DOCSLIB.ORG

Chapter 5 Principles of Force Convection

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Chapter 5 Principles of Force Convection Chapter 5 Principles of Force Convection 5.1 Introduction The preceding chapters have considered the mechanism and calculation of conduction heat transfer. Convection was considered only insofar as it related to the boundary conditions imposed on a conduction problem. We now wish to examine the methods of calculating convection heat transfer and, in particular, the ways of predicting the value of the convection heat-transfer coefficient h. Our development in this chapter is primarily analytical in character and is concerned only with forced-convection flow systems. Subsequent chapters will present empirical relations for calculating forced-convection heat transfer and will also treat the subjects of natural convection. 5.2 Viscous Flow 5.2.1 Flow on a flat plate (external flow) Consider the flow over a flat plate as shown in Figures 5.1 and 5.2. Beginning at the leading edge of the plate, a region develops where the influence of viscous forces is felt. These viscous forces are described in terms of a shear stress between the fluid layers. If this stress is assumed to be proportional to the normal velocity휏 gradient, we have the defining equation for the viscosity, = 5.1 푑푢 The휏 휇region푑푦 of flow that develops from the leading edge of the plate in which the effects of viscosity are observed is called the boundary layer. Some arbitrary point is used to designate the y position where the boundary layer ends; this point is usually chosen as the y coordinate where the velocity becomes 99 percent of the free-stream value. Initially, the boundary-layer development is laminar, but at some critical distance from the leading edge, depending on the flow field and fluid properties, small disturbances in the flow begin to become amplified, and a transition process takes place until the flow becomes turbulent. The turbulent-flow region may be pictured as a random churning action with chunks of fluid moving to and fro in all directions. The transition from laminar to turbulent flow occurs when = = > 5 10 (transiant) 푢∞푥 휌푢∞푥 5 휐 5 휇10 푅푒(laminar)∗ 5 푅푒Where≤ ∗ = free stream velocity, m/s. 푢 ∞= distance from leading edge, m. 2 푥 = =kinematic viscosity, m /s. 휇 휐 휌 = 5.2 푢∞푥 푅푒 푥 휐 Figure 5.1: Sketch showing different boundary-layer flow regimes on a flat plate. Figure 5.2: Laminar velocity profile on a flat plate. 5.3 Laminar Boundary Layer on a Flat Plate Consider the elemental control volume shown in Figure 5.3. We derive the equation of motion for the boundary layer by making a force-and-momentum balance on this element. To simplify the analysis we assume: 1. The fluid is incompressible and the flow is steady. 2. There are no pressure variations in the direction perpendicular to the plate. 3. The viscosity is constant. 4. Viscous-shear forces in the y direction are negligible. Figure 5.4 Elemental control volume for force balance on laminar boundary layer. The mass continuity equation for the boundary layer. + = 0 5.3 T휕푢he momentum휕푣 equation of the laminar boundary layer with constant properties. 