DOCSLIB.ORG

Weissenberg and Deborah Numbers Executive Committee Table of Contents (2009-2011)

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

wmm Wmi The News and Information Publication of The Society of Rheology Volume 79 Number 2 July 2010 A Two-fer for Durham University UK: Bingham Medalist Tom McLeish Metzner Awardee Suzanne Fielding Inside« • « : «JBSIlP I m m Society Awards to McLeish, Fielding 82nd SOR Meeting, Santa Fe 2010 Joe Starita, Father of Modern Rheometry Weissenberg and Deborah Numbers Executive Committee Table of Contents (2009-2011) President Bingham Medalist for 2010 is 4 Faith A. Morrison Tom McLeish Vice President A. Jeffrey Giacomin Metzner Award to be Presented 7 in 2010 to Suzanne Fielding Secretary Albert Co 82nd Annual Meeting of the 8 Treasurer Montgomery T. Shaw SOR: Santa Fe2010 Editor Joe Starita, Father of Modern 11 John F. Brady Rheometry Past-President by Chris Macosko Robert K. Prud'homme Members-at-Large Short Courses in Santa Fe: 12 Ole Hassager Colloidal Dispersion Rheology Norman J. Wagner and Microrheology Hiroshi Watanabe Weissenberg and Deborah 14 Numbers - Their Definition On the Cover: and Use by John M Dealy Photo of the Durham University Notable Passings 19 World Heritage Site of Durham Edward B. Bagley Castle (University College) and Durham Cathedral. Former built Tai-Hun Kwon by William the Conqueror, latter completed in 1130. Society News/Business 20 News, ExCom minutes, Treasurer's Report Calendar of Events 28 2 Rheology Bulletin, 79(2) July It) 10 Standing Committees Membership Committee (2009-2011) Metzner Award Committee Shelley L. Anna, chair Lynn Walker (2008-2010), chair Saad Khan Peter Fischer (2009-2012) Jason Maxey Charles P. Lusignan (2008-2010) Lisa Mondy Gareth McKinley (2009-2012) Chris White Michael J. Solomon (2008-2010) Education Committee (2009-2011) Meetings Policy Committee Michael J. Solomon, chair Jeffrey Giacomin, Chair (Vice President) Anne M. Grillet Victor Breed veld (2011 Program) Marie-Claude Heuzey Albert Co (Webmaster) Mary am Scpchr Saad Khan (2010 Program) Patrick Spicer Andrew Kraynik (2010 Local) Gregory McKcnna (2010 Program) Bingham Award Committee Jonathan Rothstein (2011 Program) Timothy Lodge (2007-2010), chair Jae Chun Hyun (2009-2012) Christopher Macosko (2008-2011) Kalman Miglcr (2008-2011) Jeffrey Morris (2009-2012) Susan J. Muller (2007-2010) Michael Rubinstein (2008-2011) Wehmaster Albert Co Editor, Rheology Bulletin Faith A. Morrison Associate Editor for Business, Journal of Rheology A. Jeffrey Giacomin Society of Rheology Representatives to External Committees/Organizations: AIP Governing Board Morton M. Denn AIP Committee on Public Policy Kalman Migler AIP Committee on Publishing; also Chair A. Jeffrey Giacomin AIP Liaison Committee for Under-Represented Minorities Willie E. (Skip) Rochefort U.S. National Committee on Theoretical and Applied Mechanics Michael D. Graham International Committee on Rheology Andrew M. Kraynik The Rheology Bulletin is the news and information Serial Key Title: Rheology Bulletin publication of The Society of Rheology (SOR) and is LC Control No.: 48011534 Published for The Society of Rheology published twice yearly in January and July. Subscrip- by the American Institute of Physics tion is free on membership in The Society of Rheology. ISSN: 0035-4538 CO DEN: RHBUAV Letters to the editor: [email protected]. CALL NUMBER: QC1 .R45 The Rheology Bulletin is archived on the SOR website at www.rheology.org/sor/publications/rheology_b/issues.htm 3 Rheology Bulletin, 79(2) July It) 10 Bingham Medalist 2010 Tom McLeish Lecturer in the Department of Profile by Ron Larson Physics, University of Sheffield University of Michigan USA from 1989 to 1993. He moved to the University of Leeds in 1 am delighted to profile the achieve- 1993 where he was appointed ments of Tom McLeish that merit his Professor of Polymer Physics, selection as Bingham Medalist for and director of the UK Polymer 2010. I first met Tom when he was IRC (involving also the Uni- a graduate student at Cambridge in versities of Durham, Sheffield, the mid -1980's, and have immensely and Bradford). He moved to enjoyed Tom's friendship and col- Durham University as Pro-Vice- laborations over the years, as have so Chancellor of Research in 2008, many others. Tom is a delightfully his current position. He has held gifted individual, possessing great numerous administrative posi- scientific talent, and an ever-youthful tions, including Directorship of enthusiasm for science in general and the Microscale Polymer Process- rheology in particular. His research ing Consortium. Tom has twice in polymers relevant to rheology has been a recipient of the Journal encompassed the gamut of topics, ranging from syn- of Rheology Publication Award and was awarded the thesis, molecular dynamics and polymer physics, fluid Weissenberg Medal of the European Society of