Problem 150
Kitchen water at \(10^{\circ} \mathrm{C}\) flows over a 10 -cm-diameter pipe with a velocity of \(1.1 \mathrm{~m} / \mathrm{s}\). Geothermal water enters the pipe at \(90^{\circ} \mathrm{C}\) at a rate of \(1.25 \mathrm{~kg} / \mathrm{s}\). For calculation purposes, the surface temperature of the pipe may be assumed to be \(70^{\circ} \mathrm{C}\). If the geothermal water is to leave the pipe at \(50^{\circ} \mathrm{C}\), the required length of the pipe is (a) $1.1 \mathrm{~m}$ (b) \(1.8 \mathrm{~m}\) (c) \(2.9 \mathrm{~m}\) (d) \(4.3 \mathrm{~m}\) (e) \(7.6 \mathrm{~m}\) (For both water streams, use $k=0.631 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \operatorname{Pr}=4.32\(, \)\left.\nu=0.658 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}, c_{p}=4179 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)$
Problem 151
Wind at \(30^{\circ} \mathrm{C}\) flows over a \(0.5\)-m-diameter spherical tank containing iced water at \(0^{\circ} \mathrm{C}\) with a velocity of $25 \mathrm{~km} / \mathrm{h}$. If the tank is thin-shelled with a high thermal conductivity material, the rate at which ice melts is (a) \(4.78 \mathrm{~kg} / \mathrm{h}\) (b) \(6.15 \mathrm{~kg} / \mathrm{h}\) (c) \(7.45 \mathrm{~kg} / \mathrm{h}\) (d) \(11.8 \mathrm{~kg} / \mathrm{h}\) (e) \(16.0 \mathrm{~kg} / \mathrm{h}\) (Take \(h_{i f}=333.7 \mathrm{~kJ} / \mathrm{kg}\), and use the following for air: $k=0.02588 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \quad \operatorname{Pr}=0.7282, \quad \nu=1.608 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s}\(, \)\left.\mu_{\infty}=1.872 \times 10^{-5} \mathrm{~kg} / \mathrm{m} \cdot \mathrm{s}, \mu_{s}=1.729 \times 10^{-5} \mathrm{~kg} / \mathrm{m} \cdot \mathrm{s}\right)$
Problem 152
Ambient air at \(20^{\circ} \mathrm{C}\) flows over a 30 -cm-diameter hot spherical object with a velocity of \(4.2 \mathrm{~m} / \mathrm{s}\). If the average surface temperature of the object is \(200^{\circ} \mathrm{C}\), the average convection heat transfer coefficient during this process is (a) \(8.6 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) (b) \(15.7 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) (c) \(18.6 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) (d) \(21.0 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) (e) \(32.4 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) (For air, use $k=0.2514 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \operatorname{Pr}=0.7309, \nu=1.516 \times\( \)\left.10^{-5} \mathrm{~m}^{2} / \mathrm{s}, \mu_{\infty}=1.825 \times 10^{-5} \mathrm{~kg} / \mathrm{m} \cdot \mathrm{s}, \mu_{s}=2.577 \times 10^{-5} \mathrm{~kg} / \mathrm{m} \cdot \mathrm{s}\right)$
Problem 153
Jakob (1949) suggests the following correlation be used for square tubes in a liquid crossflow situation: $$ \mathrm{Nu}=0.102 \mathrm{Re}^{0.675} \mathrm{Pr}^{1 / 3} $$ Water $(k=0.61 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \operatorname{Pr}=6)\( at \)50^{\circ} \mathrm{C}$ flows across a 1 -cm-square tube with a Reynolds number of 10,000 and surface temperature of $75^{\circ} \mathrm{C}\(. If the tube is \)3 \mathrm{~m}$ long, the rate of heat transfer between the tube and water is (a) \(9.8 \mathrm{~kW}\) (b) \(12.4 \mathrm{~kW}\) (c) \(17.0 \mathrm{~kW}\) (d) \(19.6 \mathrm{~kW}\) (e) \(24.0 \mathrm{~kW}\)
Problem 155
Jakob (1949) suggests the following correlation be used for square tubes in a liquid crossflow situation: $$ \mathrm{Nu}=0.102 \mathrm{Re}^{0.625} \mathrm{Pr}^{1 / 3} $$ Water \((k=0.61 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \mathrm{Pr}=6)\) flows across a \(1-\mathrm{cm}-\) square tube with a Reynolds number of 10,000 . The convection heat transfer coefficient is (a) \(5.7 \mathrm{~kW} / \mathrm{m}^{2} \cdot \mathrm{K}\) (b) \(8.3 \mathrm{~kW} / \mathrm{m}^{2} \cdot \mathrm{K}\) (c) \(11.2 \mathrm{~kW} / \mathrm{m}^{2} \cdot \mathrm{K}\) (d) \(15.6 \mathrm{~kW} / \mathrm{m}^{2} \cdot \mathrm{K}\) (e) \(18.1 \mathrm{~kW} / \mathrm{m}^{2} \cdot \mathrm{K}\)
Problem 156
On average, superinsulated homes use just 15 percent of the fuel required to heat the same size conventional home built before the energy crisis in the 1970 s. Write an essay on superinsulated homes, and identify the features that make them so energy efficient as well as the problems associated with them. Do you think superinsulated homes will be economically attractive in your area?
Problem 157
Conduct this experiment to determine the heat loss coefficient of your house or apartment in \(\mathrm{W} /{ }^{\circ} \mathrm{C}\) or $\mathrm{Btu} / \mathrm{h} \cdot{ }^{\circ} \mathrm{F}$. First make sure that the conditions in the house are steady and the house is at the set temperature of the thermostat. Use an outdoor thermometer to monitor outdoor temperature. One evening, using a watch or timer, determine how long the heater was on during a \(3-h\) period and the average outdoor temperature during that period. Then using the heat output rating of your heater, determine the amount of heat supplied. Also, estimate the amount of heat generation in the house during that period by noting the number of people, the total wattage of lights that were on, and the heat generated by the appliances and equipment. Using that information, calculate the average rate of heat loss from the house and the heat loss coefficient.
