Thermodynamics, Heat Transfer, And Fluid Flow. V.2. Heat Transfer (776131), страница 6
Текст из файла (страница 6)
The term thermal radiationis frequently used to distinguish this form of electromagnetic radiation from other forms, suchas radio waves, x-rays, or gamma rays. The transfer of heat from a fireplace across a room inthe line of sight is an example of radiant heat transfer.Radiant heat transfer does not need a medium, such as air or metal, to take place. Any materialthat has a temperature above absolute zero gives off some radiant energy. When a cloud coversthe sun, both its heat and light diminish. This is one of the most familiar examples of heattransfer by thermal radiation.Black Body RadiationA body that emits the maximum amount of heat for its absolute temperature is called a blackbody. Radiant heat transfer rate from a black body to its surroundings can be expressed by thefollowing equation.Q̇σAT 4(2-12)where:HT-02Q̇ =heat transfer rate (Btu/hr)σ=Stefan-Boltzman constant (0.174 Btu/hr-ft2-°R4)A=surface area (ft2)T=temperature (°R)Page 26Rev.
0Heat TransferRADIATION HEAT TRANSFERTwo black bodies that radiate toward each other have a net heat flux between them. The netflow rate of heat between them is given by an adaptation of Equation 2-12.Q̇σA ( T1A=surface area of the first body (ft2)T1=temperature of the first body (°R)T2=temperature of the second body (°R)44T2 )where:All bodies above absolute zero temperature radiate some heat. The sun and earth both radiateheat toward each other. This seems to violate the Second Law of Thermodynamics, which statesthat heat cannot flow from a cold body to a hot body. The paradox is resolved by the fact thateach body must be in direct line of sight of the other to receive radiation from it.
Therefore,whenever the cool body is radiating heat to the hot body, the hot body must also be radiatingheat to the cool body. Since the hot body radiates more heat (due to its higher temperature) thanthe cold body, the net flow of heat is from hot to cold, and the second law is still satisfied.EmissivityReal objects do not radiate as much heat as a perfect black body. They radiate less heat than ablack body and are called gray bodies.
To take into account the fact that real objects are graybodies, Equation 2-12 is modified to be of the following form.Q̇εσAT 4where:ε = emissivity of the gray body (dimensionless)Emissivity is simply a factor by which we multiply the black body heat transfer to take intoaccount that the black body is the ideal case. Emissivity is a dimensionless number and has amaximum value of 1.0.Radiation Configuration FactorRadiative heat transfer rate between two gray bodies can be calculated by the equation statedbelow.Q̇Rev.
0fa fe σA ( T144T2 )Page 27HT-02RADIATION HEAT TRANSFERHeat Transferwhere:fa =is the shape factor, which depends on the spatial arrangement of the two objects(dimensionless)fe =is the emissivity factor, which depends on the emissivities of both objects(dimensionless)The two separate terms fa and fe can be combined and given the symbol f. The heat flowbetween two gray bodies can now be determined by the following equation:Q̇4fσA (T14T2 )(2-13)The symbol (f) is a dimensionless factor sometimes called the radiation configuration factor,which takes into account the emissivity of both bodies and their relative geometry.
The radiationconfiguration factor is usually found in a text book for the given situation. Once theconfiguration factor is obtained, the overall net heat flux can be determined. Radiant heat fluxshould only be included in a problem when it is greater than 20% of the problem.Example:Calculate the radiant heat between the floor (15 ft x 15 ft) of a furnace and the roof, ifthe two are located 10 ft apart.
The floor and roof temperatures are 2000°F and 600°F,respectively. Assume that the floor and the roof have black surfaces.Solution:A1 = A2 = (15 ft) (15 ft) = 225 ft2T1 = 2000oF + 460 = 2460°RT2 = 600oF + 460 = 1060°RTables from a reference book, or supplied by the instructor, give:f1-2= f2-1 = 0.31Q1-2= σAf(T14 - T24)= (0.174Btu) (225 ft 2) (0.31) [ (2460 oR)42 o 4hr ft R(1060 oR)4]= 4.29 x 1014 Btu/hrHT-02Page 28Rev.
