Q1For one -dimension heat transfer conduction consider a shielding wall for a nuclearreactor. The wall receives a gamma-ray flux such that heat is generated within thewall according to the relation9x = 4, ( 2X+3)Where q0 is the heat generation at the inner face of the wall exposed to theray Flux. Using this relation for heat generation, derive an expression for thetemperature distribution in a wall of thickness L, where the inside and outsidetemperatures are maintained at Ti and TO, respectively. Also, obtain temperature inthe wall at X= 0.1 m. Assume, Ti-100 °C, TO=200 °C, L= 0.2 m, K = 40 w/ m.°C, and q0 = 50 W%Dgamma-%3DI 90y FLUXТоTi

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For one -dimension heat transfer conduction consider a shielding wall for a nuclear reactor. The wall receives a gamma-ray flux such that heat is generated within the wall according to the relation = 9, ( 2X+3) Where g0 is the heat generation at the inner face of the wall exposed to the gamma- ray Flux. Using this relation for heat generation, derive an expression for the temperature distribution in a wall of thickness L, where the inside and outside temperatures are maintained at Ti and TO, respectively. Also, obtain temperature in the wall at X= 0.1 m. Assume, Ti-100 °C, TO=200 °C, L= 0.2 m, K = 40 w / m. °C, and q0 = 50 W 1 90 y FLUX То Ti

For one -dimension heat transfer conduction consider a shielding wall for a nuclear reactor. The wall receives a gamma-ray flux such that heat is generated within the wall according to the relation = 9, ( 2X+3) Where g0 is the heat generation at the inner face of the wall exposed to the gamma- ray Flux. Using this relation for heat generation, derive an expression for the temperature distribution in a wall of thickness L, where the inside and outside temperatures are maintained at Ti and TO, respectively. Also, obtain temperature in the wall at X= 0.1 m. Assume, Ti-100 °C, TO=200 °C, L= 0.2 m, K = 40 w / m. °C, and q0 = 50 W 1 90 y FLUX То Ti

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 2.29P: 2.29 In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the...

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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.)
2.51 Determine by means of a flux plot the temperatures and heat flow per unit depth in the ribbed insulation shown in the accompanying sketch.
2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1 m wide and 1 m tall. The fins are to be rectangular in cross section, 2.5 cm long and 0.25 cm thick, as shown in the figure. There are to be 100 fins per meter. The convection heat transfer coefficient, both for the wall and the fins, is estimated to be K. With this information determine the percent increase in the rate of heat transfer of the finned wall compared to the bare wall.
2.29 In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation where = local rate of heat generation per unit volume at r = outside radius = rate of heat generation per unit volume at the centerline Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of if the rate of heat removal from its surface is 1.6 .
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.
Water at a temperature of 77C is to be evaporated slowly in a vessel. The water is in a low-pressure container surrounded by steam as shown in the sketch below. The steam is condensing at 107C. The overall heat transfer coefficient between the water and the steam is 1100W/m2K. Calculate the surface area of the container that is required to evaporate water at a rate of 0.01 kg/s. Problem 1.16
2.2 A small dam, which is idealized by a large slab 1.2 m thick, is to be completely poured in a short Period of time. The hydration of the concrete results in the equivalent of a distributed source of constant strength of 100 W/m3. If both dam surfaces are at 16°C, determine the maximum temperature to which the concrete will be subjected, assuming steady-state conditions. The thermal conductivity of the wet concrete can be taken as 0.84 W/m K.
3.17 A 1.4-kg aluminum household iron has a 500-W heating element. The surface area is . The ambient temperature is 21°C, and the surface heat transfer coefficient is . How long after the iron is plugged in does its temperature reach 104°C?
2.44 To determine the thermal conductivity of a long, solid 2.5-cm-diameter rod, one half of the rod was inserted into a furnace while the other half was projecting into air at . After steady state had been reached, the temperatures at two points 7.6 cm apart were measured and found to be and , respectively. The heat transfer coefficient over the surface of the rod exposed to the air was estimated to be 22.7 . What is thermal conductivity of the rod?
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.
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