Thermodynamics, Heat Transfer, And Fluid Flow. V.2. Heat Transfer (776131), страница 5
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Typically, the convective heat transfer coefficient for laminar flowis relatively low compared to the convective heat transfer coefficient for turbulent flow. This isdue to turbulent flow having a thinner stagnant fluid film layer on the heat transfer surface.Values of h have been measured and tabulated for the commonly encountered fluids and flowsituations occurring during heat transfer by convection.Example:A 22 foot uninsulated steam line crosses a room.
The outer diameter of the steam lineis 18 in. and the outer surface temperature is 280oF. The convective heat transfercoefficient for the air is 18 Btu/hr-ft2-oF. Calculate the heat transfer rate from the pipeinto the room if the room temperature is 72oF.Solution:Q̇h A ∆Th (2 π r L) ∆TBtu 18 2 (3.14) (0.75 ft) (22 ft) (280°Fhr ft 2 °F 3.88 x 10572°F)BtuhrMany applications involving convective heat transfer take place within pipes, tubes, or somesimilar cylindrical device.
In such circumstances, the surface area of heat transfer normally givenin the convection equation ( Q̇ h A ∆T ) varies as heat passes through the cylinder. In addition,the temperature difference existing between the inside and the outside of the pipe, as well as thetemperature differences along the pipe, necessitates the use of some average temperature valuein order to analyze the problem. This average temperature difference is called the log meantemperature difference (LMTD), described earlier.Rev. 0Page 19HT-02CONVECTION HEAT TRANSFERHeat TransferIt is the temperature difference at one end of the heat exchanger minus the temperature differenceat the other end of the heat exchanger, divided by the natural logarithm of the ratio of these twotemperature differences.
The above definition for LMTD involves two important assumptions:(1) the fluid specific heats do not vary significantly with temperature, and (2) the convection heattransfer coefficients are relatively constant throughout the heat exchanger.Overall Heat Transfer CoefficientMany of the heat transfer processes encountered in nuclear facilities involve a combination ofboth conduction and convection. For example, heat transfer in a steam generator involvesconvection from the bulk of the reactor coolant to the steam generator inner tube surface,conduction through the tube wall, and convection from the outer tube surface to the secondaryside fluid.In cases of combined heat transfer for a heat exchanger, there are two values for h.
There is theconvective heat transfer coefficient (h) for the fluid film inside the tubes and a convective heattransfer coefficient for the fluid film outside the tubes. The thermal conductivity (k) andthickness (∆x) of the tube wall must also be accounted for. An additional term (Uo), called theoverall heat transfer coefficient, must be used instead. It is common practice to relate the totalrate of heat transfer ( Q̇ ) to the cross-sectional area for heat transfer (Ao) and the overall heattransfer coefficient (Uo). The relationship of the overall heat transfer coefficient to the individualconduction and convection terms is shown in Figure 6.Figure 6HT-02Overall Heat Transfer CoefficientPage 20Rev.
0Heat TransferCONVECTION HEAT TRANSFERRecalling Equation 2-3:Q̇UoAo∆Towhere Uo is defined in Figure 6.An example of this concept applied to cylindrical geometry is illustrated by Figure 7, whichshows a typical combined heat transfer situation.Figure 7Combined Heat TransferUsing the figure representing flow in a pipe, heat transfer by convection occurs betweentemperatures T1 and T2; heat transfer by conduction occurs between temperatures T2 and T3; andheat transfer occurs by convection between temperatures T3 and T4.
Thus, there are threeprocesses involved. Each has an associated heat transfer coefficient, cross-sectional area for heattransfer, and temperature difference. The basic relationships for these three processes can beexpressed using Equations 2-5 and 2-9.Q̇Rev. 0h1 A1 ( T1T2 )Page 21HT-02CONVECTION HEAT TRANSFERQ̇kA (T∆r lm 2Q̇h2 A2 ( T3Heat TransferT3 )T4 )∆To can be expressed as the sum of the ∆T of the three individual processes.∆To( T1T2 )( T2T3 )( T3T4 )If the basic relationship for each process is solved for its associated temperature difference andsubstituted into the expression for ∆To above, the following relationship results.∆To1Q̇ h1 A11 h2 A2 ∆rk AlmThis relationship can be modified by selecting a reference cross-sectional area Ao.∆ToQ̇ AoAo h1 A1∆r Aok AlmAo h2 A2 Solving for Q̇ results in an equation in the form Q̇Q̇1 A oh A 1 1∆r Aok AlmAo h2 A2 Uo Ao ∆To .Ao ∆Towhere:Uo1 A oh A 1 1∆r Aok Alm(2-10)Ao h2 A2 Equation 2-10 for the overall heat transfer coefficient in cylindrical geometry is relativelydifficult to work with.
