DOCSLIB.ORG

Viscosity Variation Effects on Heat Transfer and Fluid Flow Through Two-Layered Porous Media

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Viscosity Variation Effects on Heat Transfer and Fluid Flow Through Two-Layered Porous Media Journal of ChemicalBahadori Technology Fatemeh, and Sima Metallurgy, Rezvantalab 50, 1, 2015, 35-38 VISCOSITY VARIATION EFFECTS ON HEAT TRANSFER AND FLUID FLOW THROUGH TWO-LAYERED POROUS MEDIA Bahadori Fatemeh, Sima Rezvantalab Chemical Engineering Department, Received 10 June 2014 Urmia University of Technology, Urmia, Iran Accepted 24 November 2014 E-mail: [email protected] ABSTRACT Temperature dependent viscosity effects on natural convection in a composite cavity, isothermally heated from below and cooled from the opposing surface, are analyzed. The two-layered porous media was composed of two regions with different permeability. It is observed that viscosity reduction, due to temperature rising, affects heat transfer rate and fluid motion at the interface. Keywords: two layered porous media, viscosity, heat transfer, permeability ratio (Kr), streamline. INTRODUCTION tion for calculation of the overall Nusselt number for N horizontal sub layers. Lai and Kulacki [13] discussed Heat transfer in porous media has been extensively convection in a vertically divided rectangular cavity, of studied due to its numerous engineering and environ- the right hand side wall which was heated with constant mental applications. Oil recovery, underground spread heat flux. of pollutants, grain storage, geothermal systems, solar Egorov and Polezhaev [14] investigated a theoretical power collectors, optimal design of furnaces, compact model and showed that their numerical results are in the heat exchangers, packed-bed catalytic reactors and pas- line of their experimental data for multilayer insulation. sive thermal control devices are examples of applications In addition, Merrikh and Mohamad [15], Belghazi et al. of heat transfer in porous media. [16] and Ordo´n˜ez-Miranda and Alvarado-Gil [17] and Studies concerning natural convection in porous others, have investigated multilayered porous media. media can be found in the monographs of Ingham It can be seen that composite cavity under natural and Pop [1], and Nield and Bejan [2]. The case of free convection is evaluated extensively in literature, how- convection in a rectangular porous medium, heated on ever, the viscosity variation due to temperature rising is one side and cooled at the opposing side, is also an im- considered negligible. portant problem in thermal convection in porous media. The aim of this paper is the investigation of viscosity The work of Walker and Homsy [3], Bejan [4], Prasad variation effects on the natural convection in a saturated and Kulacki [5], Manole and Lage [6], Saeid and Pop enclosure, divided into two different porous layers, with [7] and others have further contributed some classical different permeabilities and subjected to a heating from results to this problem. one side and cooling from the other side. The presence of a free-flow domain adjacent to a Governing equations porous media, has been studied in literature by Cieszko, An incompressible, 2-D, natural convection in a Kubik [8], Mharzi et al. [9], Edimilson and de Lemos two-layered cavity, filled with a saturated, isotropic Marcelo [10] and Baytas et al. [11], and others. Fur- porous medium with temperature dependent viscosity thermore, multilayered cavity has been investigated. and density variation in the buoyancy term, was studied Poulikakos and Bejan [12] studied horizontally and numerically. It was assumed that the solid matrix and vertically layered cavity and approximated a correla- the fluid are in local thermal equilibrium. As suggested 35 Journal of Chemical Technology and Metallurgy, 50, 1, 2015 by Nield and Bejan [2], the equations that govern the conservation of mass, momentum, and energy can be written as follows: ∇=u 0 (1) ρ f ∂∂∂uuP µ uv +=− u (2) ε 2 ∂∂∂x y xK ρ ∂∂∂vvP µ f +=−+ρβ − (3) 2 u v [v g() TT∞ ] ε ∂∂∂x y xK a) b) ∂∂TT 2 uv+=∇α T (4) ∂∂xy The average Nusselt number is defined by: 2L Nu= Nu dx ∫ x (5) c) 0 It was assumed that viscosity is varying with tem- Fig. 2. Streamlines for horizontally divided porous media, Ra = 104, Da = 0.001, Kr = 0.001:(a) constant viscosity, perature in the following models: 1 µ = C (6a) (b) linear variation of viscosity with temperature and (c) exponential variation of viscosity with temperature. µλ=−−T00() TT (6b) µγ= TT0 exp( ) (6c) Numerical procedure and grid independence The model equations were solved using the commer- cial flow simulation software FLUENT (version 6.3.26). Fig. 1 shows the geometry of the simulated media. As a) b) it can be seen, the rectangular enclosures with different permeability are separated at Y=L/2. The results for Ram=1000 are in line with those in the literature. c) Fig. 3. Streamlines for horizontally divided porous media, 4 Ra1 = 10 , Da = 0.001, Kr = 1000; (a) constant viscosity, (b) linear variation of viscosity with temperature and (c) exponential variation of viscosity with temperature. RESULTS AND DISCUSSION The results of simulation are presented in the next sections. Fig. 1. Scheme of the layered porous media and the coor- Effect of viscosity variation dinate system. Fig. 2 and Fig. 3 illustrate the streamlines for 36 Bahadori Fatemeh, Sima Rezvantalab a) b) Fig. 4. Variation of cavity average Nusselt number for a horizontally divided enclosure (a) Da = 0.01, Kr = 0.1 and (b) Da = 0.01, Kr = 10. a) b) Fig. 5. Variation of v-velocity at the mid-height of the horizontally divided enclosure for (a) Da = 0.01, Kr = 0.1 and (b) Da = 0.01, Kr = 10. 4 Ra1=10 , Da=0.001, Kr= 1000 for a horizontally divided Velocity profile porous media. As it can be seen, viscosity reduction due Fig. 5 illustrates the velocity profile in the horizon- to temperature raising causes increase of the flow pen- tally divided porous media. As it can be seen, decreas- etration rate from one layer to another. In addition, the ing of the velocity due to temperature rising, causes an flow penetration rate for the case, which is modeled by increase of fluid movement. In addition, comparison of considering exponential variation of viscosity, is higher Fig. 5a and Fig. 5b shows that the velocity magnitude than the case with linear variation of viscosity. in two layered porous media with Kr < 1 is higher than Heat transfer Kr > 1. Fig. 4 shows Nu numbers obtained by assuming: of (a) exponential variation of viscosity with temperature, CONCLUSIONS (b) linear variation of viscosity with temperature and (c) constant viscosity. Fig. 4 shows that the mean Nu number The viscosity variation effect on natural convection obtained when considering exponential variation with in a horizontally layered porous media was investigated temperature (Nuexp) is greater than the Nu number ob- numerically using the finite volume method. Results tained with linear variation of viscosity with temperature were presented for flow field and heat transfer of enclo- (Nulin). As it is seen, Nucon is in line with the findings of sures subjected to heated from one side, and cooled from Poulikakos and Bejan [12]. the opposite wall, while the other walls were isolated. 37 Journal of Chemical Technology and Metallurgy, 50, 1, 2015 REFERENCES and turbulent free convection in a composite porous media, Int. J. Heat Mass Mass Transfer, 52, 2009, 1. D.B. Ingham, I. Pop, Transport Phenomena in Porous 588-596. Media, Elsevier, Amsterdam, 1998. 11. A.C. Baytas, A.F. Baytas, D.B. Ingham, I. Pop, 2. D.A. Nield, A. Bejan, Convection in Porous Media, Double diffusive natural convection in an porous Springer, New York, 2006. media filled with a step type porous layer: Non- 3. K.L. Walker, G.M. Homsy, Convection in porous Darcy flow, Int. J. Thermal Sciences, 48, 2009, cavity, J. Fluid Mech., 87, 1978, 449-474. 665-673. 