Rheol- mechanics, processing, flow instabilities, neutron scat- ogy in 2007. tering, phase separation, gelation, and crystallization. In addition, he has contributed profoundly important work on the rheology of surfactant solu- tions, colloids, electrorheological fluids, and other materials, encompassing both theoretical and experimental methods. He is a Renaissance man: gifted in science and engineering, languages, music, the humanities and theology, and possessing wonderful organizational and interper- sonal skills as well. Tom received a B.S. degree from Em- manuel College, University of Cam- bridge in 1984, and an M.A. and Ph.D. also from Cambridge, in 1987. He was an IC1 Research Fellow, Theory of Condensed Matter Group, at the Cavendish Labora- tory, Cambridge, from 1987 to 1989. Not as punctual as they might be, here is the McLeish family, Julie He then became and Tom, with children Katie, Nicholas, Max and Rosie, at the Coliseum but just 1900 years too late for the big game. 4 Rheology Bulletin, 79(2) July It) 10 Tom's ability to pursue science at the highest level was gineering knowledge, as well as the collaborative skills, demonstrated very early, when during or shortly after his needed to bring such a project to fruition. All who work Ph.D. thesis, he and Robin Ball applied the idea of "dy- in the field of polymer rheology are well aware of Tom's namic dilution" to the relaxation of star polymers. Tom seminal contributions, and often turn first to his papers thereafter applied this concept to branched polymers when seeking to understand the latest developments in general, with great success. Tom added to "dynamic in this area. Besides de Gennes, Doi, Edwards, and dilution" the idea of "hierarchical relaxation," whereby Marrucci, there is no one who has contributed as much branched polymers of arbitrary architecture, including to our understanding of polymer rheology as has Tom hyperbranched polymers, relax sequentially, starting McLeish. This body of work alone qualifies Tom for the from the tips of the arms. As they relax, they release Bingham Medal. constraints on other molecules, progressively "diluting" the density of constraints in the melt, as longer time But Tom's accomplishments go well beyond this. He scales are accessed. He also created a theoretical scheme worked out a theory of polymer "spurt." He has made that allows the effects of relaxation at each stage on sub- important contributions to measurements and theory of sequent stages to be accounted for through the dynamic surfactant liquid crystal rheology. His recent work with dilution ansatz. These ideas have become the basis of Tim Lodge on the structure and properties of polymer modern theories for relaxation and rheology of long- blends is gaining a large following in polymer blend chain-branched polymers, a very important topic both structure and dynamics, with clear implications for intellectually and commercially. Not satisfied with su- rheology. He has recently developed an understanding perficial understanding, Tom has critiqued the dynamic of protein dynamics under strong stretching flows. His dilution ansatz and has shown how it can be rationalized C.V. shows his contributions to numerous other areas of as approximation to a much deeper theoretical picture. importance to rheology. Using dynamic dilution and other creative ideas, includ- These accomplishments reflect not only on Tom's ing the most rigorous version of Marrucci's "convective scientific genius, but also his skill at collaborations. constraint release" idea, Tom and his coworkers pub- The European research programs that Tom has orga- lished a series of papers predicting the linear and non- nized in the area ot polymer dynamics and rheology are linear dynamics and rheology of linear, star-branched, the best funded and most comprehensive in the world "H", and other polymers, all of which have become on this topic. Tom regularly unites people of widely the "standard" models for relaxation and rheology of varying backgrounds from both industry and academia, these polymers. Moreover, Tom and his collaborators worldwide, into productive enterprises. Tom delights in have extended these ideas to the prediction of polymer processing flows, such as the contraction flows imaged (continues page 27) by both neutron scattering and birefringence, published in Science. In this tour de force, Tom and his collaborators subjected specially synthesized monodisperse polymers to flow through a contraction, and measured poly- mer orientation through both birefringence and neutron scattering. The results of these measurements were successfully compared with the predictions of advanced rheological models for polymers, also developed by Tom and his many collaborators. This work com- bined anionic polymer synthesis, rheological
Recommended publications
  • Soret and Dufour Effects on MHD Boundary Layer Flow of Non

