DOCSLIB.ORG

Steady Mixed Convection Stagnation Point Flow of MHD Oldroyd-B Fluid

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Steady Mixed Convection Stagnation Point Flow of MHD Oldroyd-B Fluid Journal of the Egyptian Mathematical Society (2014) xxx, xxx–xxx Egyptian Mathematical Society Journal of the Egyptian Mathematical Society www.etms-eg.org www.elsevier.com/locate/joems ORIGINAL ARTICLE Steady mixed convection stagnation point flow of MHD Oldroyd-B fluid over a stretching sheet M. Sajid a, B. Ahmed b, Z. Abbas c,* a Theoretical Physics Division, PINSTECH, P.O. Nilore, Islamabad 44000, Pakistan b Department of Basic Sciences, Riphah International University, Islamabad 44000, Pakistan c Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan Received 3 June 2013; revised 30 April 2014; accepted 29 May 2014 KEYWORDS Abstract This study deals with the steady mixed convection stagnation point flow of an incom- Mixed convection; pressible Oldroyd-B fluid over the stretching sheet in the presence of a constant applied magnetic Stagnation point flow; field. It is assumed that the surface temperature varies linearly with the distance from the stagnation Oldroyd-B fluid; point. A coupled system of non-linear differential equations is developed by employing the similar- Magnetic field; ity transformations. To analyze the behavior of the velocity, temperature, skin friction coefficient Finite difference method and rate of heat transfer through the wall, a numerical solution is developed using finite difference scheme. The obtained results are used to discuss the influence of pertinent parameters of interest. 2010 MATHEMATICS SUBJECT CLASSIFICATION: 65N06; 76D05; 76R99 ª 2014 Production and hosting by Elsevier B.V. on behalf of Egyptian Mathematical Society. 1. Introduction process, manufacturing of sheets, coating and paper produc- tion. The initial work was investigated by Sakiadis [1] for The analysis regarding the fluid flow and heat transfer over a two-dimensional boundary layer flow when the plate is moving stretching sheet is a subject of interest for many researchers with constant velocity. The Sakiadis’s problem for heat transfer working in the area of the two-dimensional boundary layer analysis was studied by Erickson et al. [2]. In the above mention flows. The reasons lie in the fact that such kinds of investiga- studies the velocity of the sheet is assumed to be constant. This tions have applications in the manufacturing industry. assumption of constant velocity is adequate when we are inter- For example, in many manufacturing processes such as glass ested in the analysis of continuous extrusion of polymer sheets. fiber production, hot rolling, continuous casting, extrusion Due to the flexibility of polymer materials, a stretching may occur. Crane [3] found a closed form solution for boundary layer * Corresponding author. Tel.: +92 62 9255480. flow by imposing the condition of stretching wall. He assumed a E-mail address: [email protected] (Z. Abbas). linear variation of stretching velocity with respect to the distance Peer review under responsibility of Egyptian Mathematical Society. from the origin. The Crane’s problem for viscous fluid was extended in different directions in the literatures [4–9],etc. In above mentioned Refs. [3–9], the fluid flow is induced due to the motion of the surface. But in many real situations Production and hosting by Elsevier the thermal buoyancy is also play part for the occurrence of http://dx.doi.org/10.1016/j.joems.2014.05.013 1110-256X ª 2014 Production and hosting by Elsevier B.V. on behalf of Egyptian Mathematical Society. Please cite this article in press as: M. Sajid et al., Steady mixed convection stagnation point flow of MHD Oldroyd-B fluid over a stretching sheet, Journal of the Egyptian Mathematical Society (2014), http://dx.doi.org/10.1016/j.joems.2014.05.013 2 M. Sajid et al. @u @v fluid flow. Therefore, the flow behavior is analyzed under the þ ¼ 0; ð1Þ influence of both the mechanism; the motion of solid surface @x @y and buoyancy. These buoyancy forces occurs due to the heat- @u @u @2u @2u @2u @2u ing and cooling of stretching sheets resulting in producing u þ v ¼K u2 þ 2uv þv2 þa2x þm @x @y 1 @x2 @x@y @y2 @y2 changes to both flow and