Chapter 13: Problem 106
How does radiation transfer through a participating medium differ from that through a nonparticipating medium?
Chapter 13: Problem 106
How does radiation transfer through a participating medium differ from that through a nonparticipating medium?
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Get started for freeA 90 -cm-diameter flat black disk is placed in the center of the top surface of a \(1-m \times 1-m \times 1-m\) black box. The view factor from the entire interior surface of the box to the interior surface of the disk is (a) \(0.07\) (b) \(0.13\) (c) \(0.26\) (d) \(0.32\) (e) \(0.50\)
Consider two infinitely long concentric cylinders with diameters 20 and $25 \mathrm{~cm}\(. The inner surface is maintained at \)700 \mathrm{~K}$ and has an emissivity of \(0.40\), while the outer surface is black. If the rate of radiation heat transfer from the inner surface to the outer surface is $2400 \mathrm{~W}$ per unit area of the inner surface, the temperature of the outer surface is (a) \(605 \mathrm{~K}\) (b) \(538 \mathrm{~K}\) (c) \(517 \mathrm{~K}\) (d) \(451 \mathrm{~K}\) (e) \(415 \mathrm{~K}\)
Consider two rectangular surfaces perpendicular to each other with a common edge which is \(1.6 \mathrm{~m}\) long. The horizontal surface is $0.8 \mathrm{~m}\( wide, and the vertical surface is \)1.2 \mathrm{~m}$ high. The horizontal surface has an emissivity of \(0.75\) and is maintained at $450 \mathrm{~K}\(. The vertical surface is black and is maintained at \)700 \mathrm{~K}$. The back sides of the surfaces are insulated. The surrounding surfaces are at \(290 \mathrm{~K}\) and can be considered to have an emissivity of \(0.85\). Determine the net rate of radiation heat transfer between the two surfaces and between the horizontal surface and the surroundings.
A large ASTM A992 carbon steel plate is $(k=10 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\(. The ceramic plate has a thickness of \)10 \mathrm{~cm}$, with its lower surface at \(T_{0}=800^{\circ} \mathrm{C}\) and upper surface at \(T_{1}=700^{\circ} \mathrm{C}\). The upper surface of the ceramic plate faces the carbon steel plate. Convection occurs on the upper surface of the ceramic plate with air at \(20^{\circ} \mathrm{C}\) and a convection heat transfer coefficient of \(12 \mathrm{~W} / \mathrm{m}^{2}, \mathrm{~K}\). The ceramic and steel plates have emissivity values of \(0.93\) and \(0.75\), respectively. The ASME Code for Process Piping specifies the maximum use temperature suitable for ASTM A992 carbon steel to be \(427^{\circ} \mathrm{C}\) (ASME B31.3-2014, Table A-1M). A radiation shield is to be placed in parallel between the two plates to keep the temperature of the steel plate from exceeding its maximum use temperature. Determine the emissivity that the radiation shield needs to keep the steel plate surface from exceeding \(427^{\circ} \mathrm{C}\).
Two concentric spheres of diameters \(D_{1}=0.3 \mathrm{~m}\) and $D_{2}=0.6 \mathrm{~m}\( are maintained at uniform temperatures \)T_{1}=800 \mathrm{~K}$ and \(T_{2}=500 \mathrm{~K}\) and have emissivities \(\varepsilon_{1}=0.5\) and \(\varepsilon_{2}=0.7\), respectively. Determine the net rate of radiation heat transfer between the two spheres. Also, determine the convection heat transfer coefficient at the outer surface if both the surrounding medium and the surrounding surfaces are at \(30^{\circ} \mathrm{C}\). Assume the emissivity of the outer surface is \(0.35\).
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