    Soret and Dufour Effects on MHD Boundary Layer Flow of Non

    Pramana – J. Phys. (2020) 94:108 © Indian Academy of Sciences https://doi.org/10.1007/s12043-020-01984-z Soret and Dufour effects on MHD boundary layer flow of non-Newtonian Carreau fluid with mixed convective heat and mass transfer over a moving vertical plate ANIL KUMAR GAUTAM1, AJEET KUMAR VERMA1, KRISHNENDU BHATTACHARYYA1 ,∗ and ASTICK BANERJEE2 1Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221 005, India 2Department of Mathematics, Sidho-Kanho-Birsha University, Purulia 723 104, India ∗Corresponding author. E-mail: [email protected], [email protected] MS received 1 August 2019; revised 24 April 2020; accepted 3 May 2020 Abstract. In this analysis, the mixed convection boundary layer MHD flow of non-Newtonian Carreau fluid subjected to Soret and Dufour effects over a moving vertical plate is studied. The governing flow equations are converted into a set of non-linear ordinary differential equations using suitable transformations. For numerical computations, bvp4c in MATLAB package is used to solve the resulting equations. Impacts of various involved parameters, such as Weissenberg number, power-law index, magnetic parameter, thermal buoyancy parameter, solutal buoyancy parameter, thermal radiation, Dufour number, Soret number and reaction rate parameter, on velocity, temperature and concentration are shown through figures. Also, the local skin-friction coefficient, local Nusselt number and local Sherwood number are calculated and shown graphically and in tabular form for different parameters. Some important facts are revealed during the investigation. The temperature and concentration show decreasing trends with increasing values of power-law index, whereas velocity shows reverse trend and these trends are more prominent for larger values of Weissenberg number.
  • Chapter 5 Dimensional Analysis and Similarity

    Chapter 5 Dimensional Analysis and Similarity

    Chapter 5 Dimensional Analysis and Similarity Motivation. In this chapter we discuss the planning, presentation, and interpretation of experimental data. We shall try to convince you that such data are best presented in dimensionless form. Experiments which might result in tables of output, or even mul- tiple volumes of tables, might be reduced to a single set of curves—or even a single curve—when suitably nondimensionalized. The technique for doing this is dimensional analysis. Chapter 3 presented gross control-volume balances of mass, momentum, and en- ergy which led to estimates of global parameters: mass flow, force, torque, total heat transfer. Chapter 4 presented infinitesimal balances which led to the basic partial dif- ferential equations of fluid flow and some particular solutions. These two chapters cov- ered analytical techniques, which are limited to fairly simple geometries and well- defined boundary conditions. Probably one-third of fluid-flow problems can be attacked in this analytical or theoretical manner. The other two-thirds of all fluid problems are too complex, both geometrically and physically, to be solved analytically. They must be tested by experiment. Their behav- ior is reported as experimental data. Such data are much more useful if they are ex- pressed in compact, economic form. Graphs are especially useful, since tabulated data cannot be absorbed, nor can the trends and rates of change be observed, by most en- gineering eyes. These are the motivations for dimensional analysis. The technique is traditional in fluid mechanics and is useful in all engineering and physical sciences, with notable uses also seen in the biological and social sciences.
  • An Investigation Into the Effects of Viscoelasticity on Cavitation Bubble Dynamics with Applications to Biomedicine

