1、Chapter 6,College of Nuclear Science and Technology,Empirical and Practical Relations for Forced-Convection Heat Transfer,1,Chapter 6,College of Nuclear Science and Technology,2,6-1 Introduction,The discussion and analyses of Chapter 5 have shown how forced-convection heat transfer may be calculated
2、 for several cases of practical interest; however, the problems considered were those that could solved in an analytical fashion.,Chapter 6,College of Nuclear Science and Technology,3,But, it is not always possible to obtain analytical solutions to convection problems, and the individual is forced t
3、o resort to experimental methods to obtain design information, as well as to secure the more elusive date that increase the physical understanding of the process.,What we have to do:,Generalize the results of ones experiments in form of some empirical correlation,Chapter 6,College of Nuclear Science
4、 and Technology,4,Difficulties,Which variables should we measure? What functional form should the data be organized into? Its hard and expensive to do the experiments, so, how many experiments should we do?,Chapter 6,College of Nuclear Science and Technology,5,Similarity Considerations,Purpose: to d
5、o research on the relationship between similar physical phenomena.,For similar physical phenomena: at corresponding time with corresponding location on the physical quantity related with the phenomenon correspondence proportional. For same type of phenomena: Phenomenon described by differential equa
6、tions with the same form and content.,Chapter 6,College of Nuclear Science and Technology,6,Characteristics for physical phenomena similarity,The same characteristic numbers are equal There is somewhat relationship between different characteristics. For example,Chapter 6,College of Nuclear Science a
7、nd Technology,7,The conditions for physical phenomena similarity,Same identified characteristic numbers are equal Its similar for Monodromy conditions, which includes initial conditions, boundary conditions and Geometric conditions,Chapter 6,College of Nuclear Science and Technology,8,How to get dim
8、ensionless groups,Similarity Considerations: To establish the column proportion coefficient between the two phenomena ,relationship between the export of these similarity coefficient and obtain a dimensionless quantity based on Known mathematical description of the physical phenomena.,Chapter 6,Coll
9、ege of Nuclear Science and Technology,9,Phenomenon1：,Phenomenon2：,mathematical description,Chapter 6,College of Nuclear Science and Technology,10,Establish similar multiples,Relationship between them,Chapter 6,College of Nuclear Science and Technology,11,Berkeley number,To obtain dimensionless group
10、s,Chapter 6,College of Nuclear Science and Technology,12,Dimensional Analysis,In dimensional analysis, dimensional groups such as the Reynolds and Prandtl numbers are derived from purely dimensional and functional considerations.,Fundamental Basis,Theorem of , A consistent dimensionless equation sho
11、wing the relationship between the n physical quantities could be transferred to a relationship which contains (n-r) independent dimensionless groups.,Chapter 6,College of Nuclear Science and Technology,13,Advantages of dimensionless analysis,Simple We can still obtain dimensionless groups without kn
12、owing the Differential Equations,Fundamental quantity in the SI Units,Length m，MASSkg，times，ELECTRIC CURRENTA，thermodynamic temperatureK，amount of substancemol，luminous intensitycd,Chapter 6,College of Nuclear Science and Technology,14,Now we come back to the difficulties,Which variables should we m
13、easure? Only variables that are contained in characteristic numbers What functional form should the data be organized into? Arrange the data according to the relationship between the characteristic numbers Its hard and expensive to do the experiments, so, how many experiments should we do? Modular E
14、xperiments under the guidance of the similar consideration,Chapter 6,College of Nuclear Science and Technology,15,Chapter 6,College of Nuclear Science and Technology,16,6-2 Empirical Relations For Pipe And Tube Flow,Cases of Undeveloped Flow,The cases of undeveloped laminar flow systems where the fl
15、uid properties vary widely with temperature, and turbulent-flow systems are considerably more complicated but are of very important practical interest in heat exchangers and associated heat-transfer equipment.,Chapter 6,College of Nuclear Science and Technology,17,For design and engineering purposes
16、, empirical correlations are usually of greatest practical utility.,For laminar flow, the length of the undeveloped part,undeveloped,developed,(Average from 0 to x),Chapter 6,College of Nuclear Science and Technology,18,For turbulent flow, the length of the undeveloped part,undeveloped,developed,(Av
