In an annealing process, a 50-mm-thick stainless steel plate (ρ = 8238 kg/m3, cp = 468 J/kg⋅K, k = 13.4 W/m⋅K, and α = 3.48×10−6 m2/s) was reheated in a furnace from an initial uniform temperature of 230°C. The ambient temperature inside the furnace is uniform at 1000°C, and the convection heat transfer coefficient is 215 W/m2⋅K. If the entire stainless steel plate is to be heated to at least 620°C, determine the time that the plate should be heated in the furnace using the analytical one-term approximation method. The time that the plate should be heated in the furnace is

In an annealing process, a 50-mm-thick stainless steel plate (ρ = 8238 kg/m3, cp = 468 J/kg⋅K, k = 13.4 W/m⋅K, and α = 3.48×10−6 m2/s) was reheated in a furnace from an initial uniform temperature of 230°C. The ambient temperature inside the furnace is uniform at 1000°C, and the convection heat transfer coefficient is 215 W/m2⋅K. If the entire stainless steel plate is to be heated to at least 620°C, determine the time that the plate should be heated in the furnace using the analytical one-term approximation method. The time that the plate should be heated in the furnace is

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.
1.60 Two electric resistance heaters with a 20 cm length and a 2 cm diameter are inserted into a well-insulated 40-L tank of water that is initially at 300 K. If each heater dissipates 500 W, what is the time required for bringing the water temperature in the tank to 340 K? State your assumption for your analysis.
3. A lumped system with a volume of 0.003 m³ and a surface area of 0.08 m² is made of a material with density of 3800 kg/m³, thermal conductivity of 300 W/m K, and specific heat of 200 J/kg K. If the system is exposed to a convection environment with h = 60 W/m2 K, what is the approximate time it will take for this system to reach equilibrium with the environment? Express your answer in minutes.
Determine the time needed to decrease the temperature of a solid cylinder from 40 C to 35 C if the ambient temperature is equal to 31 C. The cylinder has a length equals to 0.9 m and diameter equals to 100 mm. The heat convective coefficient is equal to 1.3 W/m^2.K. The cylinder has a conductivity equals to 2 W/m.K, a density equals to 1200 kg/m^3 and its Cp is equal to 4.700 kJ/kgK. Select one: a. 83325 s O b. 10500s O c. 45360 s O d. 30050 s
1. For heat transfer purposes, an egg can be considered to be a 4-cm diameter sphere having the properties of water. An egg that is initially at 8°C is dropped into boiling water at 100°C. The heat transfer coefficient at the surface of the egg is estimated to be 400 W/m2°C. If the egg is considered cooked when its center temperature reaches 60°C, determine how long the egg should be kept in the boiling water? Assume negligible internal resistance í
Consider a curing kiln whose walls are made of 0.02 m thick concrete with a thermal diffusivity of α = 0.23 × 10−5 m2/s. Initially, the kiln and its walls are in equilibrium with the surroundings at 6°C. Then all the doors are closed and the kiln is heated by steam so that the temperature of the inner surface of the walls is raised to 42°C and the temperature is maintained at that level for 11.5 h. The curing kiln is then opened and exposed to the atmospheric air after the steam flow is turned off. Determine the temperature of the outer surface of the walls at 11.5 h. The temperature of the outer surface of the walls at 11.5 h is
A small copper wire with a diameter of 0.792 mm and initially at 366.5 K is suddenly immersed in a liquid held constant at 311 K. The convection coefficient h = 85.2 W/m2 · K. The physical properties can be assumed constant and are k = 374 W/m · K, cp = 0.389 kJ/kg · K, and ρ = 8890 kg/m3. Determine the time in seconds for the average temperature of the wire to drop to 338.8 K (one-half the initial temperature difference). Do the same but for h=11.36W/m2·K. Forpart(b),calculate the total amount of heat removed for a wire 1.0 m long.
We are testing a thin, transparent film heater that is bonded to the inside of an automobile window made of 3 mm thick glass. The window has a surface area of 0.6 m^2, and the air temperatures inside and outside the car are 20°C and 1°C, respectively. The convective heat transfer coefficients on the inside and outside of the window are 15 W/m^2-K and 25 W/m^2-K, respectively. The thermal conductivity of the glass is 0.5 W/m-K. 1) If the heater dissipates 200 W of heat, what are the temperatures of the inner and outer surfaces of the window? 2) Now, suppose the heater needs to account for radiation exchange with the night sky, in addition to convection. The temperature of the surrounding sky is 253 K, and the emissivity of the external surface of the window is 0.6. Assuming the window is a gray surface, what is the power needed to maintain the inner surface temperature from part (1)? 3) Identify and explain two ways in which the power required for the heater in scenario (2) can be…
4.A steel plate is exposed to solar heat flux of 800 W/m² on one side. The plate is exposed to air at 30°C on both sides. The convection coefficients are 10 W/m²K on the back side and 15 W/m²K on the front. Determine the equilibrium temperature. Neglect radiation loss
Humans are able to control their rates of heat production and heat loss to maintain a nearly constant core temperature of Tc = 37°C under a wide range of environmental conditions. This process is called thermoregulation. From the perspective of calculating heat transfer between a human body and its surroundings, we focus on a layer of skin and fat, with its outer surface exposed to the environment and its inner surface at a temperature slightly less than the core temperature, Ti = 35°C = 308 K. Consider a person with a skin/fat layer of thickness L = 2 mm and effective thermal conductivity k = 0.3 Wm ⋅ K. The person has a surface area A = 1.8 m2 and is dressed in a bathing suit. The emissivity of the skin is ε = 0.95.a). When the person is in still air at T∞ = 308 K, what is the skin surface temperature and rate of heat loss to the environment? Convection heat transfer to the air is characterized by a free convection coefficient of h = 2 W?2 ⋅ Kb). When the person is in water at T∞ =…
Steel rods (p = 7832 kg/m2, cn= 434 J/kg.K, and k = 63.9 W/m-K) are heated in a furnace to 850°C and then quenched in a water bath at 50°C for a period of 55 seconds as part of a hardening process. The convection heat transfer coefficient is 650 W/m2.K. If the steel rods have diameter of 40 mm and length of 2 m, determine their average temperature when they are taken out of the water bath. (Round off the answer to 1 decimal point.) °C
A 0.025-mm-diameter stainless steel wire having K =16 W/m • C is connected to two electrodes. The length of the wire is 80 cm and it is exposed to a convection environment at 20 •C with h = 500 W/m2 • •C. A voltage is impressed on the wire that produces temperatures at each electrode of 200 -C. Determine the total heat lost by the wire in cal/hr.