutions boundary layer flow Maxwell fluid porous shrinking sheet

Soret and Dufour effects on mixed convection unsteady MHD boundary layer flow over stretching sheet in porous medium with chemically reactive species

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Applied Mathematics and Mechanics(English Edition) 2014年第7期35卷 849-862页

作者： A.NAYAK S.PANDA D.K.PHUKAN Silicon Institute of Technology Bhubaneswar 751024 India Department of Mathematics National Institute of Technology Calicut 673601 India Department of Mathematics Moran College Moranhat Assam 785670 India

This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of t^he stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations .and solved numerically by the Runge-Kutta fourth order scheme in as- sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph- ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.

关键词： heat and mass transfer boundary layer flow porous media magnetic field,Soret number Dufour number

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Open Journal of Fluid Dynamics 2016年第4期6卷 279-302页

作者： Mohammed Nasir Uddin Md. Yeakub Ali N. M. Ridwan Zahed Md. Jashim Uddin Department of Mathematics Chittagong University of Engineering & Technology Chittagong Bangladesh Department of Electrical & Electronic Engineering International Islamic University Chittagong Chittagong Bangladesh

Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.

关键词： Similarity Solution Unsteady flow Mixed Convection boundary layer flow Horizontal Plate Incompressible Fluid

boundary layer DEVELOPMENT OF PULSATILE BLOOD flow IN A TAPERED VESSEL

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Applied Mathematics and Mechanics(English Edition) 1993年第4期14卷 319-326页

作者：岑人经秦婵 South China University of Technology Guangzhou

The problems of developing flow under unsteady oscillatory condition were studied in this paper by assuming that the tapered angle is small. The formula of velocity distribution was obtained. The analyses for the results show that the blood flow in a converging tapered vessel remains a developing flow throughout the length, and the effects of tapered angle on the developing flow increase with the tapered angle.

关键词： Biomechanics Blood boundary layer flow

TURBULENT boundary layer DEVELOPMENT IN THE ENTRANCE REGION OF A SMOOTH ROUND PIPE

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Journal of Hydrodynamics 1992年第3期4卷 17-26页

作者： Ning, Lizhong Li, Jianzhong Shaanxi Inst of Mechanical Engineering Xi'an China

Feature of the turbulent boundary layer along a smooth round pipe is a fundamental to further study of inlet length and flow resistance, therefore, it has been of great significance both in practice and in theory. In this paper, the formulae for calculating the turbulent boundary layer thickness were obtained by solving the momentum integral equation of the boundary layer in which the assumption of the logarithmic law and the exponential law of velocity distribution were adopted. The method for calculating the mean flow velocity in the developing region of turbulent boundary layer in a round pipe was proposed. The relationship between the exponent n and the factor was studied and a formula for calculating the exponent n was obtained.

关键词： boundary layer flow boundary layers Turbulent flow

HOT WIRE MEASUREMENT OF TURBULENT boundary layer ON A FILM COOLING PLATE WITH DIFFUSION HOLES

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Journal of Hydrodynamics 2001年第2期13卷 15-23页

作者： Shi, H.H. Kiriyama, K. Itoh, M. Dept. of Mechanics Zhejiang Univ. Hangzhou 310027 China

This study experimentally investigated the film cooling flowfield of a single row of diffusion holes, from which the secondary air flow was injected into a turbulent boundary layer with zero pressure gradient on a flat plate. Circular-shaped holes were also tested as a basis for comparison. All the holes were inclined downstream at 35° with respect to the surface and the lateral spacing between the holes was 3 diameters of the hole. The mainstream velocity was maintained at 17 m/s and the Reynolds number based on the injection hole diameter was almost 11000. The density ratio of the jet to mainstream was 1.0, and the jet-to-mainstream velocity ratios M were 0.5 and 1.5. Normal-type and X-type hot wire anemometries were used to measure the streamwise mean velocity and its components, the normal and shear turbulent Reynolds stress components at the locations from the backward edge of the injection hole to 25 diameters downstream.

关键词： boundary layer flow Cooling Turbulent flow Vectors Velocity Wind tunnels