    An Investigation Into the Effects of Viscoelasticity on Cavitation Bubble Dynamics with Applications to Biomedicine

    An Investigation into the Effects of Viscoelasticity on Cavitation Bubble Dynamics with Applications to Biomedicine Michael Jason Walters School of Mathematics Cardiff University A thesis submitted for the degree of Doctor of Philosophy 9th April 2015 Summary In this thesis, the dynamics of microbubbles in viscoelastic fluids are investigated nu- merically. By neglecting the bulk viscosity of the fluid, the viscoelastic effects can be introduced through a boundary condition at the bubble surface thus alleviating the need to calculate stresses within the fluid. Assuming the surrounding fluid is incompressible and irrotational, the Rayleigh-Plesset equation is solved to give the motion of a spherically symmetric bubble. For a freely oscillating spherical bubble, the fluid viscosity is shown to dampen oscillations for both a linear Jeffreys and an Oldroyd-B fluid. This model is also modified to consider a spherical encapsulated microbubble (EMB). The fluid rheology affects an EMB in a similar manner to a cavitation bubble, albeit on a smaller scale. To model a cavity near a rigid wall, a new, non-singular formulation of the boundary element method is presented. The non-singular formulation is shown to be significantly more stable than the standard formulation. It is found that the fluid rheology often inhibits the formation of a liquid jet but that the dynamics are governed by a compe- tition between viscous, elastic and inertial forces as well as surface tension. Interesting behaviour such as cusping is observed in some cases. The non-singular boundary element method is also extended to model the bubble tran- sitioning to a toroidal form.
  • RHEOLOGY #2: Anelasicity

    RHEOLOGY #2: Anelasicity

    RHEOLOGY #2: Anelas2city (aenuaon and modulus dispersion) of rocks, an organic, and maybe some ice Chris2ne McCarthy Lamont-Doherty Earth Observatory …but first, cheese Team Havar2 Team Gouda Team Jack Stress and Strain Stress σ(MPa)=F(N)/A(m2) 1 kg = 9.8N 1 Pa= N/m2 or kg/(m s2) Strain ε = Δl/l0 = (l0-l)/l0 l0 Cheese results vs. idealized curve. Not that far off! Cheese results σ n ⎛ −E + PV ⎞ ε = A exp A d p ⎝⎜ RT ⎠⎟ n=1 Newtonian! σ Pa viscosity η = ε s-1 Havarti,Jack η=3*107 Pa s Gouda η=2*108 Pa s Muenster η=6*108 Pa s How do we compare with previous studies? Havarti,Jack η=3*107 Pa s Gouda η=2*108 Pa s Muenster η=6*108 Pa s Despite significant error, not far off published results Viscoelas2city: Deformaon at a range of 2me scales Viscoelas2city: Deformaon at a range of 2me scales Viscoelas2city Elas2c behavior is Viscous behavior; strain rate is instantaneous elas2city and propor2onal to stress: instantaneous recovery. σ = ηε Follows Hooke’s Law: σ = E ε Steady-state viscosity Elas1c Modulus k or E ηSS Simplest form of viscoelas2city is the Maxwell model: t 1 J(t) = + ηSS kE SS kE Viscoelas2city How do we measure viscosity and elascity in the lab? Steady-state viscosity Elas1c Modulus k or EU ηSS σ σ η = η = effective [Fujisawa & Takei, 2009] ε ε1 Viscoelas2city: in between the two extremes? Viscoelas2city: in between the two extremes? Icy satellites velocity (at grounding line) tidal signal glaciers velocity (m per day) (m per velocity Vertical position (m) Vertical Day of year 2000 Anelas2c behavior in Earth and Planetary science
  • Computational Study of Jeffreyв€™S Non-Newtonian Fluid Past a Semi