The equation can be simplified without losing much accuracy if the tubethat is being analyzed is thin-walled, that is the tube wall thickness is small compared to the tubediameter. For a thin-walled tube, the inner surface area (A1), outer surface area (A2), and logmean surface area (A1m), are all very close to being equal. Assuming that A1, A2, and A1m areequal to each other and also equal to Ao allows us to cancel out all the area terms in thedenominator of Equation 2-11.HT-02Page 22Rev. 0Heat TransferCONVECTION HEAT TRANSFERThis results in a much simpler expression that is similar to the one developed for a flat plate heatexchanger in Figure 6.Uo1h11∆rk(2-11)1h2The convection heat transfer process is strongly dependent upon the properties of the fluid beingconsidered.
Correspondingly, the convective heat transfer coefficient (h), the overall coefficient(Uo), and the other fluid properties may vary substantially for the fluid if it experiences a largetemperature change during its path through the convective heat transfer device. This is especiallytrue if the fluid’s properties are strongly temperature dependent. Under such circumstances, thetemperature at which the properties are "looked-up" must be some type of average value, ratherthan using either the inlet or outlet temperature value.For internal flow, the bulk or average value of temperature is obtained analytically through theuse of conservation of energy.
For external flow, an average film temperature is normallycalculated, which is an average of the free stream temperature and the solid surface temperature.In any case, an average value of temperature is used to obtain the fluid properties to be used inthe heat transfer problem. The following example shows the use of such principles by solvinga convective heat transfer problem in which the bulk temperature is calculated.Convection Heat TransferExample:A flat wall is exposed to the environment. The wall is covered with a layer of insulation1 in.
thick whose thermal conductivity is 0.8 Btu/hr-ft-°F. The temperature of the wallon the inside of the insulation is 600°F. The wall loses heat to the environment byconvection on the surface of the insulation. The average value of the convection heattransfer coefficient on the insulation surface is 950 Btu/hr-ft2-°F. Compute the bulktemperature of the environment (Tb) if the outer surface of the insulation does not exceed105°F.Rev. 0Page 23HT-02CONVECTION HEAT TRANSFERHeat TransferSolution:a.Find heat flux ( Q̇ ) through the insulation.Q̇ ∆T k A ∆x Q̇A0.8Btu 600°F 105°F hr ft °F 1 ft 1 in12 in 4752b.Btuhr ft 2Find the bulk temperature of the environment.Q̇(TinsTb)Tbh A (TinsTb)Q̇h ATinsQ̇hBtuhr ft 2Btu950hr ft 2 °F4752HT-02Tb105°FTb100° FPage 24Rev.
0Heat TransferCONVECTION HEAT TRANSFERSummaryThe important information in this chapter is summarized below.Convection Heat Transfer Summary•Convection heat transfer is the transfer of thermal energy by the mixing andmotion of a fluid or gas.•Whether convection is natural or forced is determined by how the mediumis placed into motion.•When both convection and conduction heat transfer occurs, the overall heattransfer coefficient must be used to solve problems.•The heat transfer equation for convection heat transfer is Q̇Rev. 0Page 25hA∆T .HT-02RADIATION HEAT TRANSFERHeat TransferRADIANT HEAT TRANSFERRadiant heat transfer is thermal energy transferred by means of electromagneticwaves or particles.EO 1.10DESCRIBE how the following terms relate to radiantheat transfer:a.Black body radiationb.Emissivityc.Radiation configuration factorThermal RadiationRadiant heat transfer involves the transfer of heat by electromagnetic radiation that arises due tothe temperature of a body. Most energy of this type is in the infra-red region of theelectromagnetic spectrum although some of it is in the visible region.
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