temperature fields as discussed by Chen and Strobel [10]. The literature survey indicates that @3v @3u @u @2u @u @2v @u þmK u þ v À À þ rB2 ax À u ÀK v work in this direction is carried out by many workers in the 2 2 @y3 @x @y2 @y @y2 0 1 @y @x@ y field [11–14] and reference therein. On the other hand, the con- @T @T @u þgb ðT ÀT ÞþK þ v À ðTÀ T Þ ; ð2Þ stitutive relationships for rate type fluids are implicit and elim- 1 1 @x @y @x 1 ination of stress components from the equation of motion is not straightforward. This fact is the major cause for the lack @T @T k @2T l @u 2 u v ; 3 of literature on the two-dimensional flow of rate type fluids. þ ¼ 2 þ ð Þ @x @y qcp @y qcp @y The simplest class of rate type fluids is the Maxwell fluid and one can find a number of articles regarding the stretching flow where u and v are the velocity components in the x and y direc- of Maxwell fluid [15–20] and reference there in. However, for tions respectively, m is the kinematics viscosity of fluid, p is the an Oldroyd-B fluid there are only two studies regarding the pressure, q is the density of the fluid, K 1 is the relaxation time, flow over a stretching sheet [21,22]. K2 is the retardation time, g is the gravitational acceleration, b On the other hand, an extensive literature can be found on is the thermal expansion coefficient, cp is the specific heat, k is the mixed convection flow of Non-Newtonian fluids over the thermal diffusivity and T is the temperature. continuously moving surfaces. Mixed convection flow of a The appropriate boundary conditions applicable to the non-Newtonian micropolar fluid was discussed by Takhar present flow problem are: et al. [23]. Mushtaq et al. [24] considered the steady mixed con- u ¼ uwðxÞ¼cx; v ¼ 0; T ¼ TwðxÞ¼T1 þ bx at y ¼ 0; vection flow of a second grade fluid by considering the case of @u variable surface temperature. The steady mixed Convection u ¼ ueðxÞ¼ax; ! 0; T ¼ T1 as y !1: ð4Þ flow of a micropolar fluid near the stagnation point on a @y vertical surface is studied by Lok et al. [25]. In 2008 , Hayat in which both a and c have the dimension of (time)À1 and b is a et al. [26] investigated the series solution for the mixed convec- positive constant. Here, the forth condition in Eq. (4) is the tion flow of a micropolar fluid over a non-linear stretching augmented condition discussed by Grag and Rajagopal [29] . sheet using homotopy analysis method. Recently, Hsiao [27] Introducing the standard similarity transformations for a studied the heat, mass transfer and mixed convection for stretching flow MHD flow of a viscoelastic fluid past a continuously moving rffiffiffi pffiffiffiffiffi T À T c surface with Ohmic dissipation numerically. Very recently, u ¼ cxf0ðgÞ; v ¼ cmfðgÞ; hðgÞ¼ 1 ; g ¼ y: the mixed convection in the stagnation-point flow of a Maxwell Tw À T1 m fluid toward a vertical stretching sheet has been investigated by ð5Þ Abbas et al. [28]. They have discussed the results both analyti- Governing flow problem takes the form cally using homotopy analysis method (HAM) and numerically 000 02 00 a2 2 a 0 00 0 using finite difference method. To best of our knowledge, no f À f þ ff þ 2 þ M ð À f À k1ff ÞþArðÞh À k1fh c c ÀÁ ð6Þ such attention has been given for the mixed convection flow 0 00 2 000 002 iv þk1ðÞþ2ff f À f f k2 f À ff ¼ 0; of an Oldroyd-B fluid. Our aim was to discuss the mixed con- 00 0 0 002 vection in the stagnation-point flow of an Oldroyd-B fluid over h þ Prðfh À hf ÞþPrEcf ¼ 0; ð7Þ a stretching sheet. As a first step the boundary layer equations f ¼ 0; f0 ¼ 1; h ¼ 1atg ¼ 0; under these assumptions have been developed and then a a f0 ¼ ; f00 ¼ 0; h ¼ 0asg !1: ð8Þ numerical solution by employing a finite difference method is c presented for the transformed nonlinear coupled ordinary Here prime denotes derivative with respect to g and k1 = K1c differential equations. The effects of various involving physical and k2 = K2c are the dimensionless material parameters of the parameters on the flow and temperature distributions are 2 2 fluid and Ar = Gr/Re is the Archimedes number, Gr = gbb/m discussed through graphs and tables. is the Grashof number, Re = c/m is the Reynolds number and 2 2 M ¼ rB0=cq is the Hartmann number. 