Consider a sphere of diameter 5 cm, a cube of side length 5 cm, and a rectangular prism of dimension
Now all three of these geometries are exposed to ambient air at 33°C on all of their surfaces with a heat transfer coefficient of 12 W/m2 K. Determine how long it will take for the temperature of each geometry to rise to 25°C.
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HEAT+MASS TRANSFER:FUND.+APPL.
- A 2 m X 1.5 m section of wall of an industrial furnace burning gas is not insulated, and the temperature at the outer surface of this section is measured to be 80oC. The temperature of the furnace room is 30oC, and the combined convection and radiation heat transfer coefficient at the surface of the outer furnace is 10 w/oC. It is proposed to insulate this section of the furnace wall with glass wool insulation (K=0.038 W/moC) in order to reduce the heat loss by 90 percent. Assuming the outer surface temperature of the section remains at about 80oC, determine i) the thickness of the insulation that is needed and ii) the outer surface temperature of the insulation after installation.arrow_forwardA 6-m-internal-diameter spherical tank made of 1.5-cm-thick stainless steel (k = 15 W/m·K) is used to store iced water at 0°C in a room at 20°C. The walls of the room are also at 20°C. The outer surface of the tank is black (emissivity « = 1), and heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation. Assuming the entire steel tank to be at 0°C and thus the thermal resistance of the tank to be negligible, determine (a) the rate of heat transfer to the iced water in the tank and (b) the amount of ice at 0°C that melts during a 24-h period. The heat of fusion of water is 333.7 kJ/kg.arrow_forwardConsider a cold aluminum canned drink that is initially at a uniform temperature of 4°C. The can is 12.5 cm high and has a diameter of 6 cm. If the combined convection/radiation heat transfer coefficient between the can and the surrounding air at 25°C is 10 W/m2 · °C, determine how long it will take for the average temperature of the drink to rise to 15°C. In an effort to slow down the warming of the cold drink, a person puts the can in a perfectly fitting 1-cm-thick cylindrical rubber insulator (k = 0.13 W/m · °C). Now how long will it take for the average temperature of the drink to rise to 15°C? Assume the top of the can is not covered.arrow_forward
- A 2-m × 1.8-m section of wall of an industrial furnace burning natural gas is not insulated, and the temperature at the outer surface of this section is measured to be 80°C. The temperature of the furnace room is 30°C, and the combined convection and radiation heat transfer coefficient at the surface of the outer furnace is 10 W/m2·C. It is proposed to insulate this section of the furnace wall with perlite insulation (k = 0.052 W/m·C) in order to reduce the heat loss by 90 percent, Assuming the outer surface temperature of the metal section still remains at about 80°C, determine the thickness of the insulation that needs to be used.arrow_forwardA person puts a few apples into the freezer at 15°C cool them quickly for guestswho are about to arrive. Initially, the apples are at a uniform temperature of 20°C,and the heat transfer coefficient on the surfaces is 8 W/m2·K. Treating the apples as9-cm-diameter spheres and taking their properties to be 840 kg/m3, Cp 3.81 kJ/kg·K, k = 0.418 W/m·K, and α =10-7 m2/s, determine the center and surface temperatures of the apples in 1 h. Also, determine the amount of heat transfer from each apple. Solve this problem using analytical one-term approximation method (notthe Heisler charts). Answer: Center: 11.2 ℃, Surface: 2.7 ℃, heat transfer: 17.2 kJarrow_forwardA 2-m x 1.8-m section of wall of an industrial furnace burning natural gas is not insulated, and the temperature at the outer surface of this section is measured to be 80°C. The temperature of the furnace room is 30°C, and the combined convection and radiation heat transfer coefficient at the surface of the outer furnace is 10 W/m² • °C. It is proposed to insulate this section of the furnace wall with expanded perlite insulation (k = 0.052 W/m • °C) in order to reduce the heat loss by 90%. Assuming the outer surface temperature of the metal section still remains at about 80°C, determine the thickness of the insulation that needs to be used. ANSWER:_______cmarrow_forward
- Two parallel back disks are positioned coaxially with a distance of 0.25 m apart. The lower disk is 0.2 m in diameter and the upper disk is 0.4 m in diameter. If the lower disk is heated electrically at 20 W to maintain a uniform temperature of 500 K, determine the temperature of the upper disk.arrow_forwardBecause you forgot to let the pipes drip during a freezing night, a section of an outdoor pipe is now frozen. The frozen section is L = 1 m long and the inner pipe diameter is D = 1.8 cm. During the day, the pipe is exposed to the cold air, the Sun, and the radiating surroundings. The cold air temperature is T∞ = -10°C, and has convection heat transfer coefficient h = 20 W/m2·K. The Sun provides solar irradiance of Gsun = 1350 W/m2. The steel pipe surface has absorptivity α = 0.6 and emissivity ε= 0.1. The surroundings, such as vegetation, houses, ground, etc. can be assumed to be blackbody held at Tsur = 280 K. A) Using the energy conservation system illustrated below, establish an equation that describes the stored energy in the section of frozen water (Est). B) Determine the amount of time needed to melt the ice in the pipe. Ice has density ρ= 920 kg/m3, and latent heat of fusion hsf = 334 kJ/kg. The ice is Tw = 0°C. Ignore conduction through the pipe walls – assume the pipe…arrow_forwardConsider a double-paned window consisting of two panes of glass, each with a thickness of 0.500 cm and an area of 0.795 m2 , separated by a layer of air with a thickness of 1.50 cm. The temperature on one side of the window is 0.00 ∘C∘C; the temperature on the other side is 21.0 ∘C∘C. In addition, note that the thermal conductivity of glass is roughly 36 times greater than that of air. Approximate the heat transfer through this window by ignoring the glass. That is, calculate the heat flow per second through 1.50 cmcm of air with a temperature difference of 21.0 ∘C∘C. (The exact result for the complete window is 25.6 J/sJ/s .)arrow_forward
- What is the heat power lost from the cup to the air due to convection? Take the external surface of a cup (with lid) to be at a temperature of 55.0oC and take the ambient air temperature to be 20.0oC. Take the heat convection coefficient to be 7.10 W/m2K for air. The area of the cup from which heat is transferred to air consists of the lid and the sides of the cup only, where the cup radius is 4.00 cm and its height is 9.20 cm. Give your answer in units of W, accurate to 1 decimal place.arrow_forwardThe emissivity of galvanized steel sheet, a common roofing material, is ε = 0.13 at temperatures around 300 K, while its absorptivity for solar irradiation is αS = 0.65. Would the neighborhood cat be comfortable walking on a roof constructed of the material on a day when GS = 750 W/m2, T∞ = 16°C, and h = 7 W/m2 · K? Assume the bottom surface of the steel is insulated.arrow_forwardA 0.3-cm-thick, 12-cm-high, and 18-cm-long circuit board houses 80 closely spaced logic chips on one side,each dissipating 0.06 W. The board is impregnated with copper fillings and has an effective thermalconductivity of 16 W/m · °C. All the heat generated in the chips is conducted across the circuit board andis dissipated from the back side of the board to the ambient air at 30°C, which is forced to flow over thesurface by a fan at a free-stream velocity of 400 m/min. Determine the temperatures on the two sides ofthe circuit board.arrow_forward
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