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- A plane wall, 7.5 cm thick, generates heat internally at the rate of 105 W/m3. One side of the wall is insulated, and the other side is exposed to an environment at 90C. The convection heat transfer coefficient between the wall and the environment is 500 W/m2 K. If the thermal conductivity of the wall is 12 W/m K, calculate the maximum temperature in the wall.A plane wall 15 cm thick has a thermal conductivity given by the relation k=2.0+0.0005T[W/mK] where T is in kelvin. If one surface of this wall is maintained at 150C and the other at 50C, determine the rate of heat transfer per square meter. Sketch the temperature distribution through the wall.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.
- Discuss the modes of heat transfer that determine the equilibrium temperature of the space shuttle Endeavour when it is in orbit. What happens when it reenters the earths atmosphere?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?2.15 Suppose that a pipe carrying a hot fluid with an external temperature of and outer radius is to be insulated with an insulation material of thermal conductivity k and outer radius . Show that if the convection heat transfer coefficient on the outside of the insulation is and the environmental temperature is , the addition of insulation actually increases the rate of heat loss if , and the maximum heat loss occurs when . This radius, is often called the critical radius.
- 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?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.1 - A square chip, with side w = 5 mm, operates under isothermal conditions.The chip is positioned on a substrate so that its side and bottom surfaces are thermally insulated, while its top surface is exposed to theflow of a refrigerant at T∞ = 15°C. From reliability considerations, the chip temperature cannot exceed T = 85°C. The refrigerant being air, with a convection heat transfer coefficientcorresponding h = 200 W/(m2K), what is the maximum allowable power for the chip? Since the coolant is a dielectric liquid for which h = 3000 W/(m²K), what is the maximum allowed power?
- The 1 ft thick walls of a building are made of concrete (k = 2 Btu/h·ft·F). The outside temperature and heat transfer coefficient are 50 F and 2 Btu/h·ft2·F, respectively. Find the rate of heat transfer through 1000 ft2 of the wall if the inside temperature and heat transfer coefficient are 120 F and 1 Btu/h·ft2 F, respectively. Both the inside and the outside of the wall are coated with 20 mils of paint (k = 0.1Btu/h·ft·F) where 1 mil = 1E-3 in. Compare the results with a bare wall.For steady state condition, determine the heat lost by inner lining through shields to the outer lining to keep the temperature of the outside surface of a hollow brick lining of a furnace at 100°C when the temperature of the inside surface of the lining is 500°C. Take the emissivity of brick lining as well as for shield as 0.87. Heat transfer to the surrounding from the outer surface takes place by radiation and convection. The heat transfer coefficient for natural convection is given by ha = 1.44 (ΔT)^0.33 W/m2-K, ta (air temperature) = 25°C. Neglect the heat transfer by conduction and convection between the brick lining.Heat Transfer A wall of an oven with a wire in it. Across the wire a voltage of 50 Volts and a current of 2 Amps is applied, and 80% of the electrical power is converted to thermal energy. The oven is a convection oven and has air flowing through it at 240 C and h = 10 W/m^2 K. The wall of the oven is 0.1 m thick and 1.5 m tall and 1.5 m wide and is made of steel (k = 15 W/m K). Find the surface energy balance on the inner wall of the oven and determine the temperature of the ineer wall at steady state. Then do an energy balance on the outer wall, assume that the oven is free standing and has an emissivity, e = 0.6, and the surrounding temperature is 25 C. The air in the surrounding has a convective heat transfer coefficient of 25 W/m^2 K. Just set up the balance equation that would enable to solve, no need to actually solve.