휕푥 휕푦 + = 2 5.4 휕푢 휕푢 휕 푢 휕푝 2 휌 �푢 휕푥 푣 휕푦� 휇 휕푦 − 휕푥 Figure 5.5: Elemental control volume for integral momentum analysis of laminar boundary layer. The mass flow through plane 1 in Figure 5.5 is = 퐻 푚Voṅ Kármán∫0 휌푢 approximate푑푦 solution of equations 5.3 and 5.4 gives . = 4 64푥 1 �2 훿 푅푒푥 The exact solution of the boundary-layer equations = 5.5 5푥 1 �2 훿 푅푒푥 The velosity profile of the stream in x-direction within the baundary layer is given by: = 5.6 푢 3 푦 1 푦 3 ∞ And푢 the2 훿 energy− 2 �훿 �equation of the laminar boundary layer is: + = + 2 5.7 휕푇 휕푇 휕 푇 휇 휕푢 2 2 푢 휕푥 푣 휕푦 훼 휕푦 휌푐푝 �휕푦� For low velocity incompressible flow, we have + = 2 5.8 휕푇 휕푇 휕 푇 2 There푢 휕푥 is푣 a휕푦 striking훼 휕푦 similarity between equation 5.8 and the momentum equation for costant pressure, + = 2 5.9 휕푢 휕푢 휕 푢 2 푢 휕푥 푣 휕푦 훼 휕푦 Example 5.1: Mass Flow and Boundary-Layer Thickness -3 Air at 27◦C and 1 atm flows over a flat plate at a speed of 2 m/s. Calculate the boundary-layer thickness at distances of 20 cm and 40 cm from the leading edge of the plate. Calculate the mass flow that enters the boundary layer between = 20 cm −5 and = 40 cm. The viscosity of air at 27◦C is 1.85×10 kg/m· s. Assume푥 unit depth in the푥 z direction. Solution The density of air is calculated from . 3 = = = 1.177 kg/m ( )( 5 ) 푝 1 0132∗10 푅푇 287 27+273 휌 = 푢∞푥 . 푅푒푥 = 20휐 = = = = 25,448 At : . × 푢∞푥 휌푢∞푥 1 177∗2∗0 2 푥 . 푥 = 40 푐푚 푅푒 = 휐 = 휇 1 85=1050−5,896 At : . × 휌푢∞푥 1 177∗2∗0 4 The푥 boundary푐푚 layer푅푒푥 thickness휇 is1 calculated85 10−5 from: . = 4 64푥 1 �2 훿 푅푒푥 . At = 20 , = = 0.00582 m. ( ) 4 64∗0 2 1 �2 푥 푐푚 훿 25488. At = 40 , = = 0.00823 m. ( ) 4 64∗0 4 1� 푥 푐푚 훿 50896 2 To calculate the mass flow that enters the boundary layer from the free stream between = 20 cm and = 40 cm, we simply take the difference between the mass flow in the푥 boundary layer푥 at these two x positions. At any x position the mass flow in the boundary layer is given by the integral = 훿 푚̇ ∫0 휌푢 푑푦 = 3 푦 1 푦 3 ∞ 2 훿 2 훿 푢 푢 − 3� � 1 3 5 = = 2 2 8 훿 푦 푦 ∞ ∞ 0 푢 훿 − 훿 푢 훿 푚̇ =∫ 휌 ( � )�=푑푦(1.177휌 2(0.00823 0.00582) = 0.00354 kg/s 5 5 ∞ 40 20 ∆푚̇ 8 휌푢 훿 − 훿 8 ∗ − 5.4 Thermal boundary layer Just as the hydrodynamic boundary layer was defined as that region of the flow where viscous forces are felt, a thermal boundary layer may be defined as that region where temperature gradients are present in the flow. These temperature gradients would result from a heat-exchange process between the fluid and the wall. Consider the system shown in Figure 5.6. The temperature of the wall is , the temperature of the fluid outside the thermal boundary layer is , and the thickness푇푤 of the thermal boundary layer is designated as . At the wall, the푇∞ velocity is zero, and the heat transfer into the fluid takes place by훿 conduction.푡 Thus the local heat flux per unit area is: = 5.10 푞 휕푇 퐴 −푘 휕푦� From Newton’s푤푎푙푙 law of cooling = ( ) 5.11 푞 퐴 푤 ∞ whereℎ h 푇is the− 푇convection heat-transfer coefficient. Combining these equations, we have = 휕푇 ( ) 5.12 −푘휕푦�푤푎푙푙 ℎ 푇푤−푇∞ Figure 5.6: Temperature profile in the thermal boundary layer. Then we need only find the temperature gradiant at the wall to evaluate . Therefore, the temperature distribution is: ℎ = = 5.13 휃 푇−푇푤 3 푦 1 푦 3 휃∞ 푇∞−푇푤 2 훿푡 − 2 �훿푡� The thermal boundary layer can calculated from the equation below: = 1 1 5.14 . 3 �3 훿푡 1 −1 푥표 �4 �3 훿 1 026 푃푟 � − � 푥 � � When the plate is heated over the entire length, = 0, and 표 = 푥 . 