DOCSLIB.ORG

Quadratic Convective Flow of a Micropolar Fluid Along an Inclined Plate in a Non-Darcy Porous Medium with Convective Boundary Condition

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quadratic Convective Flow of a Micropolar Fluid Along an Inclined Plate in a Non-Darcy Porous Medium with Convective Boundary Condition Nonlinear Engineering 2017; 6(2): 139–151 Ch. RamReddy*, P. Naveen, and D. Srinivasacharya Quadratic Convective Flow of a Micropolar Fluid along an Inclined Plate in a Non-Darcy Porous Medium with Convective Boundary Condition DOI 10.1515/nleng-2016-0073 rate (shear thinning or shear thickening). In contrast to Received August 6, 2016; accepted February 19, 2017. Newtonian fluids, non-Newtonian fluids display anon- linear relation between shear stress and shear rate. But, Abstract: The objective of the present study is to investi- the model of a micropolar fluid developed by Eringen [1] gate the effect of nonlinear variation of density with tem- exhibits some microscopic effects arising from the lo- perature and concentration on the mixed convective flow cal structure and micro motion of the fluid elements. It of a micropolar fluid over an inclined flat plate in anon- provides the basis for the mathematical model of non- Darcy porous medium in the presence of the convective Newtonian fluids which can be used to analyze the behav- boundary condition. In order to analyze all the essential ior of exotic lubricants, polymers, liquid crystals, animal features, the governing non-dimensional partial differen- bloods, colloidal or suspension solutions, etc. The detailed tial equations are transformed into a system of ordinary review of theory and applications of micropolar fluids can differential equations using a local non-similarity proce- be found in the books by Lukaszewicz [2] and Eremeyev et dure and then the resulting boundary value problem is al. [3]. In view of an increasing importance of mixed con- solved using a successive linearisation method (SLM). By vection in many transport processes, the topic of mixed insisting the comparison between vertical, horizontal and convection in boundary layer flow along vertical, inclined, inclined plates, the physical quantities of the flow and and horizontal flat plates has been extensively analyzed its characteristics are exhibited graphically and quanti- and some experimental/theoretical studies [4–7] on these tatively with various parameters. An increase in the mi- flow geometries in micropolar fluid have been reported. cropolar parameter and non-Darcy parameter tend to in- Transport of heat through a porous medium has been crease the skin friction and the reverse change is observed the subject of many studies due to the increasing need in wall couple stress, mass and heat transfer rates. The in- for a better understanding of the associated transport pro- fluence of the nonlinear concentration parameter is more cesses. Most of the earlier studies [8-10] in porous me- prominent on all the physical characteristics of the present dia are based on the Darcy model which assumes pro- model, compared with that of nonlinear temperature pa- portionality between the velocity and pressure gradient. rameter. The model, however, is valid only for slow flows through Keywords: Micropolar Fluid, Non-Darcy Porous Medium, porous media with low permeability, but at higher flow Nonlinear Convection, Convective Boundary Condition, rates or in highly porous media the inertial effects become Successive Linearization Method significant. For example, in petroleum reservoirs the high flow can occur in various scenarios such as near the well bore (perforations), hydraulically fractured wells, conden- sates reservoirs (low viscosity crude reservoirs), high flow 1 Introduction potential wells and gravel packs. Forchheimer [11] pro- posed a quadratic extension to the Darcian model in order In reality, most of the fluids are non-Newtonian, which to more precisely simulate the inertial effect in porous me- means that their viscosity is dependent on the shear dia. A detailed review of convective heat transfer charac- teristics of different fluids in the porous medium as well as non-Darcy porous medium can be found in the book by Nield and Bejan [12] and also see the citations therein. *Corresponding Author: Ch. RamReddy: Department of Mathe- Later, several authors to mention few [13, 14] examined the matics, National Institute of Technology Warangal-506004, India, E-mail: [email protected]; [email protected] heat and mass transfer characteristics of micropolar and P. Naveen, D. Srinivasacharya: Department of