4-26 Steel rods (p = 7832 kg/m³, c, = 434 J/kg -K, and k = 63.9W/m-K) are heated in a furnace to 850°C and then quenched in a water bath at 50°C for a period of 40 s 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.
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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.3-68 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 40°C by injecting hot steam into it. The two ends of the kiln, 4 m x 5 m in size, are made of a 3-mm-thick sheet metal covered with 2-cm-thick Styrofoam (k = 0.033 W/m K). The convection heat transfer coefficients on the inner and the outer surfaces of the kiln are 3000 W/m2-K and 25 W/m2-K, respectively. Disregarding any heat loss through the floor, determine the rate of heat loss from the kiln when the ambient air is at -4°C. FIGURE P3-68 Tout-4°C 40 m Tin=40°C 4 m 20 cm 5 m
- 4-38 Carbon steel balls (p = 7833 kg/m2, k = 54 W/m K, c = 0.465 kJ/kg°C, and a 1.474 - 10-6 m2/s) 8 mm in diameter are annealed by heating them first to 900°C in a furnace and then page 300 allowing them to cool slowly to 100°C in ambient air at 35°C. If the average heat transfer coefficient is 75 W/m2-K, determine how long the annealing process will take. If 2500 balls are to be annealed per hour, determine the total rate of heat transfer from the balls to the ambient air. FIGURE P4-38 Air, 35°C Furnace Steel ball 100C 900°CFor heat transfer purposes, an egg can be considered to be a 5.5-cm-diameter sphere having the properties of water. An egg that is initially at 8°C is dropped into the boiling water at 86°C. The heat transfer coefficient at the surface of the egg is estimated to be 800 W/m2-K. 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. Solve this problem using analytical one-term approximation method (not the Heisler charts). The length of/time for the egg to be kept in boiling water is determined to be min.3-78E Steam exiting the turbine of a steam power plant at 100°F is to be condensed in a large condenser by cooling water flowing through copper pipes (k = 223 Btu/h ft. °F) of inner diameter 0.4 in. and outer diameter 0.6 in. at an average temperature of 70°F. The heat of vaporization of water at 100°F is 1037 Btu/lbm. The heat transfer coefficients are 1500 Btu/h ft² °F on the steam side and 35 Btu/h ft² °F on the water side. Determine the length of the tube required to con- dense steam at a rate of 120 lbm/h. Answer: 1148 ft Steam, 100°F 120 lbm/h Liquid water FIGURE P3-78E Cooling water
- -3-A piece of copper as shown in figure is initially at 150 C when suddenly immersed in an environment at 38 C. Determine the Biot number and find the piece temperature after 1 minute, a) if the environment is water with h= 50 W/m2 K b) if the environment is air with h= 12 W/m2 K Data: k = 374 W/m K, c, 0.381 kJ/kg K, and p= 8938 kg/m3. Answ(a- Bi=0.0008913 ; T=136.1C b- Bi=0.0002139 ; T=146.5C). 4 cm 4 cm4- Carbon steel balls 8 mm in diameter are annealed by heating them first to 900°C in a furnace and then allowing them to cool slowly to 100°C in ambient air at 35°C. If the average heat transfer coefficient is 75 W/m -°C, determine how long the annealing process will take. If 2500 balls are to be annealed per hour Given: Carbon steel [k = 54 W/m.°C, p = 7833 kg/m, and C,= 0.465 kJ/kg. °C. and a= 1.474x 10* m²/s] Air, 35°C Fumace Steel ball 100°C 900°CSolve this with diagram: An engine cover is made from 1 cm thick stainless steel plate (k = 14 W/m K). Air on the inside of the engine cover is heated to 340°C with a heat transfer coefficient of 7 W/m2K. Outside of the engine coverthe ambient air has a temperature of 70°C. If oil was spilled on the outside of the engine cover (ambient side), it could ignite if the surface temperature were to exceed 200°C. In this configuration, would spilled oil ignite? Use calculations to justify your answer. If a 4 mm thermal coating (k = 1.1 W/m K) was applied tothe outside of the engine, what would the outside temperature of the engine cover be reduced to? Solve it with resistors method
- Solve this with diagram: An engine cover is made from 1 cm thick stainless steel plate (k = 14 W/m K). Air on the inside of the engine cover is heated to 340°C with a heat transfer coefficient of 7 W/m2K. Outside of the engine coverthe ambient air has a temperature of 70°C. If oil was spilled on the outside of the engine cover (ambient side), it could ignite if the surface temperature were to exceed 200°C. In this configuration, would spilled oil ignite? Use calculations to justify your answer. If a 4 mm thermal coating (k = 1.1 W/m K) was applied tothe outside of the engine, what would the outside temperature of the engine cover be reduced to?A long 3-mm diameter rod of steel (ρ = 7840 kg/m3, c = 460 J/kgK, k = 43 W/mK)has a uniform initial temperature of 650C. The rod is then suddenly immersed in alarge container of 25C water. The hot rod causes the water immediately surroundingthe rod to boil, giving rise to a heat transfer coefficient of 5600 W/m2K. The boilingstops when the rod reaches a temperature of 100C, at which time the heat transfercoefficient becomes 750 W/m2K. Find the time period during which boiling occursand the total time required for the rod to reach a temperature of 40C. Use acharacteristic length for this problem.A 30-cm-radius metallic sphere is having thermal conductivity of k = 100. overall density of W 7 mk p = 1500- kg m² and heat capacity of C₂ = 3000 The sphere is initially at a uniform temperature of kgk CO T₁ = 20°C and is dropped into boiling water at T = 90°C. The convective heat transfer coefficient is assumed to be only h = 50; W m²K Using lump model, compute the temperature of the sphere after t = 1200 seconds. In solving this problem, please use and show the following steps (do not use EES) 1. Compute the volume and surface area 2. Compute the characteristic length Lc = k p Cp h Lc 4. Compute the Biot number Bi k 5. Calculate the Fourier number Fo= (at)/Lc² 6. Calculate the excess temperature using 0 = exp(-Bi * Fo) T-Too 7. Compute the target temperature T using 0 = Ti-Too 3. Compute the diffusivity a = = the sphere Vol Vol As == 3 r³ and А¸ = 4πr²