5.15 훿푡 1 −1 �3 Where훿 1 026 the푃푟 Prandtl number is dimensionless when a consistent set of units is used: = = = 5.16 휇 휐 �휌 푐푝휇 푘 푃푟 훼 �휌푐푝 푘 The local convective heat transfer coefficient is calculated from the equation as below: = 0.332 1 −1 5.17 1 3 �3 1 푢∞ �2 푥표 �4 �3 ℎ푥 푘 푃푟 � 휐푥 � � − � 푥 � � The equation may be nondimensionalized by multiplying both sides by , producing the 푥 dimensionless group on the left side, 푘 = 5.18 ℎ푥푥 푥 called푁푢 the Nusselt푘 number afterWilhelm Nusselt, who made significant contributions to the theory of convection heat transfer. Finally, = 0.332 1 −1 5.19 3 �3 1 1 푥표 �4 �3 �2 푁푢푥 푃푟 푅푒푥 � − � 푥 � � or, for the plate heated over its entire length, = 0 and 표 = 0.332 푥 0.6 < > 50 5.20 a 1 1 �3 �2 푁푢푥 푃푟 푅푒푥 푃푟 Equation (5.20 a) is applicable to fluids having Prandtl numbers between about 0.6 and 50. It would not apply to fluids with very low Prandtl numbers like liquid metals or to high- Prandtl-number fluids like heavy oils or silicones. For a very wide range of Prandtl numbers, Churchill and Ozoe have correlated a large amount of data to give the following relation for laminar flow on an isothermal flat plate: . = 1 1 > 100 5.20 b �2 �3 0 3387.푅푒푥 푃푟 1 푥 2 �4 푥 푁푢 0 0468 �3 푅푒 푃푟 �1+� 푃푟 � � Equations (5.17), (5.19), and (5.20 a) express the local values of the heat-transfer coefficient in terms of the distance from the leading edge of the plate and the fluid properties. For the case where = 0 the average heat-transfer coefficient and Nusselt number may be obtained by푥표 integrating over the length of the plate: = 퐿 = 2 5.21 ∫0 ℎ푥푑푥 � 퐿 푥=퐿 assumingℎ ∫0 푑푥 the heatedℎ section is at the constant temperature . For the plate heated over the entire length, 푇푤 = = 2 5.22 ℎ�퐿 푁푢Or���� 퐿 푘 푁푢푥=퐿 = = 0.664 5.23 ℎ�퐿 1� 1 2 �3 퐿 퐿 Where:푁푢���� 푘 푅푒 푃푟 = 5.24 휌푢∞퐿 퐿 For푅푒 a plate휇 where heating starts at = , it can be shown that the average heat transfer coefficient can be expressed as푥 푥표 = 2 3� 푥표 4 1−� �퐿� 표 ℎ �푥 −퐿 ℎ푥=퐿 � 퐿 퐿−푥표 � In this case, the total heat transfer for the plate would be = ( )( ) 표 The푞푡표푡푎푙 foregoingℎ�푥 −퐿 analysis퐿 − 푥표 was푇푤 based− 푇∞ on the assumption that the fluid properties were constant throughout the flow.
Load more

Recommended publications
  • 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.
    [Show full text]
  • Heat Transfer Data
    Appendix A HEAT TRANSFER DATA This appendix contains data for use with problems in the text. Data have been gathered from various primary sources and text compilations as listed in the references. Emphasis is on presentation of the data in a manner suitable for computerized database manipulation. Properties of solids at room temperature are provided in a common framework. Parameters can be compared directly. Upon entrance into a database program, data can be sorted, for example, by rank order of thermal conductivity. Gases, liquids, and liquid metals are treated in a common way. Attention is given to providing properties at common temperatures (although some materials are provided with more detail than others). In addition, where numbers are multiplied by a factor of a power of 10 for display (as with viscosity) that same power is used for all materials for ease of comparison. For gases, coefficients of expansion are taken as the reciprocal of absolute temper­ ature in degrees kelvin. For liquids, actual values are used. For liquid metals, the first temperature entry corresponds to the melting point. The reader should note that there can be considerable variation in properties for classes of materials, especially for commercial products that may vary in composition from vendor to vendor, and natural materials (e.g., soil) for which variation in composition is expected. In addition, the reader may note some variations in quoted properties of common materials in different compilations. Thus, at the time the reader enters into serious profes­ sional work, he or she may find it advantageous to verify that data used correspond to the specific materials being used and are up to date.