Mathematics, National Institute of Technology Warangal-506004, India 140 | Ch. RamReddy et al., Quadratic Convective Flow of a Micropolar Fluid along an Inclined Plate viscous fluid flows along a vertical plate in the non-Darcy boundary is discussed by Ramreddy et al. [22] (also refer porous medium. the references given therein). The effect of buoyancy forces by taking the linear vari- The objective of the article is to analyze the effects of ations in temperature and density have been investigated nonlinear variation of density with temperature and con- by several researchers. But the relationship between tem- centration on mixed convection in a micropolar fluid sat- perature and density may become nonlinear due to differ- urated non-Darcy porous medium over an inclined plate ent physical characteristics like temperature variation, in- by considering convective boundary condition. The gov- ertia, radiation, or presence of different densities and heat erning nonlinear system of partial differential equations is released by viscous dissipation. Particularly, the flow field transformed to set of ordinary nonlinear differential equa- and heat transfer characteristics are more influenced by tions by local non-similarity procedure and then the suc- nonlinear density and temperature variations in the buoy- cessive linearization method is used to solve the result- ancy force term (for details, see Barrow and Rao [15], Va- ing boundary value problem. Typical results for the veloc- jravelu and Sastri [16]) when the temperature difference ity, temperature, microrotation and concentration distri- between the surface of the plate and the ambient fluid be- butions are presented for various governing parameters. comes significantly large. Therefore, the concept of nonlin- Also, the local skin-friction, wall couple stress, as well as ear convection in a fluid medium is of great importance in the heat and mass transfer rates are illustrated for repre- a variety of disciplines such as astrophysics, geophysics, sentative values of the major parameters. geothermal and engineering applications. Moreover, the engineering applications are applied in design of ther- mal system, cooling transpiration, combustion, cooling of 2 Mathematical Formulation electric components, areas of reactor safety, drying of the surfaces, turbine blades, solar collectors, etc. In such spe- Consider the steady laminar mixed convective flow of an cial cases, the temperature-dependent relation is nonlin- incompressible micropolar fluid along a semi-infinite in- ear and has unavoidable importance. Partha [17] studied clined flat plate in a non-Darcy porous medium, withan the effect of nonlinear convection in a non-Darcy porous acute angle Ω to the vertical, as depicted in Fig. 1. The medium and concluded that, with the increase of nonlin- coordinate system is such that x measures the distance ear temperature-concentration, the heat and mass trans- along the plate and y measures the distance normally into fer are more in the Darcy porous medium as compared the fluid. The velocity of the outer flow is of theform u , with the non-Darcy porous medium. The effects of nonlin- ∞ the free stream temperature and concentration are T and ear convection and thermophoresis in a non-Darcy porous ∞ C , respectively. The plate is either heated or cooled from a medium are discussed by Kameswaran et al. [18], and con- ∞ flow field of temperature T to the left by convection with cluded that the temperature and concentration boundary f T > T relating to a heated surface (assisting flow) and layer thickness decreases with increasing values of nonlin- f ∞ T < T relating to a cooled surface (opposing flow), re- ear temperature and concentration parameters. Recently, f ∞ spectively. On the wall the solutal concentration is taken Sachin Shaw et al. [19] investigated the effect of nonlin- to be constant and is given by C . The porous medium ear thermal convection in nanofluid flow over a stretching w is taken to be uniform with a constant permeability and sheet. porosity, and is saturated with a fluid which is in local ther- Heat transfer analysis with the convective boundary modynamic equilibrium with the solid matrix. In addition, condition attracted the interest of many researchers, since a Forchheimer model is considered. Further, the temper- this condition is more realistic and general representation ature difference between the surface of the plate andthe in engineering and industrial processes such as transpi- ambient fluid assumed to be significantly larger, so that ration cooling process, material drying, etc. Aziz [20] ob- the nonlinear density and temperature variations in the tained a similarity solution for the Blasius flow of a vis- buoyancy force term exert a strong influence on the flow cous fluid under convective boundary condition. Yacob field. Further, we follow the work of many recent authors and Ishak [21] investigated stagnation point flow towards a by assuming that γ = μ + κ j [23, 24]. stretching/shrinking sheet immersed in a micropolar fluid 2 By employing nonlinear Boussinesq approximation with a convective surface boundary condition. In recent (Ref. [15, 16]) and making use of the standard boundary times, the influence of homogeneous-heterogeneous reac- layer approximations, the governing equations for the mi- tions on convective heat flow of a micropolar fluid along a vertical plate in porous medium under convective surface Ch. RamReddy et al., Quadratic Convective Flow of a Micropolar Fluid along an Inclined Plate | 141 The boundary conditions are ∂T u =0, v =0, ω =0,−k = h (T −T), C = C at y =0 ∂y f f w (6) u = u∞, ω =0, T = T∞, C = C∞ as y → ∞ (7) where, the subscripts w and ∞ indicate the conditions at the wall and at the outer edge of the boundary layer, re- spectively, hf is the convective heat transfer coefficient and k is the thermal conductivity of the fluid.
Load more

Recommended publications
  • Separation Points of Magnetohydrodynamic Boundary
    Journal of Naval Architecture and Marine Engineering June,2018 http://dx.doi.org/10.3329/jname.v15i2.29966 http://www.banglajol.info MATHEMATICAL ANALYSIS OF NON-NEWTONIAN NANOFLUID TRANSPORT PHENOMENA PAST A TRUNCATED CONE WITH NEWTONIAN HEATING N. Nagendra1*, C. H. Amanulla2 and M. Suryanarayana Reddy3 1Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle-517325, India. *Email: [email protected] 2Department of Mathematics, Jawaharlal Nehru Technological University, Anantapur, Anantapuramu-515002, India. Email: [email protected] 3Department of Mathematics, JNTUA College of Engineering, Pulivendula-516390, India. Email: [email protected] Abstract: In the present study, we analyze the heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid past a truncated cone surface with Biot Number effect is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer Biot Number effect. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. Casson fluid parameter (β)(≥ 1), Brownian motion parameter (Nb) thermophoresis parameter (Nt), Lewis number (Le)(≥ 5), Buoyancy ratio parameter (N )( ≥ 0) Prandtl number (Pr) (7≤ Pr ≤ 100) and Biot number (Bi) (0.25 ≤ Bi ≤ 1)on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length.
    [Show full text]
  • An Experimental Approach to Determine the Heat Transfer Coefficient in Directional Solidification Furnaces
    Journal of Crystal Growth 113 (1991) 557-565 PRECEDING p_GE B,LA(]'_,,_O'_7FILMED North-Holland N9 Y. An experimental approach to determine the heat transfer coefficient in directional solidification furnaces Mohsen Banan, Ross T. Gray and William R. Wilcox Center for Co,stal Growth in Space and School of Engineering, Clarkson University, Potsdam, New York 13699, USA Received 13 November 1990; manuscript received in final form 22 April 1991 f : The heat transfer coefficient between a molten charge and its surroundings in a Bridgman furnace was experimentally determined using m-sttu temperature measurement. The ampoule containing an isothermal melt was suddenly moved from a higher temperature ' zone to a lower temperature zone. The temperature-time history was used in a lumped-capacity cooling model to evaluate the heat i transfer coefficient between the charge and the furnace. The experimentally determined heat transfer coefficient was of the same i order of magnitude as the theoretical value estimated by standard heat transfer calculations. 1. Introduction Chang and Wilcox [1] showed that increasing the Biot number in Bridgman growth affects the A variety of directional solidification tech- position and shape of the isotherms in the furnace. niques are used for preparation of materials, espe- The sensitivity of interface position to the hot and cially for growth of single crystals. These tech- cold zone temperatures is greater for small Blot niques include the vertical Bridgman-Stockbarger, number. horizontal Bridgman, zone-melting, and gradient Fu and Wilcox [2] showed that decreasing the freeze methods. It is time consuming and costly to Biot numbers in the hot and cold zones of a experimentally determine the optimal thermal vertical Bridgman-Stockbarger system results in conditions of a furnace utifized to grow a specific isotherms becoming less curved.