17、erage from 0 to x),Chapter 6,College of Nuclear Science and Technology,19,Further consideration to Bulk temperature,Chapter 6,College of Nuclear Science and Technology,20,For tube in Figure 6-1 the total energy added can be expressed in terms of bulk-temperature by,In differential equation,The Tw an
18、d Tb here are the wall and bulk temperature at the particular x location.,Chapter 6,College of Nuclear Science and Technology,21,The total heat transfer can also be expressed as,6-3,where A is the total surface area for heat transfer. Because both Tw and Tb can vary along the length of the tube, a s
19、uitable averaging process must be adopted for use with Equation (6-3). In chapter 10 well discuss different methods for taking proper account of temperature variations in heat exchangers.,Chapter 6,College of Nuclear Science and Technology,22,A tradition expression for calculation of heat transfer i
20、n fully developed turbulent flow in smooth tubes,For heating of the fluid,For cooling of the fluid,Chapter 6,College of Nuclear Science and Technology,23,Conditions,Chapter 6,College of Nuclear Science and Technology,24,Wide temperature differences,These property variations may be evidenced by a cha
21、nge in the velocity profile as indicated in the figure.,1.Inothermal flow 2.Gas heating, Liquid cooling 3.Liquid heating, gas cooling,Chapter 6,College of Nuclear Science and Technology,25,Some relations take property variations into account,Gas heating,Gas cooling,Liquid Heating,Liquid Cooling,Chap
22、ter 6,College of Nuclear Science and Technology,26,Conditions,Chapter 6,College of Nuclear Science and Technology,27,Conditions,Chapter 6,College of Nuclear Science and Technology,28,If the channel through which the fluid flows is nor circular cross the section, it is recommended that the heat-trans
23、fer correlations be based on the hydraulic diameter.,Various Sections,Definition,Hydraulic diameter,A is cross-sectional area of the flow P is the wetted perimeter,Chapter 6,College of Nuclear Science and Technology,29,The hydraulic diameter should be used in calculating the Nusselt and Reynolds num
24、bers, and in establishing the friction coefficient for use with Reynolds analogy.,Average Nusselt number for uniform heat flux in flow direction and uniform wall temperature at particular flow cross section,Average Nusselt number for uniform wall temperature,Product of friction factor and Reynolds n
25、umber based on hydraulic diameter,Chapter 6,College of Nuclear Science and Technology,30,Constant axial wall heat flux,Constant axial wall temperature,Heat transfer and fluid friction for fully developed flow in ducts of various cross sections,Geometry,Triangle,Square,Regular Hexagon,Circle,Rectangl
26、e with b=2a,Chapter 6,College of Nuclear Science and Technology,31,Air at 2atm and 200 is heated as it flows through a tube with a diameter of 1 in (2.54cm) at velocity of 10 m/s. Calculate the heat transfer per unit length of tube is constant-heat-flux condition is maintained at the wall and the wa
27、ll and the wall temperature is 20, above the air temperature , all along the length of the tube. How much would the bulk temperature increase a 3-m length of the tube?,Example,Chapter 6,College of Nuclear Science and Technology,32,Solution,We first calculate the Reynolds number to determine if the f
28、low is laminar or turbulent, and then select the appropriate empirical correlation to calculate the heat transfer. The properties of air at a bulk temperature of 200 are,Chapter 6,College of Nuclear Science and Technology,33,So the flow is turbulent. We therefore use Equation (6-4a) to calculate the
29、 heat-transfer coefficient,Chapter 6,College of Nuclear Science and Technology,34,The heat-flow per unit length is then,Chapter 6,College of Nuclear Science and Technology,35,We can now make an energy balance to calculate the increase in bulk temperature in a 3.0-m length of the tube,Chapter 6,Colle
30、ge of Nuclear Science and Technology,36,So the heat transfer per unit length is,Chapter 6,College of Nuclear Science and Technology,37,6-3 Flow Across Cylinders And Spheres,Boundary-layer Separation,Look at Figure 6-7, it is necessary to include the pressure gradient in the analysis because this inf
31、luences the boundary-layer velocity and causes separated flow region to develop on the back side of the cylinder when the free stream velocity is sufficiently large.,Chapter 6,College of Nuclear Science and Technology,38,Chapter 6,College of Nuclear Science and Technology,39,Figure 68 Velocity distr
32、ibutions indicating flow separation on a cylinder in cross flow,Boundary Layer,Separation Region,Chapter 6,College of Nuclear Science and Technology,40,In case of cylinder, one might measure x distance from the front stagnation point of the cylinder. Thus the pressure in the boundary layer should fo
33、llow that of the free stream for potential flow around a cylinder, provided this behavior would not contradict some basic principle. As the increase flow progresses along the front side of the cylinder, the pressure would decrease and then increase along the back side of the cylinder, resulting in a
