A cylindrical nuclear fuel rod generates heat at a rate of 71 MW3. It is cooled by fluid at 417 K such that the temperature profile in the rod does not change over time. The heat transfer coefficient between the rod and the fluid is 67 kW/m2K. The rod is 7.5 cm in diameter and has a thermal conductivity of 25 W/mK. Starting from the general conduction equation in cylindrical coordinates, what is the maximum temperature in the rod? Give your answer in Kelvin to the nearest integer.

A cylindrical nuclear fuel rod generates heat at a rate of 71 MW3. It is cooled by fluid at 417 K such that the temperature profile in the rod does not change over time. The heat transfer coefficient between the rod and the fluid is 67 kW/m2K. The rod is 7.5 cm in diameter and has a thermal conductivity of 25 W/mK. Starting from the general conduction equation in cylindrical coordinates, what is the maximum temperature in the rod? Give your answer in Kelvin to the nearest integer.

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.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.19P: 1.19 A cryogenic fluid is stored in a 0.3-m-diameter spherical container is still air. If the...

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1.19 A cryogenic fluid is stored in a 0.3-m-diameter spherical container is still air. If the convection heat transfer coefficient between the outer surface of the container and the air is 6.8 , the temperature of the air is 27°C, and the temperature of the surface of the sphere is –183°C, determine the rate of heat transfer by convection.
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.
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.
Show that the rate of heat conduction per unit length through a long, hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with temperature, is given by qkL=TiTo(rori)/kmA where Ti = temperature at the inner surface To = temperature at the outer surface A=2(rori)/ln(ro/ri)km=ko[1+k(Ti+To)/2]L=lenthofcyclinder
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.
A steam pipe 200 mm in diameter passes through a large basement room. The temperature of the pipe wall is 500C, while that of the ambient air in the room is 20C. Determine the heat transfer rate by convection and radiation per unit length of steam pipe if the emissivity of the pipe surface is 0.8 and the natural convection heat transfer coefficient has been determined to be 10 W/m2K.
Steam at 320°C flows in a stainless steel pipe (k = 15 W/m-°C) whose inner and outer diameters are 5 cm and 5.5 cm, respectively. The pipe is covered with 3-cm-thick glass wool insulation (k = 0.038 W/m-°C). Heat is lost to the surroundings at 5°C by natural convection and radiation, with a combined natural convection and radiation heat transfer coefficient of 15Wm2-°C. Taking the heat transfer coefficient inside the pipe to be 80 W/m2-°C, determine the rate of heat loss from the steam per unit length of the pipe. Also determine the temperature drops across the pipe shell and the insulation.
Steam at 280° C flows in a stainless steel pipe (k = 15 W/m⋅K) whose inner and outer diameters are 5 cm and 5.5 cm, respectively. The pipe is covered with 3-cm-thick glass wool insulation (k = 0.038 W/m⋅K). Heat is lost to the surroundings at 5° C by natural convection and radiation, with a combined natural convection and radiation heat transfer coefficient of 22 W/ m2⋅K.Taking the heat transfer coefficient inside the pipe to be 80 W/ m2⋅K.Determine the rate of heat loss from the steam per unit length of the pipe and Determine the temperature decrease between the inner pipe surface and the outer insulation surface.
A spherical container, with an inner radius r1= 1.4 m and an outer radius r2 = 1.45 m has its inner surface subjected to a uniform heat flux of q1= 7 kW/m2. The outer surface of the container has a temperature T2 = 25°C, and the container wall thermal conductivity is k = 1.5 W/m∙K. Determine the inner surface temperature of the container. (Round your answer to the nearest whole number.) The inner surface temperature is ____°C.
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 · °C) 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·°C. Determine the rate of heat transfer (in W) from the surface for a 1-m × 1-m section of the plate. (Hints: Round down your calculated number of fins. Refer to Table 3-3.)
1 mm thick copper plate (k=386 W/m-c) that are 15 cm x 20 cm in size if the thermal contact conductance on both sides of the copper plate is estimated to be 6,000 W/m-c, determine the % error involved in the total thermal resistance of the plate if the thermal contact conductance are ignored.
Consider a large 5-cm-thick brass plate (k = 111 W/m·°C) in which heat is generated uniformly at a rate of 2×105 W/m3. 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. (Hint: The heat transfer surfaces of the large plane walls considered in our lecture have the same temperature. The formula is slightly adjusted for this question.) Where is the maximum temperature located? What is the value of the maximum temperature in °C?