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Consider the water heater We wish to determine the energy needed to compensate for heat losses incurred while the water is stored at the prescribed temperature of 55-degreeC. The cylindrical storage tank (with flat ends) has a capacity of 100 gal, and foamed urethane is used to insulate the side and end walls from ambient air at an annual average temperature of 20-degree C. The resistance to heat transfer is dominated by conduction in the insulation and by free convection in the air, for which h 2 W/m2 middot K. If electric resistance heating is used to compensate for the losses and the cost of electric power is $0.18/kWh, specify tank and insulation dimensions for which the annual cost associated with the heat losses is less than $50.
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Chapter 3 Solutions
Introduction to Heat Transfer
- 2.7 A very thin silicon chip is bonded to a 6-mm thick aluminum substrate by a 0.02-mm thick epoxy glue. Both surfaces of this chip-aluminum system are cooled by air at , where the convective heat transfer coefficient of air flow is . If the heat dissipation per unit area from the chip is under steady-state conditions, draw the thermal circuit for the system and determine the operating temperature of the chip.arrow_forward3.14 A thin-wall cylindrical vessel (1 m in diameter) is filled to a depth of 1.2 m with water at an initial temperature of 15°C. The water is well stirred by a mechanical agitator. Estimate the time required to heat the water to 50°C if the tank is suddenly immersed in oil at 105°C. The overall heat transfer coefficient between the oil and the water is , and the effective heat transfer surface is .arrow_forward3.10 A spherical shell satellite (3-m-OD, 1.25-cm-thick stainless steel walls) re-enters the atmosphere from outer space. If its original temperature is 38°C, the effective average temperature of the atmosphere is 1093°C, and the effective heat transfer coefficient is , estimate the temperature of the shell after reentry, assuming the time of reentry is 10 min and the interior of the shell is evacuated.arrow_forward
- 2.43 A turbine blade 6.3 cm long, with cross-sectional area and perimeter , is made of stainless steel . The temperature of the root, , is . The blade is exposed to a hot gas at , and the heat transfer coefficient is K. Determine the temperature of the blade tip and the rate of heat flow at the root of the blade. Assume that the tip is insulated.arrow_forward2.42 A circumferential fin of rectangular cross section, 3.7-cm OD and 0.3 cm thick, surrounds a 2.5-cm- diameter tube as shown below. The fin is constructed of mild steel. Air blowing over the fin produces a heat transfer coefficient of K. If the temperatures of the base of the fin and the air are and , respectively, calculate the heat transfer rate from the fin.arrow_forward3.5 In a ball-bearing production facility, steel balls that are each of 15 mm in diameter are annealed by first heating them to 870°C and then slowly cooling in air to 125°C. If the cooling air stream temperature is 60°C, and it has a convective heat transfer coefficient of , determine the time required for the cooling.arrow_forward
- 3. A 3 in O.D. aluminum tube (k=133 BTU/h ft°F) has 16 longitudinal fins spaced around its outside surface as shown below. The fins are .06 in thick and extend 2 in from the outside surface of the tube. If the outside surface of the tube wall is at 200F, the surrounding air is at 70°F and the convective heat transfer coefficient is 15 BTU/h ft°F, determine the percent increase in heat transfer for the finned pipe over that for the unfinned pipe. Note: longitudinal fins are rectangular fins that extend along the length of the tube. Figure shows view looking down the tubearrow_forwardVI.2 A coolant is transported in a pipe with external wall temperature of -30 °C and with outer diameter of 10 cm. The tube is thermally isolated by two layers: 1) an internal layer of foamed polypropylene with thermal conductivity of 0.08 W.m.K and thickness of 10 cm, and 2) an external felt layer with thermal conductivity of 0.05 W.m.K and thickness of 5 cm. Temperature of the outer surface is 25 °C. Calculate the heat flow from the surroundings to the tube with length of 100 m. What is the temperature on the boundary between polypropylene and felt layers? Result: The heat flow from the surroundings is approx. 1.77 kW. Temperature between layers of isolation is 8.8 °C.arrow_forward1. A composite furnace wall is made up of a 12-in. lining of magnesite refractory brick, a 5-in.thickness of 85% magnesia, and a steel casing 0.10-in. thick. Flue gas temperature is 2200 F andthe boiler room is at 80 F. Gas side film coefficient is 15 Btu/hr-sq.ft-F and air side is 4.0.Determine:a. The thermal current Q/Ab. Interface temperaturesc. Effect on thermal current and inside refractory wall temperature if the magnesia insulation weredoubled.arrow_forward
- I need the answer as soon as possiblearrow_forwardAs part of your work-study program at HTU, you successfully got a student job at your local ‘BEST-BURGER-IN-TOWN’ to help pay your own tuition and expenses. Since cylindrical frozen burger patties are cooked when placed on a hot stainless-steel cooking top, you like to think of the case as a conduction problem:a. Write down the appropriate general heat conduction equation that describes the cooking of those beef patties.b. Clearly state all assumptions.c. After cancelling the proper terms, write down the final energy equation for the patties.Do not solve for temperature distribution or heat transfer.arrow_forwardA heater coil is completely immersed in an oil bath that is insulated on all sides except for the top where the oil is in direct contact with the surrounding air that is maintained at a constant temperature, Oair. At t=0s, the coil is switched on and provides in watts of electrical power to the oil which has a thermal mass of moil and an initial temperature of Oinit-oil. The temperature of the oil is denoted by oil and the thermal resistance between the oil and air is Roil-air- a) Draw a schematic of the system clearly labeling the (assumed) directions of the heat transfer rates and the temperature at every node. b) Derive the governing differential equation for the temperature of the oil, oil- c) Where does Oinit-oil appear in the system schematic and how does it affect the governing equations? d) Derive an expression for the steady-state temperature of the oil as a function of the various system parameters.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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