    [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]
  • External Flow Correlations (Average, Isothermal Surface)
    External Flow Correlations (Average, Isothermal Surface) Flat Plate Correlations Flow Average Nusselt Number Restrictions Conditions Note: All fluid properties are Laminar 1/ 2 1/3 Pr 0.6 evaluated at film NuL 0.664ReL Pr temperature for flat plate correlations. 4/5 1/3 NuL 0.037 ReL A Pr 0.6 Pr 60 Turbulent 4/5 1/ 2 8 where A 0.037 Re x,c 0.664Re x,c Re x,c ReL 10 Cylinders in Cross Flow Cylinder Reynolds Cross Number Average Nusselt Number Restrictions Note: All fluid properties Section Range are evaluated at film temperature for cylinder V 0.4-4 0.330 1/3 in cross flow correlations. D NuD 0.989ReD Pr Pr 0.7 V D 4-40 Nu 0.911Re0.385 Pr1/3 Pr 0.7 D D Alternative Correlations for Circular Cylinders in Cross Flow: V 0.466 1/3 D 40-4,000 NuD 0.683ReD Pr . The Zukauskas correlation (7.53) and V 4,000- 0.618 1/3 the Churchill and Bernstein correlation D Nu 0.193Re Pr 40,000 D D (7.54) may also be used V 40,000- 0.805 1/3 D Nu 0.027 Re Pr 400,000 D D V 6,000- D 0.59 1/3 NuL 0.304ReD Pr gas flow 60,000 Freely Falling Liquid Drops V 5,000- 0.66 1/3 D Nu 0.158Re Pr gas flow Average Nusselt Number 60,000 D D V 5,200- 0.638 1/3 1/ 2 1/3 D Nu 0.164Re Pr gas flow NuD 2 0.6ReD Pr 20,400 D D Note: All fluid properties are evaluated V 20,400- 0.78 1/3 D Nu 0.039Re Pr gas flow at T for the falling drop correlation.
    [Show full text]
  • Validation of Heat Transfer Coefficients – Single Pipes with Different Surface
    ÿ ÿ ÿ ÿ ÿÿÿ ÿ ÿ !"#$%!ÿ"'#!(!ÿ ÿ )0123ÿ4567589@ÿ)4ABC8DCE80C6FGÿ ÿ ÿvwwxyÿ yÿÿÿÿxxÿ )45CF7ÿHA9AH0A5IÿPQRRRRRRÿ ÿ y ÿ ÿ S4AFÿ@ÿTAH05CB0A2ÿ8BBAHHÿ ÿ U5C0A5Gÿÿ ÿ dÿeÿvÿfghh VVVVVVVVVVVVVVVVÿ WU5C0A5XHÿHC7F8015AYÿ `8B1D03ÿH14A5aCH65Gÿ vgÿxÿzhx ÿ bc0A5F8DÿH14A5aCH65WHYGÿ ÿ ve{ÿ|{sÿzrÿhÿuk ÿ deAHCHÿ0C0DAGÿ ÿiÿwÿyÿxwÿ ww xjÿkÿllxÿmyÿwwÿxw ÿhxÿÿ ÿyÿ nÿh ÿ ÿ ÿ f5A2C0HÿWbfd)YGÿop ÿ gA3ÿh652HGÿ ÿ ÿqÿÿrsÿmtsÿu sÿu sÿ ÿÿÿÿÿÿÿÿÿi87AHGÿVVVVVVVÿ ÿlÿmxsÿyÿxxsÿyÿxwsÿyÿ ÿÿÿÿÿ ÿxwÿ ww sÿ g gÿyÿxwsÿ ÿÿÿÿÿpÿAFBD6H15AGÿVVVVÿov ÿyÿxwÿ x ÿ ÿ ÿ ÿÿÿÿÿÿÿÿÿ)08a8F7A5IÿVVVVVVRwxpxyp Rÿ ÿÿÿÿÿÿq80A@3A85ÿ ÿ ÿ `56F0ÿ487Aÿr65ÿ98H0A5ÿ0eAHCHÿ `8B1D03ÿ6rÿ)BCAFBAÿ8F2ÿdABeF6D673ÿ qABCHC6Fÿ982Aÿs3ÿ0eAÿqA8FÿSB06sA5ÿtQ0eÿPQQuÿ ÿ M.Sc. Thesis Master of Science in Engineering Validation of heat transfer coefficients Single pipes with different surface treatments and heated deck element Bjarte Odin Kvamme University of Stavanger 2016 Department of Mechanical and Structural Engineering and Materials Science Faculty of Science and Technology University of Stavanger P.O. Box 8600 Forus N-4036 Stavanger, Norway Phone +47 5183 1000 [email protected] www.uis.no Summary This master thesis has been written at the suggestion of GMC Maritime AS in agreement with the University of Stavanger. The interest in the polar regions is increasing, and further research is required to evaluate the adequacy of the equipment and appliances used on vessels traversing in polar waters. The decrease in ice extent in the Arctic has renewed the interest in the Northern Sea Route. Oil and gas exploration has moved further north during the past decades, and tourism in the polar regions is becoming more popular. The introduction of the Polar Code by the International Maritime Organization attempts to mitigate some of the risks the vessels in Polar waters are exposed to.