    Computational Study of Jeffreyв€™S Non-Newtonian Fluid Past a Semi

    Ain Shams Engineering Journal (2016) xxx, xxx–xxx Ain Shams University Ain Shams Engineering Journal www.elsevier.com/locate/asej www.sciencedirect.com ENGINEERING PHYSICS AND MATHEMATICS Computational study of Jeffrey’s non-Newtonian fluid past a semi-infinite vertical plate with thermal radiation and heat generation/absorption S. Abdul Gaffar a,*, V. Ramachandra Prasad b, E. Keshava Reddy a a Department of Mathematics, Jawaharlal Nehru Technological University Anantapur, Anantapuramu, India b Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle 517325, India Received 7 October 2015; revised 13 August 2016; accepted 2 September 2016 KEYWORDS Abstract The nonlinear, steady state boundary layer flow, heat and mass transfer of an incom- Non-Newtonian Jeffrey’s pressible non-Newtonian Jeffrey’s fluid past a semi-infinite vertical plate is examined in this article. fluid model; The transformed conservation equations are solved numerically subject to physically appropriate Semi-infinite vertical plate; boundary conditions using a versatile, implicit finite-difference Keller box technique. The influence Deborah number; of a number of emerging non-dimensional parameters, namely Deborah number (De), ratio of Heat generation; relaxation to retardation times (k), Buoyancy ratio parameter (N), suction/injection parameter Thermal radiation; (fw), Radiation parameter (F), Prandtl number (Pr), Schmidt number (Sc), heat generation/absorp- Retardation time tion parameter (D) and dimensionless tangential coordinate (n) on velocity, temperature and con- centration evolution in the boundary layer regime is examined in detail. Also, the effects of these parameters on surface heat transfer rate, mass transfer rate and local skin friction are investigated. This model finds applications in metallurgical materials processing, chemical engineering flow con- trol, etc.
  • Similitude and Theory of Models - Washington Braga

    Similitude and Theory of Models - Washington Braga

    EXPERIMENTAL MECHANICS - Similitude And Theory Of Models - Washington Braga SIMILITUDE AND THEORY OF MODELS Washington Braga Mechanical Engineering Department, Pontifical Catholic University, Rio de Janeiro, RJ, Brazil Keywords: similarity, dimensional analysis, similarity variables, scaling laws. Contents 1. Introduction 2. Dimensional Analysis 2.1. Application 2.2 Typical Dimensionless Numbers 3. Models 4. Similarity – a formal definition 4.1 Similarity Variables 5. Scaling Analysis 6. Conclusion Glossary Bibliography Biographical Sketch Summary The concepts of Similitude, Dimensional Analysis and Theory of Models are presented and used in this chapter. They constitute important theoretical tools that allow scientists from many different areas to go further on their studies prior to actual experiments or using small scale models. The applications discussed herein are focused on thermal sciences (Heat Transfer and Fluid Mechanics). Using a formal approach based on Buckingham’s π -theorem, the paper offers an overview of the use of Dimensional Analysis to help plan experiments and consolidate data. Furthermore, it discusses dimensionless numbers and the Theory of Models, and presents a brief introduction to Scaling Laws. UNESCO – EOLSS 1. Introduction Generally speaking, similitude is recognized through some sort of comparison: observing someSAMPLE relationship (called similarity CHAPTERS) among persons (for instance, relatives), things (for instance, large commercial jets and small executive ones) or the physical phenomena we are interested.
  • Thermal Radiations and Mass Transfer Analysis of the Three-Dimensional Magnetite Carreau Fluid Flow Past a Horizontal Surface of Paraboloid of Revolution

    Thermal Radiations and Mass Transfer Analysis of the Three-Dimensional Magnetite Carreau Fluid Flow Past a Horizontal Surface of Paraboloid of Revolution

