Chapter 3: Problem 106
A pipe is insulated to reduce the heat loss from it. However, measurements indicate that the rate of heat loss has increased instead of decreasing. Can the measurements be right?
Chapter 3: Problem 106
A pipe is insulated to reduce the heat loss from it. However, measurements indicate that the rate of heat loss has increased instead of decreasing. Can the measurements be right?
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Get started for freeA spherical vessel, \(3.0 \mathrm{~m}\) in diameter (and negligible wall thickness), is used for storing a fluid at a temperature of $0^{\circ} \mathrm{C}\(. The vessel is covered with a \)5.0$-cm-thick layer of an insulation \((k=0.20 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\). The surrounding air is at \(22^{\circ} \mathrm{C}\). The inside and outside heat transfer coefficients are 40 and 10 $\mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}\(, respectively. Calculate \)(a)$ all thermal resistances, in \(\mathrm{K} / \mathrm{W},(b)\) the steady rate of heat transfer, and \((c)\) the temperature difference across the insulation layer.
Two very long, slender rods of the same diameter and length are given. One rod (Rod 1) is made of aluminum and has a thermal conductivity $k_{1}=200 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$, but the thermal conductivity of Rod \(2, k_{2}\), is not known. To determine the thermal conductivity of Rod 2 , both rods at one end are thermally attached to a metal surface which is maintained at a constant temperature \(T_{b}\). Both rods are losing heat by convection, with a convection heat transfer coefficient \(h\) into the ambient air at \(T_{\infty}\). The surface temperature of each rod is measured at various distances from the hot base surface. The measurements reveal that the temperature of the aluminum rod (Rod 1) at \(x_{1}=40 \mathrm{~cm}\) from the base is the same as that of the rod of unknown thermal conductivity (Rod 2) at \(x_{2}=20 \mathrm{~cm}\) from the base. Determine the thermal conductivity \(k_{2}\) of the second rod \((\mathrm{W} / \mathrm{m} \cdot \mathrm{K})\).
In a combined heat and power (CHP) generation process, by-product heat is used for domestic or industrial heating purposes. Hot steam is carried from a CHP generation plant by a tube with diameter of \(127 \mathrm{~mm}\) centered at a square crosssection solid bar made of concrete with thermal conductivity of \(1.7 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). The surface temperature of the tube is constant at \(120^{\circ} \mathrm{C}\), while the square concrete bar is exposed to air with temperature of \(-5^{\circ} \mathrm{C}\) and convection heat transfer coefficient of \(20 \mathrm{~W} / \mathrm{m}^{2}\). \(\mathrm{K}\). If the temperature difference between the outer surface of the square concrete bar and the ambient air is to be maintained at $5^{\circ} \mathrm{C}$, determine the width of the square concrete bar and the rate of heat loss per meter length. Answers: $1.32 \mathrm{~m}, 530 \mathrm{~W} / \mathrm{m}$
Hot water is to be cooled as it flows through the tubes exposed to atmospheric air. Fins are to be attached in order to enhance heat transfer. Would you recommend attaching the fins inside or outside the tubes? Why?
The overall heat transfer coefficient (the \(U\)-value) of a wall under winter design conditions is \(U=2.25 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Now a layer of \(100-\mathrm{mm}\) face brick is added to the outside, leaving a 20 -mm airspace between the wall and the bricks. Determine the new \(U\)-value of the wall. Also, determine the rate of heat transfer through a \(3-\mathrm{m}\)-high, 7-m-long section of the wall after modification when the indoor and outdoor temperatures are \(22^{\circ} \mathrm{C}\) and $-25^{\circ} \mathrm{C}$, respectively.
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