A steel plate having a thickness of 100 mm is suddenly exposed to a hot gas at 1000 °C in a furnace. One surface of the plate is heated while the other surface of the plate can be approximated to be adiabatic. The initial temperature of the steel plate is 20 °C. The thermal conductivity and thermal diffusivity of the steel plate are 34.8 W/m K and 0.555 x 10-5 m²/s respectively. The convective heat-transfer coefficient is 174 W/m² K. a) Determine the time necessary to raise the surface temperature of the steel plate to 500 °C. b) Determine the maximum temperature difference in the cross-section of the steel plate at the time evaluated in part a) above. c) Determine the heat energy transferred to the steel plate per unit wall surface area by the time evaluated in part a) above.

A steel plate having a thickness of 100 mm is suddenly exposed to a hot gas at 1000 °C in a furnace. One surface of the plate is heated while the other surface of the plate can be approximated to be adiabatic. The initial temperature of the steel plate is 20 °C. The thermal conductivity and thermal diffusivity of the steel plate are 34.8 W/m K and 0.555 x 10-5 m²/s respectively. The convective heat-transfer coefficient is 174 W/m² K. a) Determine the time necessary to raise the surface temperature of the steel plate to 500 °C. b) Determine the maximum temperature difference in the cross-section of the steel plate at the time evaluated in part a) above. c) Determine the heat energy transferred to the steel plate per unit wall surface area by the time evaluated in part a) above.

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 2.55P: 2.55 A long, 1-cm-diameter electric copper cable is embedded in the center of a 25-cm-square...

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2.55 A long, 1-cm-diameter electric copper cable is embedded in the center of a 25-cm-square concrete block. If the outside temperature of the concrete is 25oC and the rate of electrical energy dissipation in the cable is 150 W per meter length, determine temperatures at the outer surface and at the center of the cable.
A 10-cm diameter copper ball is to be heated from 80°C to an average temperature of 160°C in 30 minutes. Taking the average density and specific heat of copper in this temperature range to be 8950 kg/m3 and Cp = 0.395 kJ/kg · °C, respectively, determine the average heat flux.
Consider a cold aluminum canned drink that is initially at a uniform temperature of 4°C. The can is 12.5 cm high and has a diameter of 6 cm. If the combined convection/radiation heat transfer coefficient between the can and the surrounding air at 25°C is 10 W/m2 · °C, determine how long it will take for the average temperature of the drink to rise to 15°C. In an effort to slow down the warming of the cold drink, a person puts the can in a perfectly fitting 1-cm-thick cylindrical rubber insulator (k = 0.13 W/m · °C). Now how long will it take for the average temperature of the drink to rise to 15°C? Assume the top of the can is not covered.
During a fire, the trunks of some dry oak trees (k = 0.17 W/m·K and a = 1.28 * 10-7 m2/s) that are initially at a uniform temperature of 30°C are exposed to hot gases at 520°C for a period of 5 h, with a heat transfer coefficient of 65 W/m2·K on the surface. The ignition temperature of the trees is 410°C. Treating the trunks of the trees as long cylindrical rods of diameter 20 cm, determine if these dry trees will ignite as the fire sweeps through them. Solve this problem using analytical one-term approximation method (not the Heisler charts).
In a production facility, 3-cm-thick large brass plates (k =110 W/m·K, ρ= 8530kg/m3, Cp = 380 J/kg·K, and α= 33.9 x10-6 m2/s) that are initially at a uniform temperature of 25°C are heated by passing them through an oven maintained at 700°C. The plates remain in the oven for a period of 10 min. Taking the convection heat transfer coefficient to be h = 80 W/m2·K, determine the surface temperature ofthe plates when they come out of the oven. Solve this problem using analytical oneterm approximation method (not the Heisler charts). Can this problem be solved using lumped system analysis? Justify your answer. Answer: 445 ℃
Consider steady heat transfer between two parallel plates at a constant temperature
A 0.3-cm-thick, 12-cm-high, and 18-cm-long circuit board houses 80 closely spaced logic chips on one side,each dissipating 0.06 W. The board is impregnated with copper fillings and has an effective thermalconductivity of 16 W/m · °C. All the heat generated in the chips is conducted across the circuit board andis dissipated from the back side of the board to the ambient air at 30°C, which is forced to flow over thesurface by a fan at a free-stream velocity of 400 m/min. Determine the temperatures on the two sides ofthe circuit board.
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.
An average man has a body surface area of 1.8 m2 and a skin temperature of 330C. The convective heat transfer coefficient for a clothed person walking in still air is expressed as h= 8.6V0.53 where V is the walking velocity in m/s. Assuming the average surface temperature of the clothed person to be 300C, determine the rate of heat lost by convection from an average man walking in still air at 100C at a walking velocity of 1.2 m/s.
Consider a 1.2-m-high and 2-m-wide double-pane window consisting of two 0.0023-m-thick layers of glass (k = 0.78 W/m·K) separated by a 12-mm-wide vacuum space. Take the convection heat transfer coefficients on the inner and outer surfaces of the window to be h1 = 10 W/m2·K and h2 = 25 W/m2·K, and disregard any heat transfer by radiation. Assume that the space between the two glass layers is evacuated.Determine the steady rate of heat transfer (in W) through the glass window. The room is maintained at 24°C while the temperature of the outdoors is –5°C. (Radiation in outer side of the double-pane window should be disregarded but in the inner part, the only mechanism of heat transfer in vacuum is by radiation. Emissivity for glass is around 1, and the temperature of inner surfaces of the double-pane window should be assumed to be 5 and 15 'C.)
A cylindrical fuel rod of 2 cm in diameter is encased in a concentric tube and cooled by water. The fuel generates heat uniformly at a rate of 150 MW/m3. The convection heat transfer coefficient on the fuel rod is 5000 W/m2∙K, and the average temperature of the cooling water, sufficiently far from the fuel rod, is 70°C. Determine the surface temperature of the fuel rod and discuss whether the value of the given convection heat transfer coefficient on the fuel rod is reasonable.
A pot with a diameter of 20 cm is placed on the stove. The pot is made of stainless plate (k = 15 W / [m ° C]), and contains boiling water at 98 ° C. The bottom of the pan is 0.4 cm thick. The surface temperature in the bottom of the pan in contact with water is 105 ° C. a. If the heat transfer rate through the bottom of the pan is 500 W, determine the temperature of the outside surface of the pan that is exposed to the heating stove. = Answer ° C. b. Determine the convective heat transfer coefficient of boiling water = Answer W / m2 ° C