John H. Lienhard IV, John H. Lienhard V. A Heat Transfer Textbook (776116), страница 64
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Comment on theresult. should the line be straight?8.16A 77◦ C vertical wall heats 27◦ C air. Evaluate δtop /L, RaL , andL where the line in Fig. 8.3 ceases to be straight. Comment onthe implications of your results. [δtop /L 0.6.]8.17A horizontal 8 cm O.D. pipe carries steam at 150◦ C througha room at 17◦ C. The pipe has a 1.5 cm layer of 85% magnesiainsulation on it. Evaluate the heat loss per meter of pipe. [Q =97.3 W/m.]8.18What heat rate (in W/m) must be supplied to a 0.01 mm horizontal wire to keep it 30◦ C above the 10◦ C water around it?8.19A vertical run of copper tubing, 5 mm in diameter and 20 cmlong, carries condensation vapor at 60◦ C through 27◦ C air.What is the total heat loss?8.20A body consists of two cones joined at their bases.
The diameter is 10 cm and the overall length of the joined cones is25 cm. The axis of the body is vertical, and the body is keptat 27◦ C in 7◦ C air. What is the rate of heat removal from thebody? [Q = 3.38 W.]8.21Consider the plate dealt with in Example 8.3. Plot h as a function of the angle of inclination of the plate as the hot side istilted both upward and downward.
Note that you must makedo with discontinuous formulas in different ranges of θ.8.22You have been asked to design a vertical wall panel heater,1.5 m high, for a dwelling. What should the heat flux be if nopart of the wall should exceed 33◦ C? How much heat will beadded to the room if the panel is 7 m in width?8.23A 14 cm high vertical surface is heated by condensing steamat 1 atm. If the wall is kept at 30◦ C, how would the averageProblems447heat transfer coefficient change if ammonia, R22, methanol,or acetone were used instead of steam to heat it? How wouldthe heat flux change? (Data for methanol and acetone must beobtained from sources outside this book.)8.24A 1 cm diameter tube extends 27 cm horizontally through aregion of saturated steam at 1 atm.
The outside of the tube canbe maintained at any temperature between 50◦ C and 150◦ C.Plot the total heat transfer as a function of tube temperature.8.25A 2 m high vertical plate condenses steam at 1 atm. Below whattemperature will Nusselt’s prediction of h be in error? Belowwhat temperature will the condensing film be turbulent?8.26A reflux condenser is made of copper tubing 0.8 cm in diameterwith a wall temperature of 30◦ C. It condenses steam at 1 atm.Find h if α = 18◦ and the coil diameter is 7 cm.8.27The coil diameter of a helical condenser is 5 cm and the tubediameter is 5 mm. The condenser carries water at 15◦ C and isin a bath of saturated steam at 1 atm.
Specify the number ofcoils and a reasonable helix angle if 6 kg/hr of steam is to becondensed. hinside = 600 W/m2 K.8.28A schedule 40 type 304 stainless steam pipe with a 4 in. nominal diameter carries saturated steam at 150 psia in a processing plant. Calculate the heat loss per unit length of pipe if it isbare and the surrounding air is still at 68◦ F.
How much wouldthis heat loss be reduced if the pipe were insulated with a 1 in.layer of 85% magnesia insulation? [Qsaved 127 W/m.]8.29What is the maximum speed of air in the natural convectionb.l. in Example 8.1?8.30All of the uniform-Tw , natural convection formulas for Nu takethe same form, within a constant, at high Pr and Ra. What isthat form? (Exclude any equation that includes turbulence.)8.31A large industrial process requires that water be heated by alarge horizontal cylinder using natural convection. The wateris at 27◦ C.
The diameter of the cylinder is 5 m, and it is kept at67◦ C. First, find h. Then suppose that D is increased to 10 m.448Chapter 8: Natural convection in single-phase fluids and during film condensationWhat is the new h? Explain the similarity of these answers inthe turbulent natural convection regime.8.32A vertical jet of liquid of diameter d and moving at velocity u∞impinges on a horizontal disk rotating ω rad/s. There is noheat transfer in the system.
Develop an expression for δ(r ),where r is the radial coordinate on the disk. Contrast the rdependence of δ with that of a condensing film on a rotatingdisk and explain the difference qualitatively.8.33We have seen that if properties are constant, h ∝ ∆T 1/4 innatural convection. If we consider the variation of propertiesas Tw is increased over T∞ , will h depend more or less stronglyon ∆T in air? in water?8.34A film of liquid falls along a vertical plate. It is initially saturated and it is surrounded by saturated vapor. The film thickness is δo .
If the wall temperature below a certain point onthe wall (call it x = 0) is raised to a value of Tw , slightly aboveTsat , derive expressions for δ(x), Nux , and xf —the distance atwhich the plate becomes dry. Calculate xf if the fluid is waterat 1 atm, if Tw = 105◦ C and δo = 0.1 mm.8.35In a particular solar collector, dyed water runs down a verticalplate in a laminar film with thickness δo at the top.