    [Show full text]
  • Chemically Reactive MHD Micropolar Nanofluid Flow with Velocity Slips
    www.nature.com/scientificreports OPEN Chemically reactive MHD micropolar nanofuid fow with velocity slips and variable heat source/sink Abdullah Dawar1, Zahir Shah 2,3*, Poom Kumam 4,5*, Hussam Alrabaiah 6,7, Waris Khan 8, Saeed Islam1,9,10 & Nusrat Shaheen11 The two-dimensional electrically conducting magnetohydrodynamic fow of micropolar nanofuid over an extending surface with chemical reaction and secondary slips conditions is deliberated in this article. The fow of nanofuid is treated with heat source/sink and nonlinear thermal radiation impacts. The system of equations is solved analytically and numerically. Both analytical and numerical approaches are compared with the help of fgures and tables. In order to improve the validity of the solutions and the method convergence, a descriptive demonstration of residual errors for various factors is presented. Also the convergence of an analytical approach is shown. The impacts of relevance parameters on velocity, micro-rotation, thermal, and concentration felds for frst- and second-order velocity slips are accessible through fgures. The velocity feld heightens with the rise in micropolar, micro-rotation, and primary order velocity parameters, while other parameters have reducing impact on the velocity feld. The micro-rotation feld reduces with micro-rotation, secondary order velocity slip, and micropolar parameters but escalates with the primary order velocity slip parameter. The thermal feld heightens with escalating non-uniform heat sink/source, Biot number, temperature ratio factor, and thermal radiation factor. The concentration feld escalates with the increasing Biot number, while reduces with heightening chemical reaction and Schmidt number. The assessment of skin factor, thermal transfer, and mass transfer are calculated through tables.
    [Show full text]
  • Strongly-Coupled Conjugate Heat Transfer Investigation of Internal Cooling of Turbine Blades Using the Immersed Boundary Method
    Strongly-Coupled Conjugate Heat Transfer Investigation of Internal Cooling of Turbine Blades using the Immersed Boundary Method Tae Kyung Oh Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science In Mechanical Engineering Danesh K. Tafti – Chair Roop L. Mahajan Wing F. Ng May 13th 2019 Blacksburg, Virginia, USA Keywords: Conjugate heat transfer, immersed boundary method, internal cooling, fully developed assumption Strongly-Coupled Conjugate Heat Transfer Investigation of Internal Cooling of Turbine Blades using the Immersed Boundary Method Tae Kyung Oh ABSTRACT The present thesis focuses on evaluating a conjugate heat transfer (CHT) simulation in a ribbed cooling passage with a fully developed flow assumption using LES with the immersed boundary method (IBM-LES-CHT). The IBM with the LES model (IBM-LES) and the IBM with CHT boundary condition (IBM-CHT) frameworks are validated prior to the main simulations by simulating purely convective heat transfer (iso-flux) in the ribbed duct, and a developing laminar boundary layer flow over a two dimensional flat plate with heat conduction, respectively. For the main conjugate simulations, a ribbed duct geometry with a blockage ratio of 0.3 is simulated at a bulk Reynolds number of 10,000 with a conjugate boundary condition applied to the rib surface. The nominal Biot number is kept at 1, which is similar to the comparative experiment. As a means to overcome a large time scale disparity between the fluid and the solid regions, the use of a high artificial solid thermal diffusivity is compared to the physical diffusivity.
