John H. Lienhard IV, John H. Lienhard V. A Heat Transfer Textbook (776116), страница 85
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10.14.10.15Find F1–5 for the surfaces shown in Fig. 10.31.10.16Find F1–(2+3+4) for the surfaces shown in Fig. 10.32.10.17A cubic box 1 m on the side is black except for one side, whichhas an emittance of 0.2 and is kept at 300◦ C. An adjacent sideis kept at 500◦ C. The other sides are insulated. Find Qnet insidethe box. [2494 W.]Problems587Figure 10.31 Configuration forProb. 10.15.Figure 10.32 Configuration forProb. 10.16.10.18Rework Problem 10.17, but this time set the emittance of theinsulated walls equal to 0.6. Compare the insulated wall temperature with the value you would get if the walls were black.10.19An insulated black cylinder, 10 cm in length and with an insidediameter of 5 cm, has a black cap on one end and a cap withan emittance of 0.1 on the other.
The black end is kept at100◦ C and the reflecting end is kept at 0◦ C. Find Qnet insidethe cylinder and Tcylinder .10.20Rework Example 10.2 if the shield has an inside emittance of0.34 and the room is at 20◦ C. How much cooling must be provided to keep the shield at 100◦ C?Chapter 10: Radiative heat transfer58810.21A 0.8 m long cylindrical burning chamber is 0.2 m in diameter.The hot gases within it are at a temperature of 1500◦ C and apressure of 1 atm, and the absorbing components consist of12% by volume of CO2 and 18% H2 O. Neglect end effects anddetermine how much cooling must be provided the walls tohold them at 750◦ C if they are black.10.22A 30 ft by 40 ft house has a conventional 30◦ sloping roof witha peak running in the 40 ft direction. Calculate the temperature of the roof in 20◦ C still air when the sun is overhead(a) if the roofing is of wooden shingles and (b) if it is commercial aluminum sheet.
The incident solar energy is 670 W/m2 ,Kirchhoff’s law applies for both roofs, and the effective skytemperature is 22◦ C.10.23Calculate the radiant heat transfer from a 0.2 m diameter stainless steel hemisphere (εss = 0.4) to a copper floor (εCu = 0.15)that forms its base. The hemisphere is kept at 300◦ C and thebase at 100◦ C. Use the algebraic method. [21.24 W.]10.24A hemispherical indentation in a smooth wrought-iron platehas an 0.008 m radius. How much heat radiates from the 40◦ Cdent to the −20◦ C surroundings?10.25A conical hole in a block of metal for which ε = 0.5 is 5 cm indiameter at the surface and 5 cm deep. By what factor will theradiation from the area of the hole be changed by the presenceof the hole? (This problem can be done to a close approximation using the methods in this chapter if the cone does notbecome very deep and slender.
If it does, then the fact thatthe apex is receiving far less radiation makes it incorrect touse the network analogy.)10.26A single-pane window in a large room is 4 ft wide and 6 ft high.The room is kept at 70◦ F, but the pane is at 67◦ F owing to heatloss to the colder outdoor air. Find (a) the heat transfer byradiation to the window; (b) the heat transfer by natural convection to the window; and (c) the fraction of heat transferredto the window by radiation.10.27Suppose that the windowpane temperature is unknown in Problem 10.26.
The outdoor air is at 40◦ F and h is 62 W/m2 K on theProblems589outside of the window. It is nighttime and the effective temperature of the sky is 15◦ F. Assume Fwindow−sky = 0.5. Takethe rest of the surroundings to be at 40◦ F. Find Twindow anddraw the analogous electrical circuit, giving numerical valuesfor all thermal resistances. Discuss the circuit.
(It will simplifyyour calculation to note that the window is opaque to infraredradiation but that it offers very little resistance to conduction.Thus, the window temperature is almost uniform.)10.28A very effective low-temperature insulation is made by evacuating the space between parallel metal sheets. Convection iseliminated, conduction occurs only at spacers, and radiationis responsible for what little heat transfer occurs. Calculateq between 150 K and 100 K for three cases: (a) two sheets ofhighly polished aluminum, (b) three sheets of highly polishedaluminum, and (c) three sheets of rolled sheet steel.10.29Three parallel black walls, 1 m wide, form an equilateral triangle.