    processes Article Thermal Radiations and Mass Transfer Analysis of the Three-Dimensional Magnetite Carreau Fluid Flow Past a Horizontal Surface of Paraboloid of Revolution T. Abdeljawad 1,2,3 , Asad Ullah 4 , Hussam Alrabaiah 5,6, Ikramullah 7, Muhammad Ayaz 8, Waris Khan 9 , Ilyas Khan 10,∗ and Hidayat Ullah Khan 11 1 Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11 586, Saudi Arabia; [email protected] 2 Department of Medical Research, China Medical University, Taichung 40402, Taiwan 3 Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan 4 Institute of Numerical Sciences, Kohat University of Science & Technology, Kohat 26000, Khyber Pakhtunkhwa, Pakistan; [email protected] 5 College of Engineering, Al Ain University, Al Ain 64141, UAE; [email protected] 6 Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan 7 Department of Physics, Kohat University of Science & Technology, Kohat 26000, Khyber Pakhtunkhwa, Pakistan; [email protected] 8 Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Khyber Pakhtunkhwa, Pakistan; [email protected] 9 Department of Mathematics, Islamia College University Peshawar, Peshawar 25000, Khyber Pakhtunkhwa, Pakistan; [email protected] 10 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam 11 Department of Economics, Abbottabad University of Science and Technology (AUST), Abbottabad Havelian 22500, Khyber Pakhtunkhwa, Pakistan; [email protected] * Correspondence: [email protected] Received: 18 April 2020; Accepted: 22 May 2020; Published: 1 June 2020 Abstract: The dynamics of the 3-dimensional flow of magnetized Carreau fluid past a paraboloid surface of revolution is studied through thermal radiation and mass transfer analysis.
  • Rheology Bulletin 2010, 79(2)

    Rheology Bulletin 2010, 79(2)

    The News and Information Publication of The Society of Rheology Volume 79 Number 2 July 2010 A Two-fer for Durham University UK: Bingham Medalist Tom McLeish Metzner Awardee Suzanne Fielding Rheology Bulletin Inside: Society Awards to McLeish, Fielding 82nd SOR Meeting, Santa Fe 2010 Joe Starita, Father of Modern Rheometry Weissenberg and Deborah Numbers Executive Committee Table of Contents (2009-2011) President Bingham Medalist for 2010 is 4 Faith A. Morrison Tom McLeish Vice President A. Jeffrey Giacomin Metzner Award to be Presented 7 Secretary in 2010 to Suzanne Fielding Albert Co 82nd Annual Meeting of the 8 Treasurer Montgomery T. Shaw SOR: Santa Fe 2010 Editor Joe Starita, Father of Modern 11 John F. Brady Rheometry Past-President by Chris Macosko Robert K. Prud’homme Members-at-Large Short Courses in Santa Fe: 12 Ole Hassager Colloidal Dispersion Rheology Norman J. Wagner Hiroshi Watanabe and Microrheology Weissenberg and Deborah 14 Numbers - Their Definition On the Cover: and Use by John M. Dealy Photo of the Durham University World Heritage Site of Durham Notable Passings 19 Castle (University College) and Edward B. Bagley Durham Cathedral. Former built Tai-Hun Kwon by William the Conqueror, latter completed in 1130. Society News/Business 20 News, ExCom minutes, Treasurer’s Report Calendar of Events 28 2 Rheology Bulletin, 79(2) July 2010 Standing Committees Membership Committee (2009-2011) Metzner Award Committee Shelley L. Anna, chair Lynn Walker (2008-2010), chair Saad Khan Peter Fischer (2009-2012) Jason Maxey Charles P. Lusignan (2008-2010) Lisa Mondy Gareth McKinley (2009-2012) Chris White Michael J.
  • The Effect of Induced Magnetic Field and Convective Boundary Condition

