A cylindrical tank is constructed from aluminum (kal = 240 W/m2.K) with 1 m inner diameter and 10 mm thick. The tank having uniform volumetric heat generation of 1 MW/m3. The outer surface of the tank is covered with a 5 mm thick layer of stainless steel (kst = 15 W/m2.K). The heat transfer from the tank is assumed to the radial direction only as the both cross sections of the tank are properly insulated. It is proposed to submerge the tank into oceanic water at 20˚C flowing at a velocity of 0.5 m/s. The properties of the oceanic water are kwater = 0.606 W/m.K, ρ = 1000 kg/m3, μ = 959 x 10-6 N.s/m2, Pr = 6.62. Analyze the acceptability of the proposal if the melting point of aluminum is 667˚C.

A cylindrical tank is constructed from aluminum (kal = 240 W/m2.K) with 1 m inner diameter and 10 mm thick. The tank having uniform volumetric heat generation of 1 MW/m3. The outer surface of the tank is covered with a 5 mm thick layer of stainless steel (kst = 15 W/m2.K). The heat transfer from the tank is assumed to the radial direction only as the both cross sections of the tank are properly insulated. It is proposed to submerge the tank into oceanic water at 20˚C flowing at a velocity of 0.5 m/s. The properties of the oceanic water are kwater = 0.606 W/m.K, ρ = 1000 kg/m3, μ = 959 x 10-6 N.s/m2, Pr = 6.62. Analyze the acceptability of the proposal if the melting point of aluminum is 667˚C.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.30P: 2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is...

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1.10 A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.
1.1 On a cold winter day, the outer surface of a 0.2-m-thick concrete wall of a warehouse is exposed to temperature of –5°C, while the inner surface is kept at 20°C. The thermal conductivity of the concrete is 1.2 W/m K. Determine the heat loss through the wall, which is 10-m long and 3-m high. Problem 1.1
3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on one side is and on the other side is . If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it takes for the copper plate to reach a temperature of 82°C.
A high-speed computer is located in a temperature-controlled room at 26C. When the machine is operating, its internal heat generation rate is estimated to be 800 W. The external surface temperature of the computer is to be maintained below 85C. The heat transfer coefficient for the surface of the computer is estimated to be 10W/m2K. What surface area would be necessary to assure safe operation of this machine? Comment on ways to reduce this area.
2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of ohm-centimeter. The operating temperature of the stainless steel is to be no more than 1260°C. The heat transfer coefficient at the outer surface is expected to be no less than in a medium whose maximum temperature is 93°C. A transformer capable of delivering current at 9 and 12 V is available. Determine a suitable size for the wire, the current required, and discuss what effect a reduction in the heat transfer coefficient would have. (Hint: Demonstrate first that the temperature drop between the center and the surface of the wire is independent of the wire diameter, and determine its value.)
2.45 Heat is transferred from water to air through a brass wall . The addition of rectangular brass fins, 0.08 cm thick and 2.5 cm long, spaced 1.25 cm apart, is contemplated. Assuming a water-side heat transfer coefficient of and an airside heat transfer coefficient of , compare the gain in heat transfer rate achieved by adding fins to (a) the water side, (b) the air side, and (c) both sides. (Neglect temperature drop through the wall.)
2.9 In a large chemical factory, hot gases at 2273 K are cooled by a liquid at 373 K with gas-side and liquid-side convection heat transfer coefficients of 50 and , respectively. The wall that separates the gas and liquid streams is composed of a 2-cm thick oxide layer on the gas side and a 4-cm thick slab of stainless steel on the liquid side. There is a contact resistance between the oxide layer and the steel of . Determine the rate of heat loss from hot gases through the composite wall to the liquid.
An electronic device that internally generates 600 mW of heat has a maximum permissible operating temperature of 70C. It is to be cooled in 25C air by attaching aluminum fins with a total surface area of 12cm2. The convection heat transfer coefficient between the fins and the air is 20W/m2K. Estimate the operating temperature when the fins are attached in such a way that (a) there is a contact resistance of approximately 50 K/W between the surface of the device and the fin array and (b) there is no contact resistance (in this case, the construction of the device is more expensive). Comment on the design options.
The outer facing of a room is constructed from 25 cm thick brick, 2.5 cm of mortar, 10 cm of limestone (k = 0.186 W/m-K) and 1.2 cm of plaster (k = 0.096 W/m-K). Thermal conductivities of mortar and brick are both 0.52 W/m-K. Assume that the heat transfer coefficients on the inside (plaster side) and the outside (brick side) surfaces of the wall to be 6 and 12 W/sq. m, respectively. Calculate the rate of heat transfer per 10 sq. m of the wall surface from the room at 18 C to the outside air at 36 C.
The efficiency of a single cylindrical cross-section fin is 85%. The diameter of the fin is 13 mm and it extends 32 mm from the base. The base is 65 K hotter than the surrounding fluid, and the heat transfer coefficient is 32 W/m2K. How many fins would be required to increase heat transfer from the base by 50 W? Give your answer as an integer.
A hot surface at 100°C is to be cooled by attaching 3-cm-long, 0.25-cm-diameter aluminum pin fins (k = 237 W/m·K) to it, with a center-to-center distance of 0.6 cm. The temperature of the surrounding medium is 30°C, and the heat transfer coefficient on the surfaces is 35 W/m2 ·K. Determine the rate of heat transfer from the surface for a 1-m x 1-m section of the plate. Also determine the overall effectiveness of the fins.
The wall of a furnace consists of 200 mm thick refractory brick (k = 3 Btu / hr-ft2-0F), 100 mm thick bricks (k = 0.050 Btu / hr-ft2-0F) and 6 mm thick steel. The temperature on the side of the refractory brick layer of the furnace is 1150 C, and the temperature on the outer steel surface is 30C. There is a heat loss of 300 W / square meter at the wall of the furnace. It is difficult to prevent the thin air additions between the brick layers and the brick layer and the steel wall. How many mm of brick layers is the total thickness of these air layers equivalent?