Find the temperature at r = 0.5 cm after 75 seconds of exposure.
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Aluminum balls are heated up to 580 K and then exposed to air at 283 K to cool down with an average heat transfer coefficient of 25 W/m2·K. The balls are 3 cm in diameter. Find the temperature at r = 0.5 cm after 75 seconds of exposure. Is the lumped capacitance an acceptable solution here? [Ans.: 329 K].
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- 8 mm diameter carbon steel (ρ = 7833 kg / m3, k = 54 W / (m K), Cp = 0.466 kJ / (kg K)) ball-shaped balls at 35°C with a temperature of 900°C for annealing heat treatment put in the oven. During this heating process, the coefficient of convection is 40 W / (m2K). The balls are wanted to be brought to a temperature of about 900°C in this oven. When the balls reach 899°C, the heating process is considered sufficient and taken from the oven. a) Find the time required for the balls to reach 899°C. b) After the balls are taken out of the oven, they are left in the ambient temperature and cooled to 100°C. Find the heat released by a ball during this cooling process.A 10 cm outer diameter pipe carrying saturated steam at a temperature of 195C is lagged to 20 cm diameter with magnesia and further lagged with laminated asbestos to 25 cm diameter. The entire pipe is further protected by a layer of canvas. If the temperature under the canvas is 20°C, find the mass of steam condensed in 8 hrs on a 100m length of pipe and interface temperature. Take thermal conductivity of magnesia as 0.07 W/m – K and that of asbestos as 0.082 W/m – k. Neglect the thermal conductivity of the pipe material. The latent heat of steam for given conditions can be taken as 1951 kJ/kg–K.A long wire of diameter D = 2 mm is submerged in an oil bath of temperature T∞ = 23°C. The wire has an electrical resistance per unit length of Re′=0.01 Ω/m. If a current of I = 180 A flows through the wire and the convection coefficient is h = 529 W/m2 · K, what is the steady-state temperature of the wire? From the time the current is applied, how long does it take for the wire to reach a temperature that is within 2°C of the steady-state value? The properties of the wire are ρ = 2,334 kg/m3, c = 537 J/kg · K, and k = 43 W/m · K.
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