Chapter 1: Problem 36
What are the mechanisms of heat transfer? How are they distinguished from each other?
Chapter 1: Problem 36
What are the mechanisms of heat transfer? How are they distinguished from each other?
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Get started for freeConsider a 3-m \(\times 3-\mathrm{m} \times 3-\mathrm{m}\) cubical furnace whose top and side surfaces closely approximate black surfaces at a temperature of \(1200 \mathrm{~K}\). The base surface has an emissivity of \(\varepsilon=0.7\), and is maintained at \(800 \mathrm{~K}\). Determine the net rate of radiation heat transfer to the base surface from the top and side surfaces.
A 40-cm-long, 800-W electric resistance heating element with diameter $0.5 \mathrm{~cm}\( and surface temperature \)120^{\circ} \mathrm{C}$ is immersed in \(75 \mathrm{~kg}\) of water initially at \(20^{\circ} \mathrm{C}\). Determine how long it will take for this heater to raise the water temperature to \(80^{\circ} \mathrm{C}\). Also, determine the convection heat transfer coefficients at the beginning and at the end of the heating process.
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. 1-120 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.
An AISI 316 stainless steel spherical container is mic reaction that provides a uniform heat flux of \(60 \mathrm{~kW} / \mathrm{m}^{2}\) to the container's inner surface. The container has an inner diameter of \(1 \mathrm{~m}\) and a wall thickness of \(5 \mathrm{~cm}\). To prevent thermal burns on individuals working around the container, it is necessary to keep the container's outer surface temperature below \(50^{\circ} \mathrm{C}\). If the ambient temperature is \(23^{\circ} \mathrm{C}\), determine the necessary convection heat transfer coefficient to keep the container's outer surface temperature below \(50^{\circ} \mathrm{C}\). Is the necessary convection heat transfer coefficient feasible with free convection of air? If not, discuss other options to prevent the container's outer surface temperature from causing thermal burns.
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 \(0.08 \mathrm{~W}\) 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) \(72.4^{\circ} \mathrm{C}\) (b) \(66.5^{\circ} \mathrm{C}\) (c) \(40.4^{\circ} \mathrm{C}\) (d) \(58.2^{\circ} \mathrm{C}\) (e) \(49.1^{\circ} \mathrm{C}\)
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