    [Show full text]
  • How to Calculate the Free Convection Coefficient for Vertical Or Horizontal Isothermal Planes
    How to Calculate the Free Convection Coefficient for Vertical or Horizontal Isothermal Planes The free convection coefficient can be described in terms of dimensionless groups. Familiarize yourself with the dimensionless groups described in Table 1 before continuing on with the procedures listed below for calculating the free convection coefficient. Table 1: Dimensionless groups of importance for heat transfer and fluid flow Group Definition Interpretation Biot number (Bi) Ratio of internal thermal resistance of a solid body to its surface thermal resistance Grashof number (GrL) Ratio of buoyancy to viscous forces Nusselt number (NuL) Dimensionless heat transfer coefficient; ratio of convection heat transfer to conduction in a fluid layer of thickness L Prandtl number (Pr) Ratio of molecular momentum diffusivity to thermal diffusivity Procedure for Calculating the Free Convection Coefficient of Vertical Isothermal Planes The film temperature is given as where T∞ represents the temperature of the environment and Tw represents the wall temperature. The Grashof number is found using where g is the gravitational constant, L is the length of the vertical surface, ν is the kinematic viscosity of the convective fluid evaluated at Tf and β represents the temperature coefficient of thermal conductivity. The Rayleigh is given by where Pr represents the Prandtl number of the convective fluid at Tf. The average Nusselt number given by Churchill and Chu (1975) is 9 for RaL < 10 for 10-1 < Ra < 1012 L The average free-convection heat transfer coefficient is given by where k is the thermal conductivity of the convective fluid at Tf. Procedure for Calculating the Free Convection Coefficient of Horizontal Isothermal Planes The film temperature is given as where T∞ represents the temperature of the environment and Tw represents the wall temperature.
    [Show full text]
  • 3.2 Cryogenic Convection Heat Transfer
    3.2 Cryogenic Convection Heat Transfer Involves process of heat transfer between q solid material and adjacent cryogenic fluid TTf = mean Classic heat transfer problem (Newton’s law) 2 m& f q(kW/m ) = h (Ts –Tf) Configurations of interest TT= Internal forced flow (single phase, f mean ) q Free convection (single phase,TT f = ∞ ) Internal two phase flow Pool boiling (two phase) Understanding is primarily empirical leading to correlations based on dimensionless numbers Issue is relevant to the design of: Liquid T Heat exchangers f Ts Cryogenic fluid storage Superconducting magnets Low temperature instrumentation USPAS Short Course Boston, MA 6/14 to 6/18/2010 1 Single phase internal flow heat transfer Forced T D m, f T Convection s & Q luid correlationsClassical f The heat transfer coefficient in a classical fluid system is generally correlated in the form where the Nusselt number, hD where, NuD ≡ and D is the characteristic length k f For laminar flow, NuD = constant ~ 4 (depending on b.c.) For turbulent flow (Re > 2000) D μ C n m Pr ≡ f p Nu(ReD = , f D Pr)= C D Reand Pr (Prandtl number) k f Dittus-Boelter Correlation for classical fluids (+/- 15%) 4 2 5 5 0Nu .D = 023 Re Pr Note that fluid properties should be TTs+ f computed at T (the “film temperature”): T ≡ f f 2 USPAS Short Course Boston, MA 6/14 to 6/18/2010 2 Johannes Correlation (1972) Improved correlation specifically for helium (+/- 8.3%) 0− . 716 4 2 ⎛ T ⎞ 0 .Nu = 02595 Re5 ⎜ s ⎟ Pr D D ⎜ ⎟ ⎝ Tf ⎠ Last factor takes care of temperature dependent properties Note that one often does not know Tf, so iteration may be necessary.