34、n increase in free-stream velocity on the front side of the cylinder and a decrease on the back side.,Chapter 6,College of Nuclear Science and Technology,41,The detailed behavior of the heat transfer from a heated cylinder to air are summarized in Figure 6-11,The change of heat-transfer coefficient
35、through circular Cylinders,Chapter 6,College of Nuclear Science and Technology,42,At the lower Re numbers, a minimum point in the heat-transfer coefficient occurs at approximately the point of separation. There is a subsequent increase in the heat-transfer coefficient on the rear side of the cylinde
36、r, resulting from the turbulent eddy motion in the separated flow. At higher Re numbers, two minimum points are observed,Chapter 6,College of Nuclear Science and Technology,43,Because of the complicated nature of the flow-separation, it is not possible to calculate analytically the average coefficie
37、nts in cross flow. Knudsen and Katz suggested that the correlation be extended to liquids by inclusion of,The resulting correlation for average heat-transfer coefficients in cross flow over circular cylinders is,The relationship of Flow Across Cylinders,6-17,Chapter 6,College of Nuclear Science and
38、Technology,44,The constant C and n are tabulated in the Table 6-2,Bulk temperature,Chapter 6,College of Nuclear Science and Technology,45,Still a more comprehensive relation is given by Churchill and Bernstein which is applicable over the complete range of available data.,For Bulk temperature,Chapte
39、r 6,College of Nuclear Science and Technology,46,Noncircular Cylinders,Equation6-17 is employed in order to obtain an empirical correlation for gases, and the constants for use with this equation are summarized in Table 6-3.The data upon which Table 6-3 is based were for gases with Pr 0.7 and were m
40、odified by same 1.11 factor employed for the information presented in Table 6-2,Chapter 6,College of Nuclear Science and Technology,47,Table 6-3,constants for heat transfer from non circular cylinders for use with Equation (6-17),Flat,Square,Regular Hexagon,Chapter 6,College of Nuclear Science and T
41、echnology,48,Spheres,A single Equation for gases and liquids flowing past spheres,At free-stream temperature,Chapter 6,College of Nuclear Science and Technology,49,Example,Air at 1 atm and 35 flows across a 5.0-cm-diameter cylinder at a velocity of 50m/s. The cylinder surface is maintained at a temp
42、erature of 150. Calculate the heat loss per unit length of the cylinder,Chapter 6,College of Nuclear Science and Technology,50,Solution,We first determine the Re number and then find the applicable constants from Table 6-2 for use with Equation (6-17). The properties of air are evaluated at the film
43、 length of cylinder.,Chapter 6,College of Nuclear Science and Technology,51,From Table 6-2, we have,Chapter 6,College of Nuclear Science and Technology,52,6-4 Flow Across Tube Banks,Different Arrangement of Banks,Usually, there are two kinds of arrangement of banks, they are In line & Staggered,Figu
44、re 6-14,In-line,Staggered,Chapter 6,College of Nuclear Science and Technology,53,For Staggered tube banks, they have better heat-transfer performance, but hard to clean and have more resistance loss.,6-17,On the basis of a correlation of the results of various investigators, Grimson was able to repr
45、esent data in form of Equation 6-17,Chapter 6,College of Nuclear Science and Technology,54,Number of the Rows10,The Re number is based on the maximum velocity occurring in the tube bank, that is , the velocity through the minimum-flow area.,The value of C and n are listed in the following table,Chap
46、ter 6,College of Nuclear Science and Technology,55,In-line,Staggered,Chapter 6,College of Nuclear Science and Technology,56,Zhukauskas suggested a group of formula which could be used for a wide range of Pr numbers,The bulk temperature,The Re numbers are based on Outside diameter of the tube and on
47、the velocity through the minimum-flow area.,Range of Pr number,Chapter 6,College of Nuclear Science and Technology,57,For number of tube banks 16 rows , he suggested a ratio ,Equations for heat-transfer in tube banks of 16 rows or more (IN-LINE arrangement),Equations,Range of Re number,Chapter 6,Col
48、lege of Nuclear Science and Technology,58,Equations for heat-transfer in tube banks of 16 rows or more (Staggered arrangement),Raito for tube banks 16 rows,Equations,Range of Re Number,Number of Rows,In-line,Staggered,Chapter 6,College of Nuclear Science and Technology,59,6-5 Liquid-Metal Heat Transfer,Lets first consider the simple flat plate with a liquid metal flowing across it. The Prandtl number for liquid metals is very low, of the order of 0.01, so that the thermal boundary-layer thickness should be substantially larger than the h
