Cavitation in Non-Newtonian Fluids Emil-Alexandru Brujan
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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. -
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. -
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. -
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)
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
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. -
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
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 ................................................................................................................. -
Effect of Magnetic Field and Heat Source on Upper-Convected-Maxwell Fluid in a Porous Channel
Open Phys. 2018; 16:917–928 Research Article Zeeshan Khan, Haroon Ur Rasheed, Tawfeeq Abdullah Alkanhal, Murad Ullah, Ilyas Khan*, and Iskander Tlili Effect of magnetic field and heat source on Upper-convected-maxwell fluid in a porous channel https://doi.org/10.1515/phys-2018-0113 Received Apr 12, 2018; accepted Jun 05, 2018 Nomenclature Abstract: The effect of magnetic field on the flow ofthe β Deborah number UCMF (Upper-Convected-Maxwell Fluid) with the property η Similarity variable of a heat source/sink immersed in a porous medium is ex- ν Kinematic viscosity (m2s−1) plored. A shrinking phenomenon along with the perme- θ Dimensionless temperature ability of the wall are considered. The governing equa- φ Stream function tions for the motion and transfer of heat of the UCMF along λ1 Internal heat generation/absorption parameter with boundary conditions are converted into a set of cou- λR Relaxation time (t) pled nonlinear mathematical equations. Appropriate sim- C Dimensional constant (t−1) ilarity transformations are used to convert the set of non- f Similarity variable linear partial differential equations into nonlinear ordi- K Thermal conductivity nary differential equations. The modeled ordinary differ- M Magnetic field (Te) ential equations have been solved by the Homotopy Anal- Nux Nusselt number ysis Method (HAM). The convergence of the series solu- p Density of the fluid (kg m3) tion is established. For the sake of comparison, numeri- Pr Prandtl number cal (ND-Solve method) solutions are also obtained. Spe- Q Hear source/sink parameter cial attention is given to how the non-dimensional phys- S Suctions/injection parameter(ms−1) ical parameters of interest affect the flow of the UCMF. -
Effects of Induced Magnetic Field on Electrically Conducting Oldroyd-B Nanofluid Flow Over a Perforated Linearly Extending Surfa
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 15, Number 5 (2019), pp. 623-636 c Research India Publications http://www.ripublication.com/gjpam.htm Effects of Induced Magnetic Field on Electrically Conducting Oldroyd-B Nanofluid Flow over a Perforated Linearly Extending Surface Oyier Williss Odhiambo , Mark Kimathi and Mary Wainaina Degree in M.Sc Applied Mathematics Department of Mathematics and Actuarial Science , Catholic University of Eastern Africa , Box 62157-0020 Nairobi , Kenya. Email:[email protected] Abstract This study investigated the effects of induced magnetic field on MHD boundary layer laminar flow for an Oldroyd-B nano fluid , on a heat producing or absorbing , perforated and elongating surface . Application of an externally magnetic field orthogonally to the extending sheet , affects the fluid flow . The parameters that describe the flow clearly are Lewis number , Magnetic prandtl number , Deborah’s numbers , Brownian motion parameter and Thermophoretic parameter. The governing PDES were converted to ODES using similarity transformation . The ODES obtained were reduced to systems of first order ODES and solved by collocation method in MATLAB . It was established that as magnetic induction of the fluid increases , the momentum boundary layer thickness reduces , the temperature profile rises and the diffusion of the nanoparticles is enhanced . Effects of B1 , B2 , Nt , Nb and Le are also discussed . The results of findings are presented in form of graphs for velocity , temperature and concentration profiles -
Free Convective Heat Transfer Over Truncated Cone with Convective Heating: Numerical Analysis
International Journal of Advanced Scientific Research and Management, Volume 4 Issue 3, Mar 2019 www.ijasrm.com ISSN 2455-6378 Free Convective Heat Transfer over Truncated Cone with Convective Heating: Numerical Analysis G. Raju Department of Mathematics, IIIT Ongole Campus, RGUKT-516330, Andhra Pradesh, India. Abstract cone embedded in a porous medium. Elbashbeshy et This paper is focused on the study of heat transfer al. [6] analyzed radiation effects non-Newtonian characteristics of MHD non-Newtonian Tangent fluid flow past a vertical truncated cone. Subba Rao Hyperbolic boundary layer flow over a truncated et al. [7] discussed the Newtonian heating on cone with Biot number effect. The governing partial hydrodynamic fluid flow over a circular cylinder. differential equations of the flow field are converted Reddy and Pradeepa [8] studied viscous disspation to a system of non-linear coupled non-similarity and sorret effects on natural convection flow over a ordinary differential equations. Employing Shooting truncated cone in the presence of biot number. technique followed by finite centered difference Several authors [9-11] investigated heat transfer of technique (Keller Box Method), the system is solved the non-Newtonian fluid of various physical numerically. The numerical code is validated with problems. previous studies. The results of flow and heat analysis on velocity and temperature profiles are given diagrammatically. The numerical results point The present work, we examine theoretically and out that, increasing MHD parameter (M) serves to computationally the steady-state transport decelerate the flow, but increased temperature values phenomena in magneto-hydrodynamic non- and increase in the Biot number (Bi) is observed to Newtonian fluid flow from a truncated cone with enhance velocity and temperature. -
The British Society of Rheology
THE BRITISH SOCIETY OF RHEOLOGY To cite: R J Poole (2012), The Deborah and Weissenberg numbers. The British Society of Rheology, Rheology Bulletin . 53(2) pp 32-39 1 The Deborah and Weissenberg numbers Rob Poole School of Engineering University of Liverpool, United Kingdom Since their introduction to the literature nearly fifty years ago the Deborah and Weissenberg numbers have proved invaluable for rheologists in quantifying viscoelastic effects. Despite their different origins, and the fact that they quantify different effects, they are frequently used as synonyms. This situation is perhaps partly explainable given that in a wide range of flows of complex fluids characterised by a relaxation time ( λ) the use of simple single characteristic length ( L) and velocity scales ( U) does indeed result in identical definitions! In this short article we return to the original papers to highlight the different effects that the Deborah and Weissenberg numbers measure. The Deborah number As every good rheologist knows the Deborah number owes its name to the Prophetess Deborah who, in the Book of Judges, proclaimed “The mountains flowed before the lord” A. The definition is due to Reiner and we can do no better than to quote his original paper B “Deborah knew two things. First, that the mountains flow, as everything flows. But, secondly, that they flowed before the Lord, and not before man, for the simple reason that man in his short lifetime cannot see them flowing, while the time of observation of God is infinite . We may therefore well define a nondimensional number the Deborah number D = time of relaxation/time of observation.” AAs Huilgol notes “Reiner quoted the Prophetess Deborah as saying “The mountains flowed before the Lord” while the King James version says “The mountains melted from before the Lord”, and the New English Bible has “Mountains shook in fear before the Lord,” (See Judges 5:5) [R R Huigol (1975) “On the concept of the Deborah number”.