4. A. Bejan, On the boundary layer regime in a vertical 12. D. Poulikakos, A. Bejan, Natural convection in enclosure filled with a porous medium, Lett. Heat vertically and horizontally layered porous media Mass Transfer, 6, 1979, 93-102. heated from the side, Int. J. Heat Mass Transfer, 26, 5. V. Prasad, F.A. Kulacki, Convective heat transfer in 1983, 1805-1814. a rectangular porous cavity effect of aspect ratio on 13. F.C. Lai, F.A. Kulacki, Natural convection across flow structure and heat transfer, J. Heat Transfer, 106, a vertical layered porous cavity. Int. J. Heat Mass 1984, 158-165. Transfer, 31, 1988, 1247-1260. 6. D.M. Manole, J.L. Lage, Numerical Benchmark 14. S.D. Egorov, V.I. Poleshaev, Thermal convection in Results for Natural Convection in a Porous Medium anisotropic porous insulation, Heat Transfer Res., Cavity, Heat and Mass Transfer in Porous Media, 25, 1993, 968-990. ASME Conference, Htd, 216, 1992, 55-60. 15. A.A. Merrikh, A.A. Mohamad, Non-Darcy effects 7. N.H. Saeid, I. Pop, Non-Darcy natural convection in in buoyancy driven flows in a porous media filled a square cavity filled with a porous medium, Fluid with vertically layered porous media, Int. J. Heat Dynamics Research, 36, 2005, 35-43. Mass Transfer, 45, 2002, 4305-4313. 8. M. Cieszko, J. Kubik, Derivation of matching condi- 16. H. Belghazi, M. El Ganaoui, J.C. Labbe, Analytical tions at the contact surface between fluid-saturated solution of unsteady heat conduction in a two- porous solid and bulk fluid, Transport Porous Media, layered material in imperfect contact subjected to 34, 1999, 319-336. a moving heat source, Int. J. of Thermal Sciences, 9. M. Mharzi, M. Daguenet, S. Daoudi, Thermosolutal 49, 2010, 311-318. natural convection in a vertically layered fluid- 17. J. Ordo´n˜ez-Miranda, J.J. Alvarado-Gil, Frequency- porous medium heated from the side, Energy modulated hyperbolic heat transport and effec- Conversion & Management, 41, 2000, 1065-1090. tive thermal properties in layered systems, Int. J. 10.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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
    [Show full text]
  • 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.
    [Show full text]
  • Forced Convection Heat Transfer Convection Is the Mechanism of Heat Transfer Through a Fluid in the Presence of Bulk Fluid Motion
    Forced Convection Heat Transfer Convection is the mechanism of heat transfer through a fluid in the presence of bulk fluid motion. Convection is classified as natural (or free) and forced convection depending on how the fluid motion is initiated. In natural convection, any fluid motion is caused by natural means such as the buoyancy effect, i.e. the rise of warmer fluid and fall the cooler fluid. Whereas in forced convection, the fluid is forced to flow over a surface or in a tube by external means such as a pump or fan. Mechanism of Forced Convection Convection heat transfer is complicated since it involves fluid motion as well as heat conduction. The fluid motion enhances heat transfer (the higher the velocity the higher the heat transfer rate). The rate of convection heat transfer is expressed by Newton’s law of cooling: q hT T W / m 2 conv s Qconv hATs T W The convective heat transfer coefficient h strongly depends on the fluid properties and roughness of the solid surface, and the type of the fluid flow (laminar or turbulent). V∞ V∞ T∞ Zero velocity Qconv at the surface. Qcond Solid hot surface, Ts Fig. 1: Forced convection. It is assumed that the velocity of the fluid is zero at the wall, this assumption is called no‐ slip condition. As a result, the heat transfer from the solid surface to the fluid layer adjacent to the surface is by pure conduction, since the fluid is motionless. Thus, M. Bahrami ENSC 388 (F09) Forced Convection Heat Transfer 1 T T k fluid y qconv qcond k fluid y0 2 y h W / m .K y0 T T s qconv hTs T The convection heat transfer coefficient, in general, varies along the flow direction.
