Natural Convection Heat Transfer in Horizontal Cylindrical Cavities: a Computational Fluid Dynamics (Cfd) Investigation
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Convection Heat Transfer
Convection Heat Transfer Heat transfer from a solid to the surrounding fluid Consider fluid motion Recall flow of water in a pipe Thermal Boundary Layer • A temperature profile similar to velocity profile. Temperature of pipe surface is kept constant. At the end of the thermal entry region, the boundary layer extends to the center of the pipe. Therefore, two boundary layers: hydrodynamic boundary layer and a thermal boundary layer. Analytical treatment is beyond the scope of this course. Instead we will use an empirical approach. Drawback of empirical approach: need to collect large amount of data. Reynolds Number: Nusselt Number: it is the dimensionless form of convective heat transfer coefficient. Consider a layer of fluid as shown If the fluid is stationary, then And Dividing Replacing l with a more general term for dimension, called the characteristic dimension, dc, we get hd N ≡ c Nu k Nusselt number is the enhancement in the rate of heat transfer caused by convection over the conduction mode. If NNu =1, then there is no improvement of heat transfer by convection over conduction. On the other hand, if NNu =10, then rate of convective heat transfer is 10 times the rate of heat transfer if the fluid was stagnant. Prandtl Number: It describes the thickness of the hydrodynamic boundary layer compared with the thermal boundary layer. It is the ratio between the molecular diffusivity of momentum to the molecular diffusivity of heat. kinematic viscosity υ N == Pr thermal diffusivity α μcp N = Pr k If NPr =1 then the thickness of the hydrodynamic and thermal boundary layers will be the same. -
The Influence of Magnetic Fields in Planetary Dynamo Models
Earth and Planetary Science Letters 333–334 (2012) 9–20 Contents lists available at SciVerse ScienceDirect Earth and Planetary Science Letters journal homepage: www.elsevier.com/locate/epsl The influence of magnetic fields in planetary dynamo models Krista M. Soderlund a,n, Eric M. King b, Jonathan M. Aurnou a a Department of Earth and Space Sciences, University of California, Los Angeles, CA 90095, USA b Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, USA article info abstract Article history: The magnetic fields of planets and stars are thought to play an important role in the fluid motions Received 7 November 2011 responsible for their field generation, as magnetic energy is ultimately derived from kinetic energy. We Received in revised form investigate the influence of magnetic fields on convective dynamo models by contrasting them with 27 March 2012 non-magnetic, but otherwise identical, simulations. This survey considers models with Prandtl number Accepted 29 March 2012 Pr¼1; magnetic Prandtl numbers up to Pm¼5; Ekman numbers in the range 10À3 ZEZ10À5; and Editor: T. Spohn Rayleigh numbers from near onset to more than 1000 times critical. Two major points are addressed in this letter. First, we find that the characteristics of convection, Keywords: including convective flow structures and speeds as well as heat transfer efficiency, are not strongly core convection affected by the presence of magnetic fields in most of our models. While Lorentz forces must alter the geodynamo flow to limit the amplitude of magnetic field growth, we find that dynamo action does not necessitate a planetary dynamos dynamo models significant change to the overall flow field. -
Chapter 6 Natural Convection in a Large Channel with Asymmetric
Chapter 6 Natural Convection in a Large Channel with Asymmetric Radiative Coupled Isothermal Plates Main contents of this chapter have been submitted for publication as: J. Cadafalch, A. Oliva, G. van der Graaf and X. Albets. Natural Convection in a Large Channel with Asymmetric Radiative Coupled Isothermal Plates. Journal of Heat Transfer, July 2002. Abstract. Finite volume numerical computations have been carried out in order to obtain a correlation for the heat transfer in large air channels made up by an isothermal plate and an adiabatic plate, considering radiative heat transfer between the plates and different inclination angles. Numerical results presented are verified by means of a post-processing tool to estimate their uncertainty due to discretization. A final validation process has been done by comparing the numerical data to experimental fluid flow and heat transfer data obtained from an ad-hoc experimental set-up. 111 112 Chapter 6. Natural Convection in a Large Channel... 6.1 Introduction An important effort has already been done by many authors towards to study the nat- ural convection between parallel plates for electronic equipment ventilation purposes. In such situations, since channels are short and the driving temperatures are not high, the flow is usually laminar, and the physical phenomena involved can be studied in detail both by means of experimental and numerical techniques. Therefore, a large experience and much information is available [1][2][3]. In fact, in vertical channels with isothermal or isoflux walls and for laminar flow, the fluid flow and heat trans- fer can be described by simple equations arisen from the analytical solutions of the natural convection boundary layer in isolated vertical plates and the fully developed flow between two vertical plates. -
