A long, 150-mm-diameter cylindrical metal (k = 20 W/m-K, p = 7900 kg/m³, cp = 650 J/kg-K) billet is prepared for a manufacturing process by heating it in an oven. The billet has an initial temperature of 100°C and is placed in an oven that is at 800°C with a heat transfer coefficient of 100 W/m²-K. Determine how long the billet should be left in the oven to achieve a minimum temperature of 650°C.

A long, 150-mm-diameter cylindrical metal (k = 20 W/m-K, p = 7900 kg/m³, cp = 650 J/kg-K) billet is prepared for a manufacturing process by heating it in an oven. The billet has an initial temperature of 100°C and is placed in an oven that is at 800°C with a heat transfer coefficient of 100 W/m²-K. Determine how long the billet should be left in the oven to achieve a minimum temperature of 650°C.

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 2.38P: 2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from...

See similar textbooks

Similar questions

A person puts a few apples into the freezer at 15°C cool them quickly for guestswho are about to arrive. Initially, the apples are at a uniform temperature of 20°C,and the heat transfer coefficient on the surfaces is 8 W/m2·K. Treating the apples as9-cm-diameter spheres and taking their properties to be 840 kg/m3, Cp 3.81 kJ/kg·K, k = 0.418 W/m·K, and α =10-7 m2/s, determine the center and surface temperatures of the apples in 1 h. Also, determine the amount of heat transfer from each apple. Solve this problem using analytical one-term approximation method (notthe Heisler charts). Answer: Center: 11.2 ℃, Surface: 2.7 ℃, heat transfer: 17.2 kJ
Consider a 2-m-high electric hot-water heater thathas a diameter of 40 cm and maintains the hot water at 55°C.The tank is located in a small room whose average temperatureis 27°C, and the heat transfer coefficients on the innerand outer surfaces of the heater are 50 and 12 W/m2·K,respectively. The tank is placed in another 46-cm-diametersheet metal tank of negligible thickness, and the spacebetween the two tanks is filled with foam insulation (k =0.03 W/m·K). The thermal resistances of the water tank andthe outer thin sheet metal shell are very small and can be neglected. The price of electricity is $0.08/kWh, and the home owner pays $280 a year for water heating. Determine the fraction of the hot-water energy cost of this household that is due to the heat loss from the tank. Hot-water tank insulation kits consisting of 3-cm-thick fiberglass insulation (k = 0.035 W/m·K) large enough to wrap the entire tank are available in the market for about $30. If such an insulation is installed on…
A 5-m-wide, 4-m-high, and 40-m-long kiln used to cure concrete pipes is made of 20-cm-thick concrete walls and ceiling (k = 0.9 W/m · °K). The kiln is maintained at a surface temperature of 40°C. Determine the rate of heat loss from the kiln when the outside surface temperature is -4°C
Consider a 1.2-m-high and 2-m-wide glass windowwith a thickness of 6 mm, thermal conductivity k = 0.78W/m·K, and emissivity « = 0.9. The room and the wallsthat face the window are maintained at 25°C, and the averagetemperature of the inner surface of the window is measuredto be 5°C. If the temperature of the outdoors is 25°C,determine (a) the convection heat transfer coefficient on theinner surface of the window, (b) the rate of total heat transferthrough the window, and (c) the combined natural convectionand radiation heat transfer coefficient on the outer surface ofthe window. Is it reasonable to neglect the thermal resistanceof the glass in this case?
Consider two identical people each generating 60W of metabolic heat steadily while doing sedentary work anddissipating it by convection and perspiration. The first personis wearing clothes made of 1-mm-thick leather (k =0.159 W/m·K) that covers half of the body while the secondone is wearing clothes made of 1-mm-thick synthetic fabric(k = 0.13 W/m·K) that covers the body completely. Theambient air is at 30°C, the heat transfer coefficient at theouter surface is 15 W/m2·K, and the inner surface temperatureof the clothes can be taken to be 32°C. Treating the bodyof each person as a 25-cm-diameter, 1.7-m-long cylinder,determine the fractions of heat lost from each person by perspiration.
Consider hotdog being cooked in boiling water in a pan. Would the heat transfer be modeled as one-dimensional or two-dimensional? Would the heat transfer be steady or transient? Explain.
A 40-cm-long, 800-W electric resistance heating element with diameter 0.5 cm and surface temperature 120°C is immersed in 75 kg of water initially at 20°C. Determine how long it will take for this heater to raise the water temperature to 80°C. Also, determine the convection heat transfer coefficients at the beginning and at the end of the heating process.
To warm up some milk for a baby, a mother pours milk into a thin-walled cylindrical container whose diameter is 6 cm. The height of the milk in the container is 7 cm. She then places the container into a large pan filled with hot water at 70°C. The milk is stirred constantly, so that its temperature is uniform at all times. If the heat transfer coefficient between the water and the container is 120 W/m2·K, determine how long it will take for the milk to warm up from 3°C to 38°C. Assume the entire surface area of the cylindrical container (including the top and bottom) is in thermal contact with the hot water. Take the properties of the milk to be the same as those of water. Can the milk in this case be treated as a lumped system? Why?
A 6 cm diameter sphere is initially at a temperature of 100C. Later, this sphere was thrown into water at 800C. Calculate how long it will take for the center temperature of the sphere to reach 500C by taking the convection heat transfer coefficient as 80W / m2K. Thermal properties of sphere material: k=0,627 W/moC a=0,151x10-6 m2/s
A 0.8-cm-thick,15-cm-high, and 20-cm-long circuit board houses 100 closely spaced logic chips on one side, each dissipating 0.05 W. The board is impregnated with copper fillings and has an effective thermal conductivity of 20 W/m-K. All the heat generated in the chips is conducted across the circuit board and is dissipated from the back side of the board to the ambient air. Determine the temperature difference between the two sides of the circuit board.
A person is found dead at 5PM in a room whose temperature is 20°C. Thetemperature of the body is measured to be 25°C when found, Modeling thebody as a 30-cm-diameter, 1.70-m-long cylinder and the heat transfer coefficient estimated to be 8 W/m2·K. and using the lumped system analysis as a rough approximation, estimate the time of death of the person.
A hot surface at 100°C is to be cooled by attaching3-cm-long, 0.25-cm-diameter aluminum pin fins (k = 237 W/m·K) to it, with a center-to-center distance of 0.6 cm. Thetemperature of the surrounding medium is 30°C, and the heattransfer coefficient on the surfaces is 35 W/m2·K. Determine therate of heat transfer from the surface for a 1-m * 1-m sectionof the plate. Also determine the overall effectiveness of the fins.