EGEE304Spring2018_Quiz3_Solutions.pdf - EGEE304 Spring 2018 Quiz 3 Boiling Heat Transfer Heat Exchangers Tuesday cen29305_ch10.qxd 1 3:08 PM Page 565 On

EGEE304Spring2018_Quiz3_Solutions.pdf - EGEE304 Spring 2018...

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Unformatted text preview: EGEE304 Spring 2018 Quiz 3: Boiling Heat Transfer, Heat Exchangers Tuesday April 10, 2018 cen29305_ch10.qxd 1. 11/30/05 3:08 PM Page 565 On the graph below, draw a typical boiling curve for water at 1 atm, labeling the following components (you can label with the corresponding letter) (1/2 point each; 3 points total): a. Nucleate boiling region d. Leidenfrost point b. Transition boiling region e. Critical Heat flux c. Film boiling region f. Region where bubbles collapse in liquid 56 CHAPT Natural convection boiling Bubbles collapse in the liquid 106 q· boiling, W/m2 Nucleate boiling Transition boiling C Film boiling Maximum (critical) heat flux, q· max E 105 B 104 103 Bubbles rise to the free surface A 1 ~5 10 D ~30 100 ~120 ∆Texcess = Ts – Tsat , °C Leidenfrost point, q· min 1000 Typical boil 2. Which of theNatural following variables is the rate of heat transfer in nucleate of (i.e. which of these Convection Boiling (to Point A onboiling the independent Boiling Curve) variables is not We in the nucleate heat equation that (1 point; circle one)? know fromboiling thermodynamics a pure substance at a specified pressure a. b. c. d. starts boiling when it reaches the saturation temperature at that pressure. But Viscosity of in thepractice liquid we do not see any bubbles forming on the heating surface until the Enthalpy of vaporization liquid is heated a few degrees above the saturation temperature (about 2 to Reynolds Number 6°C for water). Therefore, the liquid is slightly superheated in this case Surface tension of liquid-vapor interface (a metastable condition) and evaporates when it rises to the free surface. The fluid motion in this mode of boiling is governed by natural convection currents, and heat transfer from the heating surface to the fluid is by natural convection. 3. True or False: The amount of heat absorbed as 1 kg of saturated liquid water boils at 100°C is equal to the amount of heat released asNucleate 1 kg of saturated water vapor condenses at 100°CA (1 and point; C circle Boiling (between Points ) one)? The first bubbles start forming at point A of the boiling curve at various prefFalse Not Enough Information erential sites on the heating surface. The bubbles form at an increasing rate at an increasing number of nucleation sites as we move along the boiling curve toward point C. The nucleate boiling regime can be separated into two distinct regions. In region A–B, isolated bubbles are formed at various preferential nucleation sites on the heated surface. But these bubbles are dissipated in the liquid shortly after they separate from the surface. The space vacated by the rising True the prescribed heat transfer requirements. The procedure to be followed by the selection process is: insignificant andresistances, can be consideredas negligible. outer surface involves two convection and oneally conduction shownFinally, in theCold transfer the heat exchanger is assumed to be perfectly insulated, so that fluidthere is no Fig. 11–7. Here the subscripts i and oof represent the inner and outer surfaces of heat loss to the surrounding medium, and any heat transfer occurs between the EGEE304 Spring 2018 Ti a double-pipe heattwoexchanger, the inner tube. For fluids only. the thermal resistance of the Quiz 3: Boiling Heat Transfer, Heat Exchangers The idealizations stated above are closely approximated in practice, and tube wall is Hot from Coldsimplify the analysis of a heat exchanger with little sacrifice they greatly Tuesday April 10, 2018 accuracy. Therefore, they are commonly used. Under these assumptions, the f 2) s, e s, e o d e s, w w 6) t d f s d s 1 r - s 7) 8) e fluid fluid lnlaw (D ) exchanger first of/D thermodynamics requires that the rate of heat transfer fromthe the hot application. 1. Select the type suitable for R of !fluid heat Hot fluid equal to the rate of heat transfer to the cold(11–1) one. That is, 2bepkL Heat 2.theDetermine any unknown or outlet temperature and the heat transfer Tinlet Wall transfer o 4. Write thermal A resistance network associated with the double-pipe heat i andAo where k israte the thermal of the material and L is the of T hi conductivity exchanger shown, labeling resistances andwall inside temperature, Ti (2length points). using an energy balance. h o Cold the tube. Then the total thermal resistance becomes wheremean the subscriptstemperature c and h stand for cold and hot fluids, respectively, and"T fluid and the correction 3. Calculate the log difference Hot fluidlm ln (D /D ) 1 1 T Wall A TiRfactor ! R !F, R "if R necessary. "R ! " (11–2) " A hA 2 pkL h A h h 4. Obtain (select or calculate) the value of the overall heat transfer 1 1 R R = ––– Roof=the ––– wallsurface # The Ai is thei area of the inner wall that separates thetotwo fluids,quantity, andT its diNote that the heat transfer rate Q is taken be a positive h A A h o co-efficient isounderstood be from the hotA fluid