    The Effect of Induced Magnetic Field and Convective Boundary Condition

    Propulsion and Power Research 2016;5(2):164–175 HOSTED BY http://ppr.buaa.edu.cn/ Propulsion and Power Research www.sciencedirect.com ORIGINAL ARTICLE The effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer of upper-convected Maxwell fluid in the presence of nanoparticle past a stretching sheet Wubshet Ibrahimn Department of Mathematics, Ambo University, P.O. Box 19, Ambo, Ethiopia Received 5 February 2015; accepted 17 July 2015 Available online 30 May 2016 KEYWORDS Abstract The present study examines the effect of induced magnetic field and convective fl fl boundary condition on magnetohydrodynamic (MHD) stagnation point ow and heat transfer due Nano uid; fl Stagnation point flow; to upper-convected Maxwell uid over a stretching sheet in the presence of nanoparticles. fi Heat transfer; Boundary layer theory is used to simplify the equation of motion, induced magnetic eld, energy Convective boundary and concentration which results in four coupled non-linear ordinary differential equations. The condition; study takes into account the effect of Brownian motion and thermophoresis parameters. The Induced magnetic governing equations and their associated boundary conditions are initially cast into dimensionless field; form by similarity variables. The resulting system of equations is then solved numerically using Upper-convected Max- fourth order Runge-Kutta-Fehlberg method along with shooting technique. The solution for the well fluid governing equations depends on parameters such as, magnetic, velocity ratio parameter B,Biot number Bi, Prandtl number Pr, Lewis number Le, Brownian motion Nb, reciprocal of magnetic Prandtl number A, the thermophoresis parameter Nt, and Maxwell parameter β.
  • Chapter 8 Dimensional Analysis and Similitude

    Chapter 8 Dimensional Analysis and Similitude

    Chapter 8 Dimensional Analysis and Similitude Ahmad Sana Department of Civil and Architectural Engineering Sultan Qaboos University Sultanate of Oman Email: [email protected] Webpage: http://ahmadsana.tripod.com Significant learning outcomes Conceptual Knowledge State the Buckingham Π theorem. Identify and explain the significance of the common π-groups. Distinguish between model and prototype. Explain the concepts of dynamic and geometric similitude. Procedural Knowledge Apply the Buckingham Π theorem to determine number of dimensionless variables. Apply the step-by-step procedure to determine the dimensionless π- groups. Apply the exponent method to determine the dimensionless π-groups. Distinguish the significant π-groups for a given a flow problem. Applications (typical) Drag force on a blimp from model testing. Ship model tests to evaluate wave and friction drag. Pressure drop in a prototype nozzle from model measurements. CIVL 4046 Fluid Mechanics 2 8.1 Need for dimensional analysis • Experimental studies in fluid problems • Model and prototype • Example: Flow through inverted nozzle CIVL 4046 Fluid Mechanics 3 Pressure drop through the nozzle can shown as: p p d V d 1 2 f 0 , 1 0 2 V / 2 d1 p p d For higher Reynolds numbers 1 2 f 0 V 2 / 2 d 1 CIVL 4046 Fluid Mechanics 4 8.2 Buckingham pi theorem In 1915 Buckingham showed that the number of independent dimensionless groups of variables (dimensionless parameters) needed to correlate the variables in a given process is equal to n - m, where n is the number of variables involved and m is the number of basic dimensions included in the variables.
  • Research Article a Combined Convection Carreau–Yasuda Nanofluid Model Over a Convective Heated Surface Near a Stagnation Point: a Numerical Study

    Research Article a Combined Convection Carreau–Yasuda Nanofluid Model Over a Convective Heated Surface Near a Stagnation Point: a Numerical Study

    Hindawi Mathematical Problems in Engineering Volume 2021, Article ID 6665743, 14 pages https://doi.org/10.1155/2021/6665743 Research Article A Combined Convection Carreau–Yasuda Nanofluid Model over a Convective Heated Surface near a Stagnation Point: A Numerical Study Azad Hussain,1 Aysha Rehman ,1 Sohail Nadeem,2 M. Y. Malik ,3 Alibek Issakhov,4,5 Lubna Sarwar,1 and Shafiq Hussain6 1Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan 2Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan 3Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia 4Department of Mathematical and Computer Modeling, Al-Farabi Kazakh National University, Almaty, Kazakhstan 5Department of Mathematical and Computer Modeling, Kazakh British-Technical University, Almaty, Kazakhstan 6Department of Computer Science, University of Sahiwal, Sahiwal, Pakistan Correspondence should be addressed to Aysha Rehman; [email protected] Received 18 November 2020; Revised 1 March 2021; Accepted 22 March 2021; Published 5 April 2021 Academic Editor: Adrian Neagu Copyright © 2021 Azad Hussain et al. 'is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 'e focus of this manuscript is on two-dimensional mixed convection non-Newtonian nanofluid flow near stagnation point over a stretched surface with convectively heated boundary conditions.
  • On Dimensionless Numbers

    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 .................................................................................................................