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Consider a 15-cm-diameter sphere placed within a cubical enclosure with a side length of \(15 \mathrm{~cm}\). The view factor from any of the square-cube surfaces to the sphere is (a) \(0.09\) (b) \(0.26\) (c) \(0.52\) (d) \(0.78\) (e) 1

Consider two concentric spheres with diameters \(12 \mathrm{~cm}\) and \(18 \mathrm{~cm}\) forming an enclosure. The view factor from the inner surface of the outer sphere to the inner sphere is (a) 0 (b) \(0.18\) (c) \(0.44\) (d) \(0.56\) (e) \(0.67\)

Consider two concentric spheres forming an enclosure with diameters of \(12 \mathrm{~cm}\) and \(18 \mathrm{~cm}\) and surface temperatures \(300 \mathrm{~K}\) and \(500 \mathrm{~K}\), respectively. Assuming that the surfaces are black, the net radiation exchange between the two spheres is (a) \(21 \mathrm{~W}\) (b) \(140 \mathrm{~W}\) (c) \(160 \mathrm{~W}\) (d) \(1275 \mathrm{~W}\) (e) \(3084 \mathrm{~W}\)

Two gray surfaces that form an enclosure exchange heat with one another by thermal radiation. Surface 1 has a temperature of \(400 \mathrm{~K}\), an area of \(0.2 \mathrm{~m}^{2}\), and a total emissivity of \(0.4\). Surface 2 has a temperature of \(600 \mathrm{~K}\), an area of \(0.3 \mathrm{~m}^{2}\), and a total emissivity of \(0.6\). If the view factor \(F_{12}\) is \(0.3\), the rate of radiation heat transfer between the two surfaces is (a) \(135 \mathrm{~W}\) (b) \(223 \mathrm{~W}\) (c) \(296 \mathrm{~W}\) (d) \(342 \mathrm{~W}\) (e) \(422 \mathrm{~W}\)

Two concentric spheres are maintained at uniform temperatures \(T_{1}=45^{\circ} \mathrm{C}\) and \(T_{2}=280^{\circ} \mathrm{C}\) and have emissivities \(\varepsilon_{1}=0.25\) and \(\varepsilon_{2}=0.7\), respectively. If the ratio of the diameters is \(D_{1} / D_{2}=0.30\), the net rate of radiation heat transfer between the two spheres per unit surface area of the inner sphere is (a) \(86 \mathrm{~W} / \mathrm{m}^{2}\) (b) \(1169 \mathrm{~W} / \mathrm{m}^{2}\) (c) \(1181 \mathrm{~W} / \mathrm{m}^{2}\) (d) \(2510 \mathrm{~W} / \mathrm{m}^{2}\) (e) \(3306 \mathrm{~W} / \mathrm{m}^{2}\)

Consider a \(3-\mathrm{m} \times 3-\mathrm{m} \times 3-\mathrm{m}\) cubical furnace. The base surface of the furnace is black and has a temperature of \(400 \mathrm{~K}\). The radiosities for the top and side surfaces are calculated to be \(7500 \mathrm{~W} / \mathrm{m}^{2}\) and \(3200 \mathrm{~W} / \mathrm{m}^{2}\), respectively. The net rate of radiation heat transfer to the bottom surface is (a) \(2.61 \mathrm{~kW}\) (b) \(8.27 \mathrm{~kW}\) (c) \(14.7 \mathrm{~kW}\) (d) \(23.5 \mathrm{~kW}\) (e) \(141 \mathrm{~kW}\)

Consider an enclosure consisting of \(N\) diffuse and gray surfaces. The emissivity and temperature of each surface as well as the view factors between the surfaces are specified. Write a program to determine the net rate of radiation heat transfer for each surface.