2. Formulation of the problem 3. Results and discussion Consider an incompressible, two-dimensional Oldroyd-B fluid in the region of a stagnation point over a semi-infinite, imper- The numerical procedure explained in detail by Sajid et al. [22] meable stretching sheet at y = 0. The assumed stretching is adopted for the solution of the transformed Eqs. (6)–(8). The velocity and wall temperature of the sheet is uw(x)=cx, with effects of the involving parameters for example, the dimension- c > o and Tw(x)=bx, with b > 0, respectively. Far away less relaxation/retardation times (k1,k2), the Hartmann number from the plate the external flow velocity is ue(x)=ax, with M, the ratio of the external flow rate to the stretching rate a/c , a > 0 and we assume that body attains a uniform temperature the Archimedes number Ar , the Prandtl number Pr and the 0 T1 outside the boundary layer.
Load more

Recommended publications
  • A Two-Layer Turbulence Model for Simulating Indoor Airflow Part I
    Energy and Buildings 33 +2001) 613±625 A two-layer turbulence model for simulating indoor air¯ow Part I. Model development Weiran Xu, Qingyan Chen* Department of Architecture, Massachusetts Institute of Technology, 77 Massachusetts Avenue, MA 02139, USA Received 2 August 2000; accepted 7 October 2000 Abstract Energy ef®cient buildings should provide a thermally comfortable and healthy indoor environment. Most indoor air¯ows involve combined forced and natural convection +mixed convection). In order to simulate the ¯ows accurately and ef®ciently, this paper proposes a two-layer turbulence model for predicting forced, natural and mixed convection. The model combines a near-wall one-equation model [J. Fluid Eng. 115 +1993) 196] and a near-wall natural convection model [Int. J. Heat Mass Transfer 41 +1998) 3161] with the aid of direct numerical simulation +DNS) data [Int. J. Heat Fluid Flow 18 +1997) 88]. # 2001 Published by Elsevier Science B.V. Keywords: Two-layer turbulence model; Low-Reynolds-number +LRN); k±e Model +KEM) 1. Introduction This paper presents a new two-layer turbulence model that performs two tasks: 1.1. Objectives 1. It can accurately predict flows under various conditions, i.e. from purely forced to purely natural convection. This Energy ef®cient buildings should provide a thermally model allows building ventilation designers to use one comfortable and healthy indoor environment. The comfort single model to calculate flows instead of selecting and health parameters in indoor environment include the different turbulence models empirically from many distributions of velocity, air temperature, relative humidity, available models. and contaminant concentrations. These parameters can be 2.
    [Show full text]
  • Sedimentation of Finite-Size Spheres in Quiescent and Turbulent Environments
    Under consideration for publication in J. Fluid Mech. 1 Sedimentation of finite-size spheres in quiescent and turbulent environments Walter Fornari1y, Francesco Picano2 and Luca Brandt1 1Linn´eFlow Centre and Swedish e-Science Research Centre (SeRC), KTH Mechanics, SE-10044 Stockholm, Sweden 2Department of Industrial Engineering, University of Padova, Via Venezia 1, 35131 Padua, Italy (Received ?; revised ?; accepted ?. - To be entered by editorial office) Sedimentation of a dispersed solid phase is widely encountered in applications and envi- ronmental flows, yet little is known about the behavior of finite-size particles in homo- geneous isotropic turbulence. To fill this gap, we perform Direct Numerical Simulations of sedimentation in quiescent and turbulent environments using an Immersed Boundary Method to account for the dispersed rigid spherical particles. The solid volume fractions considered are φ = 0:5 − 1%, while the solid to fluid density ratio ρp/ρf = 1:02. The par- ticle radius is chosen to be approximately 6 Komlogorov lengthscales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reduction with respect to a single particle in quiescent fluid is about 12% and 14% for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated to the intermittent fast sedimentation of particle pairs in drafting-kissing-tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable mag- nitude as a consequence of the highly intermittent behavior observed in the quiescent fluid.
