A nuclear fuel element has the form of a plate 6 mm thick sandwiched between two stainless steel containing sheets. The fuel generates heat at a uniform rate of 0.18 x 106 kW/n3 and has a thermal conductivit of 0.002 kW/mK. The element is cooled by water at 50°C and the heat transfer coefficient on one side is 0.6 kW/m2K and on the other is 1.0 kW/m2K. The contact resistance between the fuel and the stainless steel is equivalent to a transfer coefficient of 20 kW/m2K. Assuming the resistance of the stainless steel to be negligible, determine the position and magnitude of the maximum temperature and the heat flux on each side of the element.

A nuclear fuel element has the form of a plate 6 mm thick sandwiched between two stainless steel containing sheets. The fuel generates heat at a uniform rate of 0.18 x 106 kW/n3 and has a thermal conductivit of 0.002 kW/mK. The element is cooled by water at 50°C and the heat transfer coefficient on one side is 0.6 kW/m2K and on the other is 1.0 kW/m2K. The contact resistance between the fuel and the stainless steel is equivalent to a transfer coefficient of 20 kW/m2K. Assuming the resistance of the stainless steel to be negligible, determine the position and magnitude of the maximum temperature and the heat flux on each side of the element.

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.

Chapter3: Transient Heat Conduction

Section: Chapter Questions

Problem 3.3P

See similar textbooks

Similar questions

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?
The tip of a soldering iron consists of a 0.6-cm- diameter copper rod, 7.6 cm long. If the tip must be 204C, what are the required minimum temperature of the base and the heat flow, in watts, into the base? Assume that h=22.7W/m2KandTair=21C.
A cylindrical liquid oxygen (LOX) tank has a diameter of 1.22 m, a length of 6.1 m, and hemispherical ends. The boiling point of LOX is -179.4C. An insulation is sought that will reduce the boil-off rate in the steady state to no more than 11.3 kg/h. The heat of vaporization of LOX is 214 kJ/kg. If the thickness of this insulation is to be no more than 7.5 cm, what would the value of its thermal conductivity have to be?
A welding heat source is capable of transferring 160 kJ/min to the surface of a metal part. The heated area is approximately circular, and the heat intensity decreases with increasing radius as follows: 50% of the power is transferred within a circle of diameter = 0.25 cm and 75% is transferred within a concentric circle of diameter = 0.625 cm. What are the power densities in (a) the 0.25 cm diameter inner circle and (b) the 0.625 cm diameter ring that lies around the inner circle? (c) Are these power densities sufficient for melting metal?
the outer surface is at 350°C, then the design A plane wall has a thermal conductivity of 1.15 W/mK. If the inner surface is at 1100°C and 1.15 W/mK. If the inner surface is at 1100°Cand the outer surface is at 350°C, then the desion thickness (in meter) of the wall to maintain a steady heat flux of 2500 W/m2 should be
A piece of chromium steel of length 7.4 cm (density = 8780 kg/m³, K = 50 W/m.K, and Cp = 200 j/kg.K) with mass 1.27 kg, is rolled into a solid cylinder with the same length and heated to a temperature of 600 C and quenched in oi at 36 C. You may take the convective heat rate coefficient between the oil and the cylinder at 280 W/m².K. a) Show that the lumped capacitance system analysis is applicable by calculating the Bi Number b) Find the temperature of the cylinder after 4 min. c) Find the total energy loss during this period. The temperature of the cylinder after 4 min is: The Bi Number is: The total energy loss during this 4 min period is: Choose Choose Choose
b. Consider a 1000-W iron whose base plate is made of 0.005-m-thick aluminum alloy 195, Cast. The base plate has a surface area of 0.03 m?. Initially, the iron is in thermal equilibrium with the ambient air at 22 °C. Taking the heat transfer coefficient at the surface of the base plate to be 12 w/m²K and assuming 80 percent of the heat generated in the resistance wires is transferred to the plate, i. determine how long it will take for the plate temperature to reach 150 °C. Is it realistic to assume the plate temperature to be uniform at all times? ii. Air 22°C 1000 W iron
Blowtorch is used to connect the two pipes together. Length of the pipe section shown is 150 cm with an inner diameter of 85 cm. The thickness of the pipe wall is 4 mm. The conductivity of the pipe section is 167 W/m^2K. Environment has a temperature of 30 C and convective heat transfer coefficient of 28 WI(mC), find the required heat transfer to join the pipe sections at 220 C? HINT: Assume that the welding section is the base plate and the pipe is 1D extended surface (fin) symmetric about the torch melting line. Heat transfer happens by conduction along the pipe thickness in horizontal direction and by convection to the environment. Length thickness Torch melting line
An exothermic chemical reaction takes place in a 20 cm thick slab and the energy generation rate per unit volume is 1 x 106 W/m³. The steady-state heat transfer rate into the slab at the left-hand side, i.e., at x = 0, is 280 W. Calculate the heat transfer rate to the surroundings from the right- hand side of the slab, i.e., at x = L. The surface area of each face is 40 cm². (1080 W)
A vertical furnace wall is made-up on an inner wall of firebrick 20 cm thick followed by insulating brick 15 cm thick and an outer wall of steel 1 cm thick. The surface temperature of the wall adjacent to the combustion chamber is 1200oC while that of the outer surface of steel is 50oC. The thermal conductivities of the wall material in W/m-K are firebrick, 10; insulating brick, 0.26; and steel, 45; neglecting film resistances and contact resistance of joints, determine the percent of the total maintenance due to insulating brick.
"Consider a heat engine with a piston chamber that has a diameter of 30 mm, a cold reservoir at 285 K and hot reservoir at 350 K. It is also equipped with a metal can cylinder that has a volume of 0.0002 m3. What is the total volume of air in the system if the metal can cylinder is in the hot reservoir and the measured pressure and height of the piston are 103850 Pa and 60 mm, respectively?" O 4.24x10-5 m3 O 4.25x10-2 m3 O 2,42x10-4 m3 O 3.70x10-4 m3
1. A small metal building is to be constructed of corrugated steel sheet walls with a total wall surface area of about 300 m². The air conditioner consumes about 1 kW of electricity for every 4 kW of cooling supplied and two wall construction are to be compared on the basis of cooling costs. Assume that electricity costs S0.15/kWh. Determine the electrical energy savings per week of using 260 mm of fiberglass batt insulation to the steel sheet wall (U-0.17 W/m² "C) instead of 159 mm of fiberglass insulation (U-0.31 W/m² °C) assuming an overall temperature difference of 20 °C across the wall.