    [Show full text]
  • Chaotic Flow in a 2D Natural Convection Loop
    International Journal of Heat and Mass Transfer 61 (2013) 565–576 Contents lists available at SciVerse ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt Chaotic flow in a 2D natural convection loop with heat flux boundaries ⇑ William F. Louisos a,b, , Darren L. Hitt a,b, Christopher M. Danforth a,c a College of Engineering & Mathematical Sciences, The University of Vermont, Votey Building, 33 Colchester Avenue, Burlington, VT 05405, United States b Mechanical Engineering Program, School of Engineering, The University of Vermont, Votey Building, 33 Colchester Avenue, Burlington, VT 05405, United States c Department of Mathematics & Statistics, Vermont Complex Systems Center, Vermont Advanced Computing Core, The University of Vermont, Farrell Hall, 210 Colchester Avenue, Burlington, VT 05405, United States article info abstract Article history: This computational study investigates the nonlinear dynamics of unstable convection in a 2D thermal Received 13 August 2012 convection loop (i.e., thermosyphon) with heat flux boundary conditions. The lower half of the thermosy- Received in revised form 1 February 2013 phon is subjected to a positive heat flux into the system while the upper half is cooled by an equal-but- Accepted 3 February 2013 opposite heat flux out of the system. Water is employed as the working fluid with fully temperature dependent thermophysical properties and the system of governing equations is solved using a finite vol- ume method. Numerical simulations are performed for varying levels of heat flux and varying strengths Keywords: of gravity to yield Rayleigh numbers ranging from 1.5 Â 102 to 2.8 Â 107.
    [Show full text]
  • Enhancement of Natural Convection Heat Transfer Coefficient by Using V-Fin Array
    International Journal of Engineering Research and General Science Volume 3, Issue 2, March-April, 2015 ISSN 2091-2730 Enhancement of Natural convection heat transfer coefficient by using V-fin array Rameshwar B. Hagote, Sachin K. Dahake Student of mechanical Engg. Department, MET’s IOE, Adgaon, Nashik (Maharashtra,India). Email. Id: [email protected], Contact No. +919730342211 Abstract— Extended surfaces known as fins are, used to enhance convective heat transfer in a wide range of engineering applications, and offer an economical and trouble free solution in many situations demanding natural convection heat transfer. Fin arrays on horizontal, inclined and vertical surfaces are used in variety of engineering applications to dissipate heat to the surroundings. Studies of heat transfer and fluid flow associated with such arrays are therefore of considerable engineering significance. The main controlling variables generally available to the designer are the orientation and the geometry of the fin arrays. An experimental work on natural convection adjacent to a vertical heated plate with a multiple V- type partition plates (fins) in ambient air surrounding is already done. Boundary layer development makes vertical fins inefficient in the heat transfer enhancement. As compared to conventional vertical fins, this V-type partition plate works not only as extended surface but also as flow turbulator. This V-type partition plate is compact and hence highly economical. The numerical analysis of this technique is done using Computational Fluid Dynamics (CFD) software, Ansys CFX , for natural convection adjacent to a vertical heated plate in ambient air surrounding. In numerical analysis angle of V-fin is further optimized for maximum average heat transfer coefficient.
    [Show full text]
  • Chapter 7. Convection and Complexity
    Chapter 7 Convection and complexity ... if your theory is found to be convection has been taken as the classic exam­ against the second law of ple of thermal convection, and the hexagonal planform has been considered to be typical of thermodynamics, I can give you no convective patterns at the onset of thermal con­ hope; there is nothing for it but to vection. Fifty years went by before it was real­ collapse in deepest humiliation. ized that Benard's patterns were actually driven from above, by surface tension. not from below by Eddington an unstable thermal boundary layer. Experiments Contrary to current textbooks ... the showed the san1.e style of convection when the fluid was heated from above, cooled from below observed world does not proceed or when performed in the absence of gravity. This from lower to higher "degrees of confirmed the top-down surface-driven nature of disorder", since when all the convection which is now called Marangoni or B€mard-Marangoni convection. gravitationally-induced phenomena Although it is not generally recognized as are taken into account the emerging such, mantle convection is a branch of the newly result indicates a net decrease in the renamed science of complexity. Plate tectonics may be a self-drivenfarjrom-equilibrium system that orga­ "degrees of disorder", a greater nizes itself by dissipation in and between the "degree of structuring" ... classical plates, the mantle being a passive provider of equilibrium thermodynamics ... has energy and material. Far-from-equilibrium sys­ to be completed by a theory of tems, particularly those in a gravity field, can locally evolve toward a high degree of order.