to the cold one in accordance 1 1 area iof ithe outer U. surfacerection of the wall. In to other words, and Ao is the i and Ao are R = ––– R R = ––– with the second law of thermodynamics. hA h A surface areas of the separating wall wetted by the inner and the outer fluids, 2 points: ½ point each T , R’s InFIGURE heat exchanger analysis, it is often convenient 5 . Calculate the heat transfer surface areato combine As . the product of 11–7 the mass flow rate and the specific heat of a fluid into a single quantity. This o i wall o total wall i o i i # # Q ! mccpc(Tc, out " Tc, in) (11–9) # # Q ! mhcph(Th, in " Th, out) (11–10) i # # m c , m h ! mass flow rates cpc , cph ! specific heats o outlet temperatures Tc, out , Th,oout ! Tc, in , Th, in ! inlet temperatures i i i o o o i i i wall i i o o o respectively. When one fluid flows inside a circular tube and the other outside FIGURE 11–7 quantity is called the heat capacity rate and is defined for the hot and cold Thermal network pDi L and Aresistance ! pD L (Fig. 11–8). of it, we have Ai ! Thermal resistance network o fluidostreams as In the analysis of heat exchangers, it is convenientCh to #combine all the # therassociated with heat transfer ! mhcph and Cc ! mccpc (11–11) associated with from heatthetransfer in a double-pipe heat exchanger. mal resistances in the path of heat flow hot fluid to the cold one into The heat capacity rate of a fluid stream represents the rate of heat transfer T 5. What doin youaknow about the twoheat fluidtostreams the heat double-pipe exchanger. Hot fluid needed change thefrom temperature ofsthe exchanger’s fluid stream by 1#C as it flows Ch a heat exchanger. Note that in a heat exchanger, the fluid with a large data shown in the Figure to the rightthrough (1 point)? ∆T1 heat capacity rate experiences a small temperature change, and the fluid with a. They fluids must bea small the heat same fluid capacity rate experiences a large temperature change. Therefore, ∆T doubling the mass flow rate of a fluid while leaving everything else unb. The fluids must have the same heat capacity rate changed will halve the temperature change of that fluid. ∆T2 c. The fluids must be flowing at theofsame rate With the definition the heatflow capacity rate above, Eqs. 11–9 and 11–10 can Cold fluid expressed Cc = Ch d. The cold fluid exitsalso at bethe sameastemperature as the hot fluid. # The task is completed by selecting a heat exchanger that has a heat transfer surface area equal to or larger than A . A second kind of problem encountered in heat exchanger analysis is the determination of the heat transfer rate and the outlet temperatures of the hot and cold fluids for prescribed fluid mass flow rates and inlet temperatures when 625 and size of the heat exchanger are specified. The heat transfer surface the CHAPTER type and 11 T area of the heat exchanger in this case is known, but the outlet temperatures is, the heat transfer rate in a heat exchanger is equal to the heat capacity T FIGURE 11–12 are not. Here the taskThat tofluid determine the heat of rate is of either multiplied by the temperature change oftransfer that fluid. Note performance Two fluid streams that have the samea specthat the only time the temperature rise of a cold fluid is equal to the temperaHot fluid capacity rates experience the same 6.ture The temperature shown theofleft represents whatavailable type of heat in storage of thedetermine hot fluid is profile when the heat rates the two fluids are temperature change in a well-insulated ified heat exchanger ordrop to ifcapacity a toheat exchanger T equal to each other (Fig. 11–12). heat exchanger. exchanger (1 point; circle one)? T will do the∆Tjob. a. Double-pipe counter-flow Double-pipe co-current flow alternative problem, but the Cold The TLMTD method could b.c.still be used for this fluid Double-pipe parallel flow T procedure would require tedious iterations, and thus it is not practical. In an T d. Not enough information. attempt to eliminate the iterations from the solution of such problems, Kays and London came up with a method in 1955 called the effectiveness–NTU T Cold fluid method, which greatly simplified heat exchanger analysis. Hot fluid This method is based on a dimensionless parameter called the heat transT e, defined 7. fer What effectiveness is the definition,T in words, of the heat as transfer effectiveness, e (1 point)? Q ! Cc(Tc, out " Tc, in) (11–12) # Q ! Ch(Th, in " Th, out) (11–13) ∆T = ∆T1 = ∆T2 = constant Inlet Outlet x h,in c,out h c h,out c,in c,in h,in h,out Tc,out # Actual heat transfer rate Q ! e! Qmax Maximum possible heat transfer rate FIGURE 11–16 The variation of the fluid temperatures in a counter-flow double-pipe heat exchanger. (11–29) The actualColdheat transfer rate in a heat exchanger can be determined from an T fluid energy balance∆Ton the hot or cold fluids and can be expressed as c,in Hot fluid Th,in ∆T1 2 Cross-flow or multipass shell-and-tube heat exchanger Tc,out Th,out # Q ! Cc(Tc, out # Tc, in) ! Ch(Th, in # Th, out) (11–30) # # where C ! m c and C ! m c are the heat capacity rates of the cold and Heat transfer rate: . Q = UAs F∆Tlm,CF ...
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