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0: In a nuclear reactor, 1-cm-diameter cylindrical uranium rods cooled by water from outside serve as the fuel. Heat is generated uniformly in the rods (k = 29.5 W/m - "C) at a rate of 7 x10 w/m?. If the outer surface temperature of rods is 175°c, determine the temperature at their center.

0: In a nuclear reactor, 1-cm-diameter cylindrical uranium rods cooled by water from outside serve as the fuel. Heat is generated uniformly in the rods (k = 29.5 W/m - "C) at a rate of 7 x10 w/m?. If the outer surface temperature of rods is 175°c, determine the temperature at their center.

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Q10: In a nuclear reactor, 1-cm-diameter cylindrical uranium rods cooled by water from outside serve as the fuel. Heat is generated uniformly in the rods (k = 29.5 W/m - °C) at a rate of 7 x10 w/m?. If the outer surface temperature of rods is 175°C, determine the temperature at their center. Q11: Consider a homogeneous spherical piece of radioactive material of radius ro =0.04 m that is generating heat at a constant rate of g'= 4 x 10' w/m. The heat generated is dissipated to the environment steadily. The outer surface of the sphere is maintained at a uniform temperature of 80°C and the thermal conductivity of the sphere is k = 15 W/m "C. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the sphere, (b) obtain a relation for the variation of temperature in the sphere by solving the differential equation, and (c) determine the temperature at the center of the sphere. Q12: Consider a large 3-cm-thick stainless steel plate (k =15.1 W/m- C) in which heat is generated uniformly at a rate of 5 x10° W/m?. Both sides of the plate are exposed to an environment at 30°C with a heat transfer coefficient of 60 W/m² . °C. Explain where in the plate the highest and the lowest temperatures will occur, and determine their values. Q13: Consider a large 5-cm-thick brass plate (k = 111 W/m - C) in which heat is generated uniformly at a rate of 2 x 10 w/m. One side of the plate is insulated while the other side is exposed to an environment at 25°C with a heat transfer coefficient of 44 W/m2. "C. Explain where in the plate the highest and the lowest temperatures will occur, and determine their values. Q14: A 6-m-long 2-kW electrical resistance wire is made of 0.2-cm-diameter stainless steel (k = 15.1 W/m "C). The resistance wire operates in an environment at 30°C with a heat transfer coefficient of 140 W/m? . "C at the outer surface. Determine 1) The surface temperature of the wire. 2) The center temperature of the wire. Q15: Consider a 1.5-m-high and 0.6-m-wide plate whose thickness is 0.15 m. One side of the plate is maintained at a constant temperature of 500 K while the other side is maintained at 350 K. The thermal conductivity of the plate can be assumed to vary linearly in that temperature range as: k(T) = k( 1 + B7) where ko = 25 w/m Kand B = 8.7 x 10 * K'. Disregarding the edge effects and assuming steady one dimensional heat transfer, determine the rate of heat conduction through the plate. Answer: 30,800 w Q16: In a nuclear reactor, heat is generated in 1-cm diameter cylindrical uranium fuel rods at a rate of 4 x10 W/m. Determine the temperature difference between the center and the surface of the fuel rod. Answer: 9.0°C Q17: Consider a 20-cm-thick large concrete plane wall (k = 0.77 W/m C) subjected to convection on both sides with T1 = 27°C and h1 = 5 W/m? . "C on the inside, and T2 = 8°C and h2 = 12 W/m? . °C on the outside. Assuming constant thermal conductivity with no heat generation and negligible radiation, (a) express the differential equations and the boundary conditions for steady one- dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the temperatures at the inner and outer surfaces of the wall. Q18: Heat is generated uniformly at a rate of 2.6 x10 W/m2 in a spherical ball (k = 45 W/m C) of diameter 30 cm. The ball is exposed to iced-water at 0°C with a heat transfer coefficient of 1200 W/m? . "C. Determine the temperatures at the center and the surface of the ball.
Transcribed Image Text:Q10: In a nuclear reactor, 1-cm-diameter cylindrical uranium rods cooled by water from outside serve as the fuel. Heat is generated uniformly in the rods (k = 29.5 W/m - °C) at a rate of 7 x10 w/m?. If the outer surface temperature of rods is 175°C, determine the temperature at their center. Q11: Consider a homogeneous spherical piece of radioactive material of radius ro =0.04 m that is generating heat at a constant rate of g'= 4 x 10' w/m. The heat generated is dissipated to the environment steadily. The outer surface of the sphere is maintained at a uniform temperature of 80°C and the thermal conductivity of the sphere is k = 15 W/m "C. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the sphere, (b) obtain a relation for the variation of temperature in the sphere by solving the differential equation, and (c) determine the temperature at the center of the sphere. Q12: Consider a large 3-cm-thick stainless steel plate (k =15.1 W/m- C) in which heat is generated uniformly at a rate of 5 x10° W/m?. Both sides of the plate are exposed to an environment at 30°C with a heat transfer coefficient of 60 W/m² . °C. Explain where in the plate the highest and the lowest temperatures will occur, and determine their values. Q13: Consider a large 5-cm-thick brass plate (k = 111 W/m - C) in which heat is generated uniformly at a rate of 2 x 10 w/m. One side of the plate is insulated while the other side is exposed to an environment at 25°C with a heat transfer coefficient of 44 W/m2. "C. Explain where in the plate the highest and the lowest temperatures will occur, and determine their values. Q14: A 6-m-long 2-kW electrical resistance wire is made of 0.2-cm-diameter stainless steel (k = 15.1 W/m "C). The resistance wire operates in an environment at 30°C with a heat transfer coefficient of 140 W/m? . "C at the outer surface. Determine 1) The surface temperature of the wire. 2) The center temperature of the wire. Q15: Consider a 1.5-m-high and 0.6-m-wide plate whose thickness is 0.15 m. One side of the plate is maintained at a constant temperature of 500 K while the other side is maintained at 350 K. The thermal conductivity of the plate can be assumed to vary linearly in that temperature range as: k(T) = k( 1 + B7) where ko = 25 w/m Kand B = 8.7 x 10 * K'. Disregarding the edge effects and assuming steady one dimensional heat transfer, determine the rate of heat conduction through the plate. Answer: 30,800 w Q16: In a nuclear reactor, heat is generated in 1-cm diameter cylindrical uranium fuel rods at a rate of 4 x10 W/m. Determine the temperature difference between the center and the surface of the fuel rod. Answer: 9.0°C Q17: Consider a 20-cm-thick large concrete plane wall (k = 0.77 W/m C) subjected to convection on both sides with T1 = 27°C and h1 = 5 W/m? . "C on the inside, and T2 = 8°C and h2 = 12 W/m? . °C on the outside. Assuming constant thermal conductivity with no heat generation and negligible radiation, (a) express the differential equations and the boundary conditions for steady one- dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the temperatures at the inner and outer surfaces of the wall. Q18: Heat is generated uniformly at a rate of 2.6 x10 W/m2 in a spherical ball (k = 45 W/m C) of diameter 30 cm. The ball is exposed to iced-water at 0°C with a heat transfer coefficient of 1200 W/m? . "C. Determine the temperatures at the center and the surface of the ball.
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