    [Show full text]
  • Suspensions of Finite-Size Rigid Particles in Laminar and Turbulent
    Suspensions of finite-size rigid particles in laminar and turbulentflows by Walter Fornari November 2017 Technical Reports Royal Institute of Technology Department of Mechanics SE-100 44 Stockholm, Sweden Akademisk avhandling som med tillst˚andav Kungliga Tekniska H¨ogskolan i Stockholm framl¨agges till offentlig granskning f¨or avl¨aggande av teknologie doctorsexamenfredagen den 15 December 2017 kl 10:15 i sal D3, Kungliga Tekniska H¨ogskolan, Lindstedtsv¨agen 5, Stockholm. TRITA-MEK Technical report 2017:14 ISSN 0348-467X ISRN KTH/MEK/TR-17/14-SE ISBN 978-91-7729-607-2 Cover: Suspension offinite-size rigid spheres in homogeneous isotropic turbulence. c Walter Fornari 2017 � Universitetsservice US–AB, Stockholm 2017 “Considerate la vostra semenza: fatti non foste a viver come bruti, ma per seguir virtute e canoscenza.” Dante Alighieri, Divina Commedia, Inferno, Canto XXVI Suspensions offinite-size rigid particles in laminar and tur- bulentflows Walter Fornari Linn´eFLOW Centre, KTH Mechanics, Royal Institute of Technology SE-100 44 Stockholm, Sweden Abstract Dispersed multiphaseflows occur in many biological, engineering and geophysical applications such asfluidized beds, soot particle dispersion and pyroclastic flows. Understanding the behavior of suspensions is a very difficult task. Indeed particles may differ in size, shape, density and stiffness, their concentration varies from one case to another, and the carrierfluid may be quiescent or turbulent. When turbulentflows are considered, the problem is further complicated by the interactions between particles and eddies of different size, ranging from the smallest dissipative scales up to the largest integral scales. Most of the investigations on this topic have dealt with heavy small particles (typically smaller than the dissipative scale) and in the dilute regime.
    [Show full text]
  • Dimensional Analysis and Modeling
    cen72367_ch07.qxd 10/29/04 2:27 PM Page 269 CHAPTER DIMENSIONAL ANALYSIS 7 AND MODELING n this chapter, we first review the concepts of dimensions and units. We then review the fundamental principle of dimensional homogeneity, and OBJECTIVES Ishow how it is applied to equations in order to nondimensionalize them When you finish reading this chapter, you and to identify dimensionless groups. We discuss the concept of similarity should be able to between a model and a prototype. We also describe a powerful tool for engi- I Develop a better understanding neers and scientists called dimensional analysis, in which the combination of dimensions, units, and of dimensional variables, nondimensional variables, and dimensional con- dimensional homogeneity of equations stants into nondimensional parameters reduces the number of necessary I Understand the numerous independent parameters in a problem. We present a step-by-step method for benefits of dimensional analysis obtaining these nondimensional parameters, called the method of repeating I Know how to use the method of variables, which is based solely on the dimensions of the variables and con- repeating variables to identify stants. Finally, we apply this technique to several practical problems to illus- nondimensional parameters trate both its utility and its limitations. I Understand the concept of dynamic similarity and how to apply it to experimental modeling 269 cen72367_ch07.qxd 10/29/04 2:27 PM Page 270 270 FLUID MECHANICS Length 7–1 I DIMENSIONS AND UNITS 3.2 cm A dimension is a measure of a physical quantity (without numerical val- ues), while a unit is a way to assign a number to that dimension.