0Heat TransferRADIATION HEAT TRANSFERSummaryThe important information in this chapter is summarized below.Radiant Heat Transfer SummaryBlack body radiation is the maximum amount of heat that can betransferred from an ideal object.Emissivity is a measure of the departure of a body from the ideal blackbody.Radiation configuration factor takes into account the emittance andrelative geometry of two objects.Rev. 0Page 29HT-02HEAT EXCHANGERSHeat TransferHEAT EXCHANGERSHeat exchangers are devices that are used to transfer thermal energyfrom one fluid to another without mixing the two fluids.EO 1.11DESCRIBE the difference in the temperature profilesfor counter-flow and parallel flow heat exchangers.EO 1.12DESCRIBE the differences between regenerative andnon-regenerative heat exchangers.EO 1.13Given the temperature changes across a heat exchanger,CALCULATE the log mean temperature difference forthe heat exchanger.EO 1.14Given the formulas for calculating the conduction andconvection heat transfer coefficients, CALCULATE theoverall heat transfer coefficient of a system.Heat ExchangersThe transfer of thermal energy between fluids is one of the most important and frequently usedprocesses in engineering.
The transfer of heat is usually accomplished by means of a deviceknown as a heat exchanger. Common applications of heat exchangers in the nuclear field includeboilers, fan coolers, cooling water heat exchangers, and condensers.The basic design of a heat exchanger normally has two fluids of different temperatures separatedby some conducting medium. The most common design has one fluid flowing through metaltubes and the other fluid flowing around the tubes.
On either side of the tube, heat is transferredby convection. Heat is transferred through the tube wall by conduction.Heat exchangers may be divided into several categories or classifications. In the most commonlyused type of heat exchanger, two fluids of different temperature flow in spaces separated by atube wall. They transfer heat by convection and by conduction through the wall. This type isreferred to as an "ordinary heat exchanger," as compared to the other two types classified as"regenerators" and "cooling towers."An ordinary heat exchanger is single-phase or two-phase.
In a single-phase heat exchanger, bothof the fluids (cooled and heated) remain in their initial gaseous or liquid states. In two-phaseexchangers, either of the fluids may change its phase during the heat exchange process. Thesteam generator and main condenser of nuclear facilities are of the two-phase, ordinary heatexchanger classification.HT-02Page 30Rev.
0Heat TransferHEAT EXCHANGERSSingle-phase heat exchangers are usually of the tube-and-shell type; that is, the exchangerconsists of a set of tubes in a container called a shell (Figure 8). At the ends of the heatexchanger, the tube-side fluid is separated from the shell-side fluid by a tube sheet. The designof two-phase exchangers is essentially the same as that of single-phase exchangers.Figure 8Typical Tube and Shell Heat ExchangerParallel and Counter-Flow DesignsAlthough ordinary heat exchangers may be extremely different in design and construction andmay be of the single- or two-phase type, their modes of operation and effectiveness are largelydetermined by the direction of the fluid flow within the exchanger.The most common arrangements for flow paths within a heat exchanger are counter-flow andparallel flow.
A counter-flow heat exchanger is one in which the direction of the flow of oneof the working fluids is opposite to the direction to the flow of the other fluid. In a parallel flowexchanger, both fluids in the heat exchanger flow in the same direction.Figure 9 represents the directions of fluid flow in the parallel and counter-flow exchangers. Undercomparable conditions, more heat is transferred in a counter-flow arrangement than in a parallelflow heat exchanger.Rev. 0Page 31HT-02HEAT EXCHANGERSHeat TransferFigure 9Fluid Flow DirectionThe temperature profiles of the two heat exchangers indicate two major disadvantages in theparallel-flow design.
First, the large temperature difference at the ends (Figure 10) causes largethermal stresses. The opposing expansion and contraction of the construction materials due todiverse fluid temperatures can lead to eventual material failure. Second, the temperature of thecold fluid exiting the heat exchanger never exceeds the lowest temperature of the hot fluid.
Thisrelationship is a distinct disadvantage if the design purpose is to raise the temperature of the coldfluid.HT-02Page 32Rev. 0Heat TransferHEAT EXCHANGERSFigure 10Heat Exchanger Temperature ProfilesThe design of a parallel flow heat exchanger is advantageous when two fluids are required to bebrought to nearly the same temperature.The counter-flow heat exchanger has three significant advantages over the parallel flow design.First, the more uniform temperature difference between the two fluids minimizes the thermalstresses throughout the exchanger. Second, the outlet temperature of the cold fluid can approachthe highest temperature of the hot fluid (the inlet temperature). Third, the more uniformtemperature difference produces a more uniform rate of heat transfer throughout the heatexchanger.Whether parallel or counter-flow, heat transfer within the heat exchanger involves bothconduction and convection.
One fluid (hot) convectively transfers heat to the tube wall whereconduction takes place across the tube to the opposite wall. The heat is then convectivelytransferred to the second fluid. Because this process takes place over the entire length of theexchanger, the temperature of the fluids as they flow through the exchanger is not generallyconstant, but varies over the entire length, as indicated in Figure 10. The rate of heat transfervaries along the length of the exchanger tubes because its value depends upon the temperaturedifference between the hot and the cold fluid at the point being viewed.Rev.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
