Chapter 1: Problem 40
How does forced convection differ from natural convection?
Chapter 1: Problem 40
How does forced convection differ from natural convection?
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Get started for freeAn ice skating rink is located in a building where the air is at $T_{\text {air }}=20^{\circ} \mathrm{C}\( and the walls are at \)T_{w}=25^{\circ} \mathrm{C}$. The convection heat transfer coefficient between the ice and the surrounding air is \(h=10 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). The emissivity of ice is \(\varepsilon=0.95\). The latent heat of fusion of ice is \(h_{i f}=333.7 \mathrm{~kJ} / \mathrm{kg}\), and its density is $920 \mathrm{~kg} / \mathrm{m}^{3}$. (a) Calculate the refrigeration load of the system necessary to maintain the ice at \(T_{s}=0^{\circ} \mathrm{C}\) for an ice rink of \(12 \mathrm{~m}\) by \(40 \mathrm{~m}\). (b) How long would it take to melt \(\delta=3 \mathrm{~mm}\) of ice from the surface of the rink if no cooling is supplied and the surface is considered insulated on the back side?
A series of ASME SA-193 carbon steel bolts are bolted to the upper surface of a metal plate. The bottom surface of the plate is subjected to a uniform heat flux of \(5 \mathrm{~kW} / \mathrm{m}^{2}\). The upper surface of the plate is exposed to ambient air with a temperature of \(30^{\circ} \mathrm{C}\) and a convection heat transfer coefficient of \(10 \mathrm{~W} / \mathrm{m}^{2}\). K. The ASME Boiler and Pressure Vessel Code (ASME BPVC.IV-2015, HF-300) limits the maximum allowable use temperature to \(260^{\circ} \mathrm{C}\) for the SA-193 bolts. Determine whether the use of these SA-193 bolts complies with the ASME code under these conditions. If the temperature of the bolts exceeds the maximum allowable use temperature of the ASME code, discuss a possible solution to lower the temperature of the bolts.
A thin metal plate is insulated on the back and exposed to solar radiation on the front surface. The exposed surface of the plate has an absorptivity of \(0.7\) for solar radiation. If solar radiation is incident on the plate at a rate of \(550 \mathrm{~W} / \mathrm{m}^{2}\) and the surrounding air temperature is \(10^{\circ} \mathrm{C}\), determine the surface temperature of the plate when the heat loss by convection equals the solar energy absorbed by the plate. Take the convection heat transfer coefficient to be $25 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$, and disregard any heat loss by radiation.
In the metal processing industry, heat treatment of metals is commonly done using electrically heated draw batch furnaces. Consider a furnace that is situated in a room with surrounding air temperature of \(30^{\circ} \mathrm{C}\) and an average convection heat transfer coefficient of $12 \mathrm{~W} / \mathrm{m}^{2}\(. \)\mathrm{K}$. The furnace front is made of a steel plate with thickness of \(20 \mathrm{~mm}\) and a thermal conductivity of $25 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$. The outer furnace front surface has an emissivity of \(0.23\), and the inside surface is subjected to a heat flux of $8 \mathrm{~kW} / \mathrm{m}^{2}$. Determine the outside surface temperature of the furnace front.
Consider a 20-cm-thick granite wall with a thermal conductivity of $2.79 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$. The temperature of the left surface is held constant at \(50^{\circ} \mathrm{C}\), whereas the right face is exposed to a flow of \(22^{\circ} \mathrm{C}\) air with a convection heat transfer coefficient of \(15 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Neglecting heat transfer by radiation, find the right wall surface temperature and the heat flux through the wall.
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