    [Show full text]
  • On Dimensionless Numbers
    chemical engineering research and design 8 6 (2008) 835–868 Contents lists available at ScienceDirect Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd Review On dimensionless numbers M.C. Ruzicka ∗ Department of Multiphase Reactors, Institute of Chemical Process Fundamentals, Czech Academy of Sciences, Rozvojova 135, 16502 Prague, Czech Republic This contribution is dedicated to Kamil Admiral´ Wichterle, a professor of chemical engineering, who admitted to feel a bit lost in the jungle of the dimensionless numbers, in our seminar at “Za Plıhalovic´ ohradou” abstract The goal is to provide a little review on dimensionless numbers, commonly encountered in chemical engineering. Both their sources are considered: dimensional analysis and scaling of governing equations with boundary con- ditions. The numbers produced by scaling of equation are presented for transport of momentum, heat and mass. Momentum transport is considered in both single-phase and multi-phase flows. The numbers obtained are assigned the physical meaning, and their mutual relations are highlighted. Certain drawbacks of building correlations based on dimensionless numbers are pointed out. © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Dimensionless numbers; Dimensional analysis; Scaling of equations; Scaling of boundary conditions; Single-phase flow; Multi-phase flow; Correlations Contents 1. Introduction .................................................................................................................
    [Show full text]
  • Dimensional Analysis and Modeling
    cen72367_ch07.qxd 10/29/04 2:27 PM Page 269 CHAPTER DIMENSIONAL ANALYSIS 7 AND MODELING n this chapter, we first review the concepts of dimensions and units. We then review the fundamental principle of dimensional homogeneity, and OBJECTIVES Ishow how it is applied to equations in order to nondimensionalize them When you finish reading this chapter, you and to identify dimensionless groups. We discuss the concept of similarity should be able to between a model and a prototype. We also describe a powerful tool for engi- ■ Develop a better understanding neers and scientists called dimensional analysis, in which the combination of dimensions, units, and of dimensional variables, nondimensional variables, and dimensional con- dimensional homogeneity of equations stants into nondimensional parameters reduces the number of necessary ■ Understand the numerous independent parameters in a problem. We present a step-by-step method for benefits of dimensional analysis obtaining these nondimensional parameters, called the method of repeating ■ Know how to use the method of variables, which is based solely on the dimensions of the variables and con- repeating variables to identify stants. Finally, we apply this technique to several practical problems to illus- nondimensional parameters trate both its utility and its limitations. ■ Understand the concept of dynamic similarity and how to apply it to experimental modeling 269 cen72367_ch07.qxd 10/29/04 2:27 PM Page 270 270 FLUID MECHANICS Length 7–1 ■ DIMENSIONS AND UNITS 3.2 cm A dimension is a measure of a physical quantity (without numerical val- ues), while a unit is a way to assign a number to that dimension.
    [Show full text]
  • Three-Dimensional Buoyant Turbulent Flows in a Scaled Model, Slot-Ventilated, Livestock Conhnement Facility
    THREE-DIMENSIONAL BUOYANT TURBULENT FLOWS IN A SCALED MODEL, SLOT-VENTILATED, LIVESTOCK CONHNEMENT FACILITY S. J. Hoff, K. A. Janni, L. D. Jacobson MEMBER MEMBER MEMBER ASAE ASAE ASAE ABSTRACT influences the velocity and temperature distributions A three-dimensional turbulence model was used to throughout the space. determine the effects of animal-generated buoyant forces Little information exists on velocity and temperature on the airflow patterns and temperature and airspeed distributions throughout a ventilated space beyond the distributions in a ceiling-slot, ventilated, swine grower inlet-jet-affected region. Spatial conditions generally have facility. The model incorporated the Lam-Bremhorst been described qualitatively based on overall airflow turbulence model for low-Reynolds Number airflow typical patterns. The microclimate of the animal, as a function of of slot-ventilated, livestock facilities. The predicted results the inlet conditions for winter conditions when the from the model were compared with experimental results potential for animal chilling is the greatest, is of prime from a scaled-enclosure. The predicted and measured concern. results indicated a rather strong cross-stream recirculation Mixed-flow ventilation research related to animal zone in the chamber that resulted in substantial three- confinement facilities has attempted to characterize the dimensional temperature distributions for moderate to desired inlet conditions based on the inlet jet behavior as it highly buoyancy-affected flows. Airflow patterns were enters the ventilated space. In the past, recommendations adequately predicted for Ar^ > 40 and J values < 0.00053. specified that the desired inlet velocity be maintained For Ar^ < 40 and J values > 0.00053, the visualized between 4.0 and 5.0 m/s.