    [Show full text]
  • Estimation of Film Boiling Heat Transfer Coefficients for Cylindrical Heaters in Corresponding States Fluids
    Scholars' Mine Masters Theses Student Theses and Dissertations 1968 Estimation of film boiling heat transfer coefficients for cylindrical heaters in corresponding states fluids Gary Joseph Capone Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses Part of the Chemical Engineering Commons Department: Recommended Citation Capone, Gary Joseph, "Estimation of film boiling heat transfer coefficients for cylindrical heaters in corresponding states fluids" (1968). Masters Theses. 5298. https://scholarsmine.mst.edu/masters_theses/5298 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]. ESTL"1A'riON OF FIU1 BOIJ... ING HEAT TRANSFER COEFFICIEN.rS FOR CYLII\TDRICAL HEATERS IN CORRESPONDING STATES FLUIDS BY ' GARY JOSEPH CAPONE I A THESIS submitted to the faculty of THE UNIVERSITY OF MISSOURI - ROLLA in partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE IN CHEMICAL ENGIN~ERING Rolla, Missouri 1968 TABLE OF CONTENTS Page Abstract • • • • . iii Acknowledgements . • iv List of Illustrations •• v List of Tables • . • • vi CHAPTER Introduction. 1 II. Previous Work 4 III. Film Boiling of Corresponding States Fluids • • • 10 IV. Experimental Equipment •• • • 13 v. Experimental Procedure •• • • • • 17 vr. Results • • • . • • • 19 \~I. Discussion of Results • 24 VIII. Conclusions • • • • • 33 Nomenclature • • • • • 35 Bibliography • • • • 37 Appendices • • • • • 39 A. Discussion of Errors •• . 40 B. Sample Calculations . • • • 41 c. Calculated Data •• . • 44 D. Operating Conditions. 53 Vlta • • • • 55 iii ABSTRACT An investigation of film boiling heat transfer was made with cylindrical heaters.
    [Show full text]
  • CHAPTER 5 HEAT TRANSFER THEORY Heat Transfer Is An
    CHAPTER 5 HEAT TRANSFER THEORY Heat transfer is an operation that occurs repeatedly in the food industry. Whether it is called cooking, baking, drying, sterilizing or freezing, heat transfer is part of the processing of almost every food. An understanding of the principles that govern heat transfer is essential to an understanding of food processing. Heat transfer is a dynamic process in which heat is transferred spontaneously from one body to another cooler body. The rate of heat transfer depends upon the differences in temperature between the bodies, the greater the difference in temperature, the greater the rate of heat transfer. Temperature difference between the source of heat and the receiver of heat is therefore the driving force in heat transfer. An increase in the temperature difference increases the driving force and therefore increases the rate of heat transfer. The heat passing from one body to another travels through some medium which in general offers resistance to the heat flow. Both these factors, the temperature difference and the resistance to heat flow, affect the rate of heat transfer. As with other rate processes, these factors are connected by the general equation: rate of transfer = driving force / resistance For heat transfer: rate of heat transfer = temperature difference/ heat flow resistance of medium During processing, temperatures may change and therefore the rate of heat transfer will change. This is called unsteady-state heat transfer, in contrast to steady-state heat transfer when the temperatures do not change. An example of unsteady-state heat transfer is the heating and cooling of cans in a retort to sterilize the contents.