    [Show full text]
  • Dimensionless Numbers
    Dimensionless Numbers 3.185 November 24, 2003 Note: you are not responsible for knowing the different names of the mass transfer dimensionless numbers, just call them, e.g., “mass transfer Prandtl number”, as many people do. Those names are given here because some people use them, and you’ll probably hear them at some point in your career. Heat Transfer Mass Transfer Biot Number M.T. Biot Number Ratio of conductive to convective H.T. resistance Ratio of diffusive to reactive or conv MT resistance Determines uniformity of temperature in solid Determines uniformity of concentration in solid Bi = hL/ksolid Bi = kL/Dsolid or hD L/Dsolid Fourier Number Ratio of current time to time to reach steady­state Dimensionless time in temperature curves, used in explicit finite difference stability criterion 2 2 Fo = αt/L Fo = Dt/L Knudsen Number: Ratio of gas molecule mean free path to process lengthscale Indicates validity of line­of­sight (> 1) or continuum (< 0.01) gas models λ kT Kn = = √ L 2πσ2 P L Reynolds Number: Ratio of convective to viscous momentum transport Determines transition to turbulence, dynamic pressure vs. viscous drag Re = ρU L/µ = U L/ν Prandtl Number M.T. Prandtl (Schmidt) Number Ratio of momentum to thermal diffusivity Ratio of momentum to species diffusivity Determines ratio of fluid/HT BL thickness Determines ratio of fluid/MT BL thickness Pr = ν/α = µcp/k Pr = ν/D = µ/ρD Nusselt Number M.T. Nusselt (Sherwood) Number Ratio of lengthscale to thermal BL thickness Ratio of lengthscale to diffusion BL thickness Used to calculate heat transfer
    [Show full text]
  • 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.
    [Show full text]
  • Heat Transfer to Droplets in Developing Boundary Layers at Low Capillary Numbers
    Heat Transfer to Droplets in Developing Boundary Layers at Low Capillary Numbers A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Everett A. Wenzel IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE Professor Francis A. Kulacki August, 2014 c Everett A. Wenzel 2014 ALL RIGHTS RESERVED Acknowledgements I would like to express my gratitude to Professor Frank Kulacki for providing me with the opportunity to pursue graduate education, for his continued support of my research interests, and for the guidance under which I have developed over the past two years. I am similarly grateful to Professor Sean Garrick for the generous use of his computational resources, and for the many hours of discussion that have been fundamental to my development as a computationalist. Professors Kulacki, Garrick, and Joseph Nichols have generously served on my committee, and I appreciate all of their time. Additional acknowledgement is due to the professors who have either provided me with assistantships, or have hosted me in their laboratories: Professors Van de Ven, Li, Heberlein, Nagasaki, and Ito. I would finally like to thank my family and friends for their encouragement. This work was supported in part by the University of Minnesota Supercom- puting Institute. i Abstract This thesis describes the heating rate of a small liquid droplet in a develop- ing boundary layer wherein the boundary layer thickness scales with the droplet radius. Surface tension modifies the nature of thermal and hydrodynamic bound- ary layer development, and consequently the droplet heating rate. A physical and mathematical description precedes a reduction of the complete problem to droplet heat transfer in an analogy to Stokes' first problem, which is numerically solved by means of the Lagrangian volume of fluid methodology.