One wall is held at 400 K, one is at 300 K, and the third isinsulated. Find Q W/m and the temperature of the third wall.10.30Two 1 cm diameter rods run parallel, with centers 4 cm apart.One is at 1500 K and black. The other is unheated, and ε =0.66. They are both encircled by a cylindrical black radiationshield at 400 K. Evaluate Q W/m and the temperature of theunheated rod.10.31A small-diameter heater is centered in a large cylindrical radiation shield. Discuss the relative importance of the emittanceof the shield during specular and diffuse radiation.10.32Two 1 m wide commercial aluminum sheets are joined at a120◦ angle along one edge.
The back (or 240◦ angle) side isinsulated. The plates are both held at 120◦ C. The 20◦ C surroundings are distant. What is the net radiant heat transferfrom the left-hand plate: to the right-hand side, and to thesurroundings?10.33Two parallel discs of 0.5 m diameter are separated by an infinite parallel plate, midway between them, with a 0.2 m diameter hole in it. The discs are centered on the hole. What is theview factor between the two discs if they are 0.6 m apart?Chapter 10: Radiative heat transfer59010.34An evacuated spherical cavity, 0.3 m in diameter in a zerogravity environment, is kept at 300◦ C.
Saturated steam at 1 atmis then placed in the cavity. (a) What is the initial flux of radiantheat transfer to the steam? (b) Determine how long it will takefor qconduction to become less than qradiation . (Correct for therising steam temperature if it is necessary to do so.)10.35Verify cases (1), (2), and (3) in Table 10.2 using the stringmethod described in Problem 10.14.10.36Two long parallel heaters consist of 120◦ segments of 10 cm diameter parallel cylinders whose centers are 20 cm apart. Thesegments are those nearest each other, symmetrically placedon the plane connecting their centers.
Find F1–2 using thestring method described in Problem 10.14.)10.37Two long parallel strips of rolled sheet steel lie along sides ofan imaginary 1 m equilateral triangular cylinder. One piece is11 m wide and kept at 20◦ C. The other is 2 m wide, centeredin an adjacent leg, and kept at 400◦ C. The surroundings aredistant and they are insulated. Find Qnet . (You will need ashape factor; it can be found using the method described inProblem 10.14.)10.38Find the shape factor from the hot to the cold strip in Problem 10.37 using Table 10.2, not the string method. If yourinstructor asks you to do so, complete Problem 10.37 whenyou have F1–2 .10.39Prove that, as the figure becomes very long, the view factorfor the second case in Table 10.3 reduces to that given for thethird case in Table 10.2.10.40Show that F1–2 for the first case in Table 10.3 reduces to theexpected result when plates 1 and 2 are extended to infinity.10.41In Problem 2.26 you were asked to neglect radiation in showingthat q was equal to 8227 W/m2 as the result of conductionalone.
Discuss the validity of the assumption quantitatively.10.42A 100◦ C sphere with ε = 0.86 is centered within a secondsphere at 300◦ C with ε = 0.47. The outer diameter is 0.3 mand the inner diameter is 0.1 m. What is the radiant heat flux?Problems59110.43Verify F1–2 for case 4 in Table 10.2. (Hint: This can be donewithout integration.)10.44Consider the approximation made in eqn. (10.30) for a smallgray object in a large isothermal enclosure. How small mustA1 /A2 be in order to introduce less than 10% error in F1–2 ifthe small object has an emittance of ε1 = 0.5 and the enclosure is: a) commerical aluminum sheet; b) rolled sheet steel;c) rough red brick; d) oxidized cast iron; or e) polished electrolytic copper. Assume both the object and its environmenthave temperatures of 40 to 90◦ C.10.45Derive eqn.
(10.42), starting with eqns. (10.36–10.38).10.46(a) Derive eqn. (10.31), which is for a single radiation shieldbetween two bodies. Include a sketch of the radiation network. (b) Repeat the calculation in the case when two radiation shields lie between body (1) and body (2), with the secondshield just outside the first.10.47Use eqn. (10.32) to find the net heat transfer from between twospecularly reflecting bodies that are separated by a specularlyreflecting radiation shield.
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