    [Show full text]
  • Convective Mass Transfer Correlations 5.9 Fluid Flow Through Pipes 5.10 Hot Wire Anemometer
    SCH1309 TRANSPORT PHENOMENA UNIT-V UNIT 5: Analogies for Transport processes Contents 5.1 Analogy for mass transfer 5.2 Application of dimensional analysis 5.3 Analogy among Mass, Heat and Momentum Transfer 5.4 Reynolds Analogy 5.5 Chilton Colburn analogy 5.6 Prandtl analogy 5.7 VanKarman analogy 5.8 Convective mass transfer correlations 5.9 Fluid flow through pipes 5.10 Hot wire anemometer 1 SCH1309 TRANSPORT PHENOMENA UNIT-V 5.1 Analogy of Mass Transfer Mass transfer by convection involves the transport of material between a boundary surface (such as solid or liquid surface) and a moving fluid or between two relatively immiscible, moving fluids. There are two different cases of convective mass transfer: 1. Mass transfer takes place only in a single phase either to or from a phase boundary, as in sublimation of naphthalene (solid form) into the moving air. 2. Mass transfer takes place in the two contacting phases as in extraction and absorption. Convective Mass Transfer Coefficient In the study of convective heat transfer, the heat flux is connected to heat transfer coefficient as Q A q h t s t m -------------------- (1.1) The analogous situation in mass transfer is handled by an equation of the form N A k c C As C A -------------------- (1.2) The molar flux N A is measured relative to a set of axes fixed in space. The driving force is the difference between the concentration at the phase boundary, CAS (a solid surface or a fluid interface) and the concentration at some arbitrarily defined point in the fluid medium, C A .
    [Show full text]
  • A Numerical Study of Natural Convection Properties of Supercritical Water (H2O) Using Redlich–Kwong Equation of State
    Sådhanå (2019) 44:37 Ó Indian Academy of Sciences https://doi.org/10.1007/s12046-018-1035-3Sadhana(0123456789().,-volV)FT3](0123456789().,-volV) A numerical study of natural convection properties of supercritical water (H2O) using Redlich–Kwong equation of state HUSSAIN BASHA1, G JANARDHANA REDDY1,* and N S VENKATA NARAYANAN2 1 Department of Mathematics, Central University of Karnataka, Kalaburagi 585 367, India 2 Department of Chemistry, Central University of Karnataka, Kalaburagi 585 367, India e-mail: [email protected]; [email protected]; [email protected] MS received 8 January 2018; revised 2 November 2018; accepted 16 November 2018; published online 25 January 2019 Abstract. In this article, the Crank-Nicolson implicit finite difference method is utilized to obtain the numerical solutions of highly nonlinear coupled partial differential equations (PDEs) for the flow of supercritical fluid (SCF) over a vertical flat plate. Based on the equation of state (EOS) approach, suitable equations are derived to calculate the thermal expansion coefficient (b) values. Redlich–Kwong equation of state (RK-EOS), Peng-Robinson equation of state (PR-EOS), Van der Waals equation of state (VW-EOS) and Virial equation of state (Virial-EOS) are used in this study to evaluate b values. The calculated values of b based on RK-EOS is closer to the experimental values, which shows the greater accuracy of the RK-EOS over PR-EOS, VW-EOS and Virial-EOS models. Numerical simulations are performed for H2O in three regions namely subcritical, supercritical and near critical regions. The unsteady velocity, temperature, average heat and momentum transport coefficients for different values of reduced pressure and reduced temperature are discussed based on the numerical results and are shown graphically across the boundary layer.