Turning up the Heat in Turbulent Thermal Convection COMMENTARY Charles R
COMMENTARY Turning up the heat in turbulent thermal convection COMMENTARY Charles R. Doeringa,b,c,1 Convection is buoyancy-driven flow resulting from the fluid remains at rest and heat flows from the warm unstable density stratification in the presence of a to the cold boundary according Fourier’s law, is stable. gravitational field. Beyond convection’s central role in Beyond a critical threshold, however, steady flows in myriad engineering heat transfer applications, it un- the form of coherent convection rolls set in to enhance derlies many of nature’s dynamical designs on vertical heat flux. Convective turbulence, character- larger-than-human scales. For example, solar heating ized by thin thermal boundary layers and chaotic of Earth’s surface generates buoyancy forces that plume dynamics mixing in the core, appears and per- cause the winds to blow, which in turn drive the sists for larger ΔT (Fig. 1). oceans’ flow. Convection in Earth’s mantle on geolog- More precisely, Rayleigh employed the so-called ical timescales makes the continents drift, and Boussinesq approximation in the Navier–Stokes equa- thermal and compositional density differences induce tions which fixes the fluid density ρ in all but the buoyancy forces that drive a dynamo in Earth’s liquid temperature-dependent buoyancy force term and metal core—the dynamo that generates the magnetic presumes that the fluid’s material properties—its vis- field protecting us from solar wind that would other- cosity ν, specific heat c, and thermal diffusion and wise extinguish life as we know it on the surface. The expansion coefficients κ and α—are constant. -
On the Inverse Cascade and Flow Speed Scaling Behavior in Rapidly Rotating Rayleigh-Bénard Convection
This draft was prepared using the LaTeX style file belonging to the Journal of Fluid Mechanics 1 On the inverse cascade and flow speed scaling behavior in rapidly rotating Rayleigh-B´enardconvection S. Maffei1;3y, M. J. Krouss1, K. Julien2 and M. A. Calkins1 1Department of Physics, University of Colorado, Boulder, USA 2Department of Applied Mathematics, University of Colorado, Boulder, USA 3School of Earth and Environment, University of Leeds, Leeds, UK (Received xx; revised xx; accepted xx) Rotating Rayleigh-B´enardconvection is investigated numerically with the use of an asymptotic model that captures the rapidly rotating, small Ekman number limit, Ek ! 0. The Prandtl number (P r) and the asymptotically scaled Rayleigh number (Raf = RaEk4=3, where Ra is the typical Rayleigh number) are varied systematically. For sufficiently vigorous convection, an inverse kinetic energy cascade leads to the formation of a depth-invariant large-scale vortex (LSV). With respect to the kinetic energy, we find a transition from convection dominated states to LSV dominated states at an asymptotically reduced (small-scale) Reynolds number of Ref ≈ 6 for all investigated values of P r. The ratio of the depth-averaged kinetic energy to the kinetic energy of the convection reaches a maximum at Ref ≈ 24, then decreases as Raf is increased. This decrease in the relative kinetic energy of the LSV is associated with a decrease in the convective correlations with increasing Rayleigh number. The scaling behavior of the convective flow speeds is studied; although a linear scaling of the form Ref ∼ Ra=Pf r is observed over a limited range in Rayleigh number and Prandtl number, a clear departure from this scaling is observed at the highest accessible values of Raf . -
Rayleigh-Bernard Convection Without Rotation and Magnetic Field
Nonlinear Convection of Electrically Conducting Fluid in a Rotating Magnetic System H.P. Rani Department of Mathematics, National Institute of Technology, Warangal. India. Y. Rameshwar Department of Mathematics, Osmania University, Hyderabad. India. J. Brestensky and Enrico Filippi Faculty of Mathematics, Physics, Informatics, Comenius University, Slovakia. Session: GD3.1 Core Dynamics Earth's core structure, dynamics and evolution: observations, models, experiments. Online EGU General Assembly May 2-8 2020 1 Abstract • Nonlinear analysis in a rotating Rayleigh-Bernard system of electrical conducting fluid is studied numerically in the presence of externally applied horizontal magnetic field with rigid-rigid boundary conditions. • This research model is also studied for stress free boundary conditions in the absence of Lorentz and Coriolis forces. • This DNS approach is carried near the onset of convection to study the flow behaviour in the limiting case of Prandtl number. • The fluid flow is visualized in terms of streamlines, limiting streamlines and isotherms. The dependence of Nusselt number on the Rayleigh number, Ekman number, Elasser number is examined. 2 Outline • Introduction • Physical model • Governing equations • Methodology • Validation – RBC – 2D – RBC – 3D • Results – RBC – RBC with magnetic field (MC) – Plane layer dynamo (RMC) 3 Introduction • Nonlinear interaction between convection and magnetic fields (Magnetoconvection) may explain certain prominent features on the solar surface. • Yet we are far from a real understanding of the dynamical coupling between convection and magnetic fields in stars and magnetically confined high-temperature plasmas etc. Therefore it is of great importance to understand how energy transport and convection are affected by an imposed magnetic field: i.e., how the Lorentz force affects convection patterns in sunspots and magnetically confined, high-temperature plasmas. -