    [Show full text]
  • Experiments on Rayleigh–Bénard Convection, Magnetoconvection
    J. Fluid Mech. (2001), vol. 430, pp. 283–307. Printed in the United Kingdom 283 c 2001 Cambridge University Press Experiments on Rayleigh–Benard´ convection, magnetoconvection and rotating magnetoconvection in liquid gallium By J. M. AURNOU AND P. L. OLSON Department of Earth and Planetary Sciences,† Johns Hopkins University, Baltimore, MD 21218, USA (Received 4 March 1999 and in revised form 12 September 2000) Thermal convection experiments in a liquid gallium layer subject to a uniform rotation and a uniform vertical magnetic field are carried out as a function of rotation rate and magnetic field strength. Our purpose is to measure heat transfer in a low-Prandtl-number (Pr =0.023), electrically conducting fluid as a function of the applied temperature difference, rotation rate, applied magnetic field strength and fluid-layer aspect ratio. For Rayleigh–Benard´ (non-rotating, non-magnetic) convection 0.272 0.006 we obtain a Nusselt number–Rayleigh number law Nu =0.129Ra ± over the range 3.0 103 <Ra<1.6 104. For non-rotating magnetoconvection, we find that the critical× Rayleigh number× RaC increases linearly with magnetic energy density, and a heat transfer law of the form Nu Ra1/2. Coherent thermal oscillations are detected in magnetoconvection at 1.4Ra∼C . For rotating magnetoconvection, we find that the convective heat transfer is∼ inhibited by rotation, in general agreement with theoretical predictions. At low rotation rates, the critical Rayleigh number increases linearly with magnetic field intensity. At moderate rotation rates, coherent thermal oscillations are detected near the onset of convection. The oscillation frequencies are close to the frequency of rotation, indicating inertially driven, oscillatory convection.
    [Show full text]
  • Numerical Investigation of the Thermal Interaction Between a Shape Memory Alloy and Low Reynolds Number Viscous Flow
    University of Alberta Numerical Investigation of the Thermal Interaction between a Shape Memory Alloy and Low Reynolds Number Viscous Flow Christopher Thomas Reaume O A thesis submitted to the Faculty of Craduate Studies and Research in partial hilfillment of the requirements for the degree of Master of Science. Department of Mechanicd Engineering Edmonton, Alberta Spring 2000 National Liitary Bibüothèque nationaie 1*1 ofCanada du Canada Acquisitions and Acquisitions et Bibliographie Se~kes senrices bibliographiques 385 wemngdon Sbwt 395. nie W~geon OttawuON K1AW ûüaviraON K1AûN4 Canada Canada The author has granted a non- L'auteur a accordé une licence non exclusive licence dowing the exc1usive pmettant à la National Li'bmy of Canada to BiblothQue nationale du Canada de reproduce, loan, distri'bute or seil reproduire, prêter, distribuer ou copies of this thesis in microform, vendre des copies de cette thèse sous paper or electronic formats. la fonne de microfiche/nim, de reproduction sur papier ou sur format électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droh d'autein qui protège cette thèse. thesis nor substantial extracts fiom it Ni la thèse ni des extraits substantiels may be printed or othemise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. A numerical scheme for the two dimensional rnodelling of the thermal interaction between a smart material and low Reynolds number cross flow has been developed. The phase change of the srnart material is modeled by the temperature dependence of the thermal conductivity and heat capacity of the solid.
    [Show full text]
  • An Investigation Into the Effects of Heat Transfer on the Motion of a Spherical Bubble
    ANZJAMJ. 45(2004), 361-371 AN INVESTIGATION INTO THE EFFECTS OF HEAT TRANSFER ON THE MOTION OF A SPHERICAL BUBBLE P. J. HARRIS1, H. AL-AWADI1 and W. K. SOH2 (Received 2 April, 1999; revised 12 November, 2002) Abstract This paper investigates the effect of heat transfer on the motion of a spherical bubble in the vicinity of a rigid boundary. The effects of heat transfer between the bubble and the surrounding fluid, and the resulting loss of energy from the bubble, can be incorporated into the simple spherical bubble model with the addition of a single extra ordinary differential equation. The numerical results show that for a bubble close to an infinite rigid boundary there are significant differences in both the radius and Kelvin impulse of the bubble when the heat transfer effects are included. 1. Introduction Over the past couple of decades there has been considerable interest in studying the motion of a gas or vapour bubble in a liquid. Typically these bubbles occur in applications such as cavitation and under-water explosions and can be responsible for considerable damage to nearby structures immersed in the liquid. The mathematical models for predicting the motion of a bubble fall into two categories. The first category consists of full numerical models, such as the boundary integral method, which completely determine the fluid motion and can predict phenomena such as the re-entrant jet which forms as the bubble collapses, but which are computationally expensive. The alternative is to use a simplified model where the bubble is assumed to remain spherical throughout its growth and collapse phases and then use techniques such as the Kelvin impulse to determine the direction of the bubble jet.