    [Show full text]
  • Introduction
    1 Chapter 1 Introduction Granular materials and their suspension in liquids are prevalent in a wide range of natural and man-made processes. These include the industrial handling of seeds and slurries, clogging of drilling wells, and geological phenomena such as landslides and debris flows. Because of the complexity of having more than one phase (the solid and the fluid one), most of the understanding of how these materials flow is based on empirical observations, hampering, for example, the design of efficient transport of a suspension of solids in a fluid medium. Therefore the goal of this research is to help develop constitutive models that predict how liquid-solid mixtures behave when sheared as a function of various physical parameters, using carefully controlled experiments to validate and refine such models. The work presented in this thesis focuses on liquid-solid mixtures, and unlike the mechanics of dry granular material flows which are dominated by collisions and friction, the mechanics for these mixtures involve the interaction between the solid particles, the inertial effects from both liquid and solid phase, and viscous effects of the liquid. In particular, the effects of particle concentration and the density ratio between the two phases are studied under shear conditions where particle collisions might become important. A review of previous rheological experiments and the key parameters that govern the behavior of liquid-solid mixtures is presented. 1.1 Rheology of non-inertial suspensions There is an extensive work done in the rheology of suspensions; however, most of these studies cover mixtures with low Reynolds number (Re) (from 10−6 to 10−3), where Re is defined as Re = ργd˙ 2/µ, ρ and µ are the density and dynamic viscosity of the suspending liquid,γ ˙ , is the shear rate and d is the particle diameter.
    [Show full text]
  • Rayleigh Number Dependence of the Archimedes Number Dependent Large- Scale Flow Structure Formation in Mixed Convection
    15TH EUROPEAN TURBULENCE CONFERENCE, 25-28 AUGUST, DELFT,. THE NETHERLANDS RAYLEIGH NUMBER DEPENDENCE OF THE ARCHIMEDES NUMBER DEPENDENT LARGE- SCALE FLOW STRUCTURE FORMATION IN MIXED CONVECTION Max Körner1, Christian Resagk1 & André Thess2 1Technische Universität Ilmenau, Ilmenau, Germany 2German Aerospace Center, Stuttgart, Germany Abstract We report on the experimental investigations of large-scale flow structure formation in mixed convection. We characterize the flow field by measuring the velocity fields within a rectangular model room using 2D2C PIV. The control parameters are the Reynolds number Re, the Rayleigh number Ra and the Prandtl number Pr. All parameters are linked through the Archimedes number Ar. In 6.410-2 ≤ Ar ≤ 1.39101, 4.2103 ≤ Re ≤ 6.35104 and Ra = 3.1107, Ra = 1.8108 and Pr = 0.713 we found flow 3 different flow structures. While keeping Ra and Pr constant and varying Ar through Re variations, we found an Ar dependence of the large- scale flow structure formation within 6.410-2 ≤ Ar ≤ 1.39101. Furthermore, we found a Ra dependence of the structure formation, which shifts the transition points between the structures to higher Archimedes numbers and reduces the mean velocities within the investigated domain. INTRODUCTION Mixed convection is defined as the temporal and spatial superposition of natural and forced convection and is driven by inlet velocity uin and a temperature gradient ∆T within a gravity field. In most applications, e.g. indoor airflows, this flow is turbulent and its temperature and velocity field is dominated by the formation of large-scale flow structures, as comprehensively studied in Rayleigh-Benard-Convection (RBC) (review of RBC see e.g.