The sun’srays pass through parallel glass plates (see Section 10.6) anddeposit qs W/m2 in the film. Assume the water to be saturatedat the inlet and the plate behind it to be insulated. Develop anexpression for δ(x) as the water evaporates. Develop an expression for the maximum length of wetted plate, and providea criterion for the laminar solution to be valid.8.36What heat removal flux can be achieved at the surface of ahorizontal 0.01 mm diameter electrical resistance wire in still27◦ C air if its melting point is 927◦ C? Neglect radiation.8.37A 0.03 m O.D.
vertical pipe, 3 m in length, carries refrigerantthrough a 24◦ C room. How much heat does it absorb from theroom if the pipe wall is at 10◦ C?8.38A 1 cm O.D. tube at 50◦ C runs horizontally in 20◦ C air. What isthe critical radius of 85% magnesium insulation on the tube?Problems4498.39A 1 in.
cube of ice is suspended in 20◦ C air. Estimate the driprate in gm/min. (Neglect ∆T through the departing water film.hsf = 333, 300 J/kg.)8.40A horizontal electrical resistance heater, 1 mm in diameter,releases 100 W/m in water at 17◦ C. What is the wire temperature?8.41Solve Problem 5.39 using the correct formula for the heat transfer coefficient.8.42A red-hot vertical rod, 0.02 m in length and 0.005 m in diameter, is used to shunt an electrical current in air at room temperature.
How much power can it dissipate if it melts at 1200◦ C?Note all assumptions and corrections. Include radiation usingFrod-room = 0.064.8.43A 0.25 mm diameter platinum wire, 0.2 m long, is to be heldhorizontally at 1035◦ C. It is black. How much electric power isneeded? Is it legitimate to treat it as a constant-wall-temperatureheater in calculating the convective part of the heat transfer?The surroundings are at 20◦ C and the surrounding room isvirtually black.8.44A vertical plate, 11.6 m long, condenses saturated steam at1 atm. We want to be sure that the film stays laminar.
What isthe lowest allowable plate temperature, and what is q at thistemperature?8.45A straight horizontal fin exchanges heat by laminar naturalconvection with the surrounding air.a. Show thatd2 θ= m2 L2 θ 5/4dξ 2where m is based on ho ≡ h(T = To ).b. Develop an iterative numerical method to solve this equation for T (x = 0) = To and an insulated tip. (Hint : linearize the right side by writing it as (m2 L2 θ 1/4 )θ, andevaluate the term in parenthesis at the previous iterationstep.)450Chapter 8: Natural convection in single-phase fluids and during film condensationc.
Solve the resulting difference equations for m2 L2 valuesranging from 10−3 to 103 . Use Gauss elimination or thetridiagonal algorithm. Express the results as η/ηo whereη is the fin efficiency and ηo is the efficiency that wouldresult if ho were the uniform heat transfer coefficient overthe entire fin.8.46A 2.5 cm black sphere (F = 1) is in radiation-convection equilibrium with air at 20◦ C. The surroundings are at 1000 K.
Whatis the temperature of the sphere?8.47Develop expressions for h(D) and NuD during condensationon a vertical circular plate.8.48A cold copper plate is surrounded by a 5 mm high ridge whichforms a shallow container. It is surrounded by saturated watervapor at 100◦ C. Estimate the steady heat flux and the rate ofcondensation.a. When the plate is perfectly horizontal and filled to overflowing with condensate.b. When the plate is in the vertical position.c. Did you have to make any idealizations? Would they result in under- or over-estimation of the condensation?8.49A proposed design for a nuclear power plant uses molten leadto remove heat from the reactor core.
The heated lead is thenused to boil water that drives a steam turbine. Water at 5 atmpressure (Tsat = 152◦ C) enters a heated section of a pipe at60◦ C with a mass flow rate of ṁ = 2 kg/s. The pipe is stainlesssteel (ks = 15 W/m·K) with a wall thickness of 12 mm and anoutside diameter of 6.2 cm. The outside surface of the pipeis surrounded by an almost-stationary pool of molten lead at477◦ C.a. At point where the liquid water has a bulk temperatureof Tb = 80◦ C, estimate the inside and outside wall temperatures of the pipe, Twi and Two , to within about 5◦ C.Neglect entry length and variable properties effects andtake β ≈ 0.000118 K−1 for lead.
Hint: Guess an outsidewall temperature above 370◦ C when computing h for thelead.Problems451b. At what distance from the inlet will the inside wall of thepipe reach Tsat ? What redesign may be needed?8.50A flat plate 10 cm long and 40 cm wide is inclined at 30◦ fromthe vertical.
It is held at a uniform temperature of 250 K. Saturated HCFC-22 vapor at 260 K condenses onto the plate. Determine the following:/hfg .a. The ratio hfgb. The average heat transfer coefficient, h, and the rate atwhich the plate must be cooled, Q (watts).c. The film thickness, δ (µm), at the bottom of the plate, andthe plate’s rate of condensation in g/s.8.51One component in a particular automotive air-conditioning system is a “receiver”, a small vertical cylindrical tank that contains a pool of liquid refrigerant, HFC-134a, with vapor aboveit.
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