Chapter 1: Problem 90
Can all three modes of heat transfer occur simultaneously (in parallel) in a medium?
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Chapter 1: Problem 90
Can all three modes of heat transfer occur simultaneously (in parallel) in a medium?
These are the key concepts you need to understand to accurately answer the question.
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A 10 -cm-high and 20-cm-wide circuit board houses on its surface 100 closely spaced chips, each generating heat at a rate of \(0.12 \mathrm{~W}\) and transferring it by convection and radiation to the surrounding medium at \(40^{\circ} \mathrm{C}\). Heat transfer from the back surface of the board is negligible. If the combined convection and radiation heat transfer coefficient on the surface of the board is \(22 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), the average surface temperature of the chips is (a) \(41^{\circ} \mathrm{C}\) (b) \(54^{\circ} \mathrm{C}\) (c) \(67^{\circ} \mathrm{C}\) (d) \(76^{\circ} \mathrm{C}\) (e) \(82^{\circ} \mathrm{C}\)
Consider a house in Atlanta, Georgia, that is maintained at \(22^{\circ} \mathrm{C}\) and has a total of \(20 \mathrm{~m}^{2}\) of window area. The windows are double-door type with wood frames and metal spacers and have a \(U\)-factor of \(2.5 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (see Prob. 1-125 for the definition of \(U\)-factor). The winter average temperature of Atlanta is \(11.3^{\circ} \mathrm{C}\). Determine the average rate of heat loss through the windows in winter.
A 2.1-m-long, 0.2-cm-diameter electrical wire extends across a room that is maintained at \(20^{\circ} \mathrm{C}\). Heat is generated in the wire as a result of resistance heating, and the surface temperature of the wire is measured to be \(180^{\circ} \mathrm{C}\) in steady operation. Also, the voltage drop and electric current through the wire are measured to be \(110 \mathrm{~V}\) and \(3 \mathrm{~A}\), respectively. Disregarding any heat transfer by radiation, determine the convection heat transfer coefficient for heat transfer between the outer surface of the wire and the air in the room. Answer: \(156 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\)
Using the conversion factors between W and Btu/h, m and \(\mathrm{ft}\), and \(\mathrm{K}\) and \(\mathrm{R}\), express the Stefan-Boltzmann constant \(\sigma=5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}^{4}\) in the English unit \(\mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2} \cdot \mathrm{R}^{4}\)
A room is heated by a \(1.2 \mathrm{~kW}\) electric resistance heater whose wires have a diameter of \(4 \mathrm{~mm}\) and a total length of \(3.4 \mathrm{~m}\). The air in the room is at \(23^{\circ} \mathrm{C}\) and the interior surfaces of the room are at \(17^{\circ} \mathrm{C}\). The convection heat transfer coefficient on the surface of the wires is \(8 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). If the rates of heat transfer from the wires to the room by convection and by radiation are equal, the surface temperature of the wire is (a) \(3534^{\circ} \mathrm{C}\) (b) \(1778^{\circ} \mathrm{C}\) (c) \(1772^{\circ} \mathrm{C}\) (d) \(98^{\circ} \mathrm{C}\) (e) \(25^{\circ} \mathrm{C}\)
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