Arxiv:1903.08882V2 [Physics.Flu-Dyn] 6 Jun 2019
Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number Ao Xua,∗, Le Shib, Heng-Dong Xia aSchool of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China bState Key Laboratory of Electrical Insulation and Power Equipment, Center of Nanomaterials for Renewable Energy, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China Abstract We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function ap- proach, which consists of a D3Q19 model for the Navier-Stokes equations to simulate fluid flows and a D3Q7 model for the convection-diffusion equation to simulate heat transfer. Relaxation parameters are adjusted to achieve the isotropy of the fourth-order error term in the thermal LB model. Two types of thermal convective flows are considered: one is laminar thermal convection in side-heated convection cell, which is heated from one vertical side and cooled from the other vertical side; while the other is turbulent thermal convection in Rayleigh-B´enardconvection cell, which is heated from the bottom and cooled from the top. In side-heated convection cell, steady results of hydrodynamic quantities and Nusselt numbers are presented at Rayleigh numbers of 106 and 107, and Prandtl number of 0.71, where the mesh sizes are up to 2573; in Rayleigh-B´enardconvection cell, statistical averaged results of Reynolds and Nusselt numbers, as well as kinetic and thermal energy dissipation rates are presented at Rayleigh numbers of 106, 3×106, and 107, and Prandtl numbers of arXiv:1903.08882v2 [physics.flu-dyn] 6 Jun 2019 ∗Corresponding author Email address: [email protected] (Ao Xu) DOI: 10.1016/j.ijheatmasstransfer.2019.06.002 c 2019. -
Forced and Natural Convection
FORCED AND NATURAL CONVECTION Forced and natural convection ...................................................................................................................... 1 Curved boundary layers, and flow detachment ......................................................................................... 1 Forced flow around bodies .................................................................................................................... 3 Forced flow around a cylinder .............................................................................................................. 3 Forced flow around tube banks ............................................................................................................. 5 Forced flow around a sphere ................................................................................................................. 6 Pipe flow ................................................................................................................................................... 7 Entrance region ..................................................................................................................................... 7 Fully developed laminar flow ............................................................................................................... 8 Fully developed turbulent flow ........................................................................................................... 10 Reynolds analogy and Colburn-Chilton's analogy between friction and heat -
Convectional Heat Transfer from Heated Wires Sigurds Arajs Iowa State College
Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1957 Convectional heat transfer from heated wires Sigurds Arajs Iowa State College Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Physics Commons Recommended Citation Arajs, Sigurds, "Convectional heat transfer from heated wires " (1957). Retrospective Theses and Dissertations. 1934. https://lib.dr.iastate.edu/rtd/1934 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. CONVECTIONAL BEAT TRANSFER FROM HEATED WIRES by Sigurds Arajs A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of The Requirements for the Degree of DOCTOR 01'' PHILOSOPHY Major Subject: Physics Signature was redacted for privacy. In Chapge of K or Work Signature was redacted for privacy. Head of Major Department Signature was redacted for privacy. Dean of Graduate College Iowa State College 1957 ii TABLE OF CONTENTS Page I. INTRODUCTION 1 II. THEORETICAL CONSIDERATIONS 3 A. Basic Principles of Heat Transfer in Fluids 3 B. Heat Transfer by Convection from Horizontal Cylinders 10 C. Influence of Electric Field on Heat Transfer from Horizontal Cylinders 17 D. Senftleben's Method for Determination of X , cp and ^ 22 III. APPARATUS 28 IV. PROCEDURE 36 V. RESULTS 4.0 A. Heat Transfer by Free Convection I4.0 B. Heat Transfer by Electrostrictive Convection 50 C. -
Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels1
Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels1 We investigate the constant-wall-temperature convective heat-transfer characteristics of a model gaseous flow in two-dimensional micro and nano-channels under hydrodynamically Nicolas G. and thermally fully developed conditions. Our investigation covers both the slip-flow Hadjiconstantinou regime 0рKnр0.1, and most of the transition regime 0.1ϽKnр10, where Kn, the Knud- sen number, is defined as the ratio between the molecular mean free path and the channel Olga Simek height. We use slip-flow theory in the presence of axial heat conduction to calculate the Nusselt number in the range 0рKnр0.2, and a stochastic molecular simulation technique Mechanical Engineering Department, known as the direct simulation Monte Carlo (DSMC) to calculate the Nusselt number in Massachusetts Institute of Technology, the range 0.02ϽKnϽ2. Inclusion of the effects of axial heat conduction in the continuum Cambridge, MA 02139 model is necessary since small-scale internal flows are typically characterized by finite Peclet numbers. Our results show that the slip-flow prediction is in good agreement with the DSMC results for Knр0.1, but also remains a good approximation beyond its ex- pected range of applicability. We also show that the Nusselt number decreases monotoni- cally with increasing Knudsen number in the fully accommodating case, both in the slip-flow and transition regimes. In the slip-flow regime, axial heat conduction is found to increase the Nusselt number; this effect is largest at Knϭ0 and is of the order of 10 percent. Qualitatively similar results are obtained for slip-flow heat transfer in circular tubes. -
Time-Periodic Cooling of Rayleigh–Bénard Convection
fluids Article Time-Periodic Cooling of Rayleigh–Bénard Convection Lyes Nasseri 1 , Nabil Himrane 2, Djamel Eddine Ameziani 1 , Abderrahmane Bourada 3 and Rachid Bennacer 4,* 1 LTPMP (Laboratoire de Transports Polyphasiques et Milieux Poreux), Faculty of Mechanical and Proceeding Engineering, USTHB (Université des Sciences et de la Technologie Houari Boumedienne), Algiers 16111, Algeria; [email protected] (L.N.); [email protected] (D.E.A.) 2 Labo of Energy and Mechanical Engineering (LEMI), Faculty of Technology, UMBB (Université M’hamed Bougara-Boumerdes, Boumerdes 35000, Algeria; [email protected] 3 Laboratory of Transfer Phenomena, RSNE (Rhéologie et Simulation Numérique des Ecoulements) Team, FGMGP (Faculté de génie Mécaniques et de Génie des Procédés Engineering), USTHB (Université des Sciences et de la Technologie Houari Boumedienne), Bab Ezzouar, Algiers 16111, Algeria; [email protected] 4 CNRS (Centre National de la Recherche Scientifique), LMT (Laboratoire de Mécanique et Technologie—Labo. Méca. Tech.), Université Paris-Saclay, ENS (Ecole National Supérieure) Paris-Saclay, 91190 Gif-sur-Yvette, France * Correspondence: [email protected] Abstract: The problem of Rayleigh–Bénard’s natural convection subjected to a temporally periodic cooling condition is solved numerically by the Lattice Boltzmann method with multiple relaxation time (LBM-MRT). The study finds its interest in the field of thermal comfort where current knowledge has gaps in the fundamental phenomena requiring their exploration. The Boussinesq approximation is considered in the resolution of the physical problem studied for a Rayleigh number taken in the range 103 ≤ Ra ≤ 106 with a Prandtl number equal to 0.71 (air as working fluid). -
Fluid Dynamics Analysis and Numerical Study of a Fluid Running Down a Flat Surface
29TH DAAAM INTERNATIONAL SYMPOSIUM ON INTELLIGENT MANUFACTURING AND AUTOMATION DOI: 10.2507/29th.daaam.proceedings.116 FLUID DYNAMICS ANALYSIS AND NUMERICAL STUDY OF A FLUID RUNNING DOWN A FLAT SURFACE Juan Carlos Beltrán-Prieto & Karel Kolomazník This Publication has to be referred as: Beltran-Prieto, J[uan] C[arlos] & Kolomaznik, K[arel] (2018). Fluid Dynamics Analysis and Numerical Study of a Fluid Running Down a Flat Surface, Proceedings of the 29th DAAAM International Symposium, pp.0801-0810, B. Katalinic (Ed.), Published by DAAAM International, ISBN 978-3-902734- 20-4, ISSN 1726-9679, Vienna, Austria DOI: 10.2507/29th.daaam.proceedings.116 Abstract The case of fluid flowing down a plate is applied in several industrial, chemical and engineering systems and equipments. The mathematical modeling and simulation of this type of system is important from the process engineering point of view because an adequate understanding is required to control important parameters like falling film thickness, mass rate flow, velocity distribution and even suitable fluid selection. In this paper we address the numerical simulation and mathematical modeling of this process. We derived equations that allow us to understand the correlation between different physical chemical properties of the fluid and the system namely fluid mass flow, dynamic viscosity, thermal conductivity and specific heat and studied their influence on thermal diffusivity, kinematic viscosity, Prandtl number, flow velocity, fluid thickness, Reynolds number, Nusselt number, and heat transfer coefficient using numerical simulation. The results of this research can be applied in computational fluid dynamics to easily identify the expected behavior of a fluid that is flowing down a flat plate to determine the velocity distribution and values range of specific dimensionless parameters and to help in the decision-making process of pumping systems design, fluid selection, drainage of liquids, transport of fluids, condensation and in gas absorption experiments.