    [Show full text]
  • THERMAL a ALYSIS of ATURAL CO VECTIO a a D RADIATIO I POROUS FI S MEHULKUMAR G. MAHERIA Bachelor of Science in Mechanical En
    THERMAL AALYSIS OF ATURAL COVECTIOA AD RADIATIO I POROUS FIS MEHULKUMAR G. MAHERIA Bachelor of Science in Mechanical Engineering Gujarat University, Gujarat, India May, 2006 Submitted in partial fulfillment of requirement for the degree Master Of Science In Mechanical Engineering At the Cleveland State University May, 2010 This thesis has been approved For the Department of MECHANICAL ENGINEERING and the College of Graduate Studies by Thesis committee chairperson, Dr. R. S. R. Gorla Department /Date Dr. Majid Rashidi Department /Date Dr. Asuquo B. Ebiana Department /Date Dedicated to My family for their blessings, continued support and encouragement throughout my career. ACKOWEDGEMET Heartfelt thanks to Dr. R. S. R. Gorla of the Department of Mechanical Engineering, Fenn College of Engineering at Cleveland State University. This work would have been impossible without his role as my advisor for the past two years. I am indebted for his invaluable guidance, critical review and suggestions towards completion of the research involved in this thesis. I am grateful to Dr. Atherton, Chairman of Department of Mechanical Engineering for the financial support during my Masters program. Many thanks to my thesis committee members, Dr. Rashidi and Dr. Ebiana for their valuable time to review and provide constructive suggestions. Finally, many thank to friends Jigar Patel, Ivan Grant, Sejal Amin and Bharat Bhungaliya. Their friendship was a much-needed tonic to boost my morale and ensure the thesis work moved on during trying times. THERMAL AALYSIS OF ATURAL COVECTIOA AD RADIATIO I POROUS FIS MEHULKUMAR G. MAHERIA ABSTRACT In this study, the effect of radiation with convection heat transfer in porous media is considered.
    [Show full text]
  • Chapter 4, Solution 1C
    Chapter 4, Solution 1C. In heat transfer analysis, some bodies are observed to behave like a "lump" whose entire body temperature remains essentially uniform at all times during a heat transfer process. The temperature of such bodies can be taken to be a function of time only. Heat transfer analysis which utilizes this idealization is known as the lumped system analysis. It is applicable when the Biot number (the ratio of conduction resistance within the body to convection resistance at the surface of the body) is less than or equal to 0.1. Chapter 4, Solution 2C. The lumped system analysis is more likely to be applicable for the body cooled naturally since the Biot number is proportional to the convection heat transfer coefficient, which is proportional to the air velocity. Therefore, the Biot number is more likely to be less than 0.1 for the case of natural convection. Chapter 4, Solution 3C. The lumped system analysis is more likely to be applicable for the body allowed to cool in the air since the Biot number is proportional to the convection heat transfer coefficient, which is larger in water than it is in air because of the larger thermal conductivity of water. Therefore, the Biot number is more likely to be less than 0.1 for the case of the solid cooled in the air Chapter 4, Solution 4C. The temperature drop of the potato during the second minute will be less than 4°C since the temperature of a body approaches the temperature of the surrounding medium asymptotically, and thus it changes rapidly at the beginning, but slowly later on.
    [Show full text]