    [Show full text]
  • Interferometric Study of Natural Convection Heat Transfer from a Vertical Flat Plate with Transverse Roughness Elements Sushil Hiroo Bhavnani Iowa State University
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1987 Interferometric study of natural convection heat transfer from a vertical flat plate with transverse roughness elements Sushil Hiroo Bhavnani Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Mechanical Engineering Commons Recommended Citation Bhavnani, Sushil Hiroo, "Interferometric study of natural convection heat transfer from a vertical flat plate with transverse roughness elements " (1987). Retrospective Theses and Dissertations. 11669. https://lib.dr.iastate.edu/rtd/11669 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]. INFORMATION TO USERS While the most advanced technology has been used to photograph and reproduce this manuscript, the quality of the reproduction is heavily dependent upon the quality of the material submitted. For example: • Manuscript pages may have indistinct print. In such cases, the best available copy has been filmed. • Manuscripts may not always be complete. In such cases, a note will indicate that it is not possible to obtain missing pages. • Copyrighted material may have been removed from the manuscript. In such cases, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, and charts) are photographed by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps.
    [Show full text]
  • Investigation of the Natural Convection Boundary Condition in Microfabricated Structures
    International Journal of Thermal Sciences 47 (2008) 820–824 www.elsevier.com/locate/ijts Investigation of the natural convection boundary condition in microfabricated structures X. Jack Hu ∗, Ankur Jain 1, Kenneth E. Goodson Mechanical Engineering Department, Stanford University, Stanford, CA 94305, USA Received 26 March 2007; received in revised form 17 July 2007; accepted 18 July 2007 Available online 30 August 2007 Abstract Heat loss through surrounding air has an important thermal effect on microfabricated structures. This effect is generally modeled as a natural convection boundary condition. However, the correct procedure for the determination of the convective coefficient (h) at microscales continues to be debated. In this paper, a microheater is fabricated on a suspended thin film membrane. The natural convection on the microheater is investigated using 3-omega measurements and complex analytical modeling. It is found that the value of h that fits experimental data should have an apparently larger value than that at larger scales; however, it is also shown that the increased h is actually contributed by heat conduction instead of heat convection. A method of determining the correct h that can be used for microfabricated structures is proposed by using the heat conduction shape factor. © 2007 Elsevier Masson SAS. All rights reserved. Keywords: Microscale natural convection; Convective coefficient; 3-omega measurement; Micro-Electrical–Mechanical-System (MEMS) device; Micro fabricated structure; Microscale heat transfer 1. Introduction the relative change of importance of driving forces at the mi- croscale. Peirs et al. [1] have proposed a scaling law for natural 2 Natural convection is a frequently encountered boundary convective coefficient and suggested h ∼ 100 W/m K for air condition in the thermal design, testing and modeling of Micro- when the scale is less than 100 µm, which is 5–10 times larger Electrical–Mechanical-System (MEMS) devices.
    [Show full text]
  • Study of Heat Transfer Phenomenon During Natural Convection
    Scholars' Mine Doctoral Dissertations Student Theses and Dissertations Spring 2016 Study of heat transfer phenomenon during natural convection Muhammad Yousaf Follow this and additional works at: https://scholarsmine.mst.edu/doctoral_dissertations Part of the Chemical Engineering Commons, and the Nuclear Engineering Commons Department: Nuclear Engineering and Radiation Science Recommended Citation Yousaf, Muhammad, "Study of heat transfer phenomenon during natural convection" (2016). Doctoral Dissertations. 2494. https://scholarsmine.mst.edu/doctoral_dissertations/2494 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. STUDY OF HEAT TRANSFER PHENOMENON DURING NATURAL CONVECTION by MUHAMMAD YOUSAF A DISSERTATION Presented to the Faculty of the Graduate School of the MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY in NUCLEAR ENGINEERING 2016 Approved by: Shoaib Usman, Advisor Ayodeji B. Alajo Joshua P. Schlegel Joseph D. Smith Muthanna H. Al-Dahhan ii 2016 Muhammad Yousaf All Rights Reserved iii PUBLICATION DISSERTATION OPTION This dissertation has been prepared in the style utilized by International Journal of Heat and Mass Transfer. These pages consist of three separate papers (i.e. Paper I (4-46), Paper II (Pages 47-79), and Paper III (Pages 80-117)). Papers I and II have been submitted for publication, while Paper III has been published in the said journal. iv ABSTRACT The purpose of the present study was to numerically investigate the effects of the roughness elements on the heat transfer during natural convection.
    [Show full text]