    [Show full text]
  • The Proposed Heat Sink Configuration Is Primarily Orientated Towards
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by City Research Online City Research Online City, University of London Institutional Repository Citation: Karathanassis, I. K., Papanicolaou, E., Belessiotis, V. & Bergeles, G. (2013). Effect of secondary flows due to buoyancy and contraction on heat transfer in a two-section plate-fin heat sink. International Journal of Heat and Mass Transfer, 61(1), pp. 583-597. doi: 10.1016/j.ijheatmasstransfer.2013.02.028 This is the accepted version of the paper. This version of the publication may differ from the final published version. Permanent repository link: http://openaccess.city.ac.uk/18287/ Link to published version: http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.02.028 Copyright and reuse: City Research Online aims to make research outputs of City, University of London available to a wider audience. Copyright and Moral Rights remain with the author(s) and/or copyright holders. URLs from City Research Online may be freely distributed and linked to. City Research Online: http://openaccess.city.ac.uk/ [email protected] Effect of secondary flows due to buoyancy and contraction on heat transfer in a two-section plate-fin heat sink I.K. Karathanassisa, b,*, E. Papanicolaoua, V. Belessiotisa and G.C. Bergelesb aSolar & other Energy Systems Laboratory, Institute of Nuclear and Radiological Sciences & Technology, Energy and Safety, National Centre for Scientific Research DEMOKRITOS, Aghia Paraskevi, 15310 Athens, Greece bLaboratory of Innovative Environmental Technologies, School of Mechanical Engineering, National Technical University of Athens, Zografos Campus, 15710 Athens, Greece * Corresponding author.
    [Show full text]
  • SASO-ISO-80000-11-2020-E.Pdf
    SASO ISO 80000-11:2020 ISO 80000-11:2019 Quantities and units - Part 11: Characteristic numbers ICS 01.060 Saudi Standards, Metrology and Quality Org (SASO) ----------------------------------------------------------------------------------------------------------- this document is a draft saudi standard circulated for comment. it is, therefore subject to change and may not be referred to as a saudi standard until approved by the boardDRAFT of directors. Foreword The Saudi Standards ,Metrology and Quality Organization (SASO)has adopted the International standard No. ISO 80000-11:2019 “Quantities and units — Part 11: Characteristic numbers” issued by (ISO). The text of this international standard has been translated into Arabic so as to be approved as a Saudi standard. DRAFT DRAFT SAUDI STANDADR SASO ISO 80000-11: 2020 Introduction Characteristic numbers are physical quantities of unit one, although commonly and erroneously called “dimensionless” quantities. They are used in the studies of natural and technical processes, and (can) present information about the behaviour of the process, or reveal similarities between different processes. Characteristic numbers often are described as ratios of forces in equilibrium; in some cases, however, they are ratios of energy or work, although noted as forces in the literature; sometimes they are the ratio of characteristic times. Characteristic numbers can be defined by the same equation but carry different names if they are concerned with different kinds of processes. Characteristic numbers can be expressed as products or fractions of other characteristic numbers if these are valid for the same kind of process. So, the clauses in this document are arranged according to some groups of processes. As the amount of characteristic numbers is tremendous, and their use in technology and science is not uniform, only a small amount of them is given in this document, where their inclusion depends on their common use.
    [Show full text]
  • Two-Phase Flow
    Chapter 11 Two-Phase Flow M.M. Awad Additional information is available at the end of the chapter http://dx.doi.org/10.5772/76201 1. Introduction A phase is defined as one of the states of the matter. It can be a solid, a liquid, or a gas. Multiphase flow is the simultaneous flow of several phases. The study of multiphase flow is very important in energy-related industries and applications. The simplest case of multiphase flow is two-phase flow. Two-phase flow can be solid-liquid flow, liquid-liquid flow, gas-solid flow, and gas-liquid flow. Examples of solid-liquid flow include flow of corpuscles in the plasma, flow of mud, flow of liquid with suspended solids such as slurries, motion of liquid in aquifers. The flow of two immiscible liquids like oil and water, which is very important in oil recovery processes, is an example of liquid-liquid flow. The injection of water into the oil flowing in the pipeline reduces the resistance to flow and the pressure gradient. Thus, there is no need for large pumping units. Immiscible liquid-liquid flow has other industrial applications such as dispersive flows, liquid extraction processes, and co- extrusion flows. In dispersive flows, liquids can be dispersed into droplets by injecting a liquid through an orifice or a nozzle into another continuous liquid. The injected liquid may drip or may form a long jet at the nozzle depending upon the flow rate ratio of the injected liquid and the continuous liquid. If the flow rate ratio is small, the injected liquid may drip continuously at the nozzle outlet.
    [Show full text]