    [Show full text]
  • Comparison of Heat Transfer Coefficients in Free and Forced Convection Using Circular Annular Finned Tubes
    International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: [email protected] Volume 5, Issue 4, April 2016 ISSN 2319 - 4847 Comparison of Heat Transfer Coefficients in Free and Forced Convection using Circular Annular Finned Tubes 1Dr. Abdul Jabbar N. Khalif, 2Israa Riyadh Aziz Al mousawi 1Assistant professor College of Engineering – AL Nahrain University 2Mechanical Engineer College of Engineering –ALNahrainUniversity ABSTRACT In this study, heat transfer coefficients in both free and forced convection heat transferusing vertical circular annular finned tubes were investigatedexperimentally. For this purpose three types of metals were used, namely,Aluminum, Copper, and Iron. These metals differ from each other intheir specific weight,cost and thermal conductivities which are 204 W/m.K for Aluminum, 386 W/m.K for Copper and 73 W/m.K for iron.Surface temperature employed during experiments varied between 40and 60 Co at 10 Co intervals. The spacing between fins is 1cm. It was found that the heat transfer coefficient increases with increasing air speed from (1to 3) m/s, and there is anoticeable increase in heat transfer coefficientwhen using Copper metal to manufacture the tube and the fins as compared to Aluminum and Ironmetals. 1. INTRODUCTION Finned surfaces are widely used in compact heat exchangers used in many applications such as air conditioners, aircrafts and chemical processing plants.Finned surfaces are also used in cooling electronic components.The general disposition of fins on the base surface is usually either longitudinal (straight fins) or circumferential (radial fins). Circular annular-finned tubes heat exchangers are also commonly used in industry.
    [Show full text]
  • A Guide to Calculate Convection Coefficients for Thermal Problems Application Note
    A Guide to Calculate Convection Coefficients for Thermal Problems Application Note Keywords: Thermal analysis, convection coefficients, computational fluid dynamics, free convection, forced convection. Abstract: The present application note is a guide that can be used to calculate thermal convection coefficients. As such it approaches the topic of computational fluid dynamics (CFD) since the problem of calculating convection coefficients is situated at the intersection between CFD and Thermal analysis. Some basic presentation of the theoretical background is also included for more clarity of the approach of the subject. A few examples of the computational process are also included and deal with practical cases of free convection as well as forced convection. Procedure to calculate convection coefficients 1. Introduction As widely known the specification of convection coefficients is a necessity in thermal applications when cooling of surfaces in contact with fluids (liquids and/or gases) occurs and a thermal convection mechanism takes place. At its core the problem is in fact one in which the thermal aspect is strongly coupled with the fluid flow aspect: temperature distribution influences the fluid flow characteristic quantities while the fluid flow parameters influence the temperature distribution. It can be said that in such a scenario convection coefficients –if necessary at all- can be obtained as one of the results of a coupled Computational Fluid Dynamics (CFD) – Thermal analysis. While the full analysis of the coupled problem is quite complicated, there are ways to simplify the computational task and produce results for the convection coefficients that have acceptable accuracy. One of the most widely spread is the method using dimensionless parameters.
    [Show full text]
  • UNIT II CONVECTIVE HEAT TRANSFER Course Material
    UNIT II CONVECTIVE HEAT TRANSFER Course material Adapted from: 1. Warren. L, McCabe, Julian,C. Smith and Peter Harriott, “Unit Operations of Chemical Engineering”, 7th Edn., McGraw Hill International Edition, NewYork 2005. 2. Holman. J.P., “Heat Transfer” , 9th Edn., Tata McGraw Hill Book Co., New Delhi, 2008. 3. R.C.Sachdeva, “Fundamentals of Engineering Heat and Mass Transfer”, 4th Edition,New Age International Publishers,2010 4. http://nptel.ac.in/courses/103103032/ - Dr. Anil Verma Dept. of Chemical Engineering,IIT Guwahati 5. www.che.utexas.edu/course/che360/lecture_notes/chapter_2.ppt CONTENTS Heat flux, average temperature of fluid stream, overall heat transfer coefficient, LMTD, individual heat transfer coefficients, relationship between individual and overall heat transfer coefficients. Concept of heat transfer by convection, natural and forced convection, application of dimensional analysis for convection, heat transfer to fluids without phase change: heat transfer coefficient calculation for natural and forced convection, heat transfer to fluids with phase change: heat transfer from condensing vapours, dropwise and film-type condensation, heat transfer coefficients calculation for film-type condensation. 2.1. Heat flux, average temperature of fluid stream Heat flux: Heat transfer calculations are based on the area of the heating surface area. The rate of heat transfer per unit area is called the heat flux. Bulk mean temperature: When a fluid is heated or cooled the temperature will vary throughout the cross section of the stream. Because of these temperature gradients through out the stream it is necessary to state what is meant by the temperature of the stream. It is the temperature that will be attained if the entire 1 fluid stream flowing across the section are withdrawn and mixed adiabatically to a uniform temperature.
    [Show full text]