6.1. Steel balls 12 mm in diameter are annealed by heating to 1150 K and then slowly cooling to 400 K in an air environment for which T∞=325 K and h = 20 W/m² • K. Assuming the properties of the steel to be k = 40 W/m• K, p = 7800 kg/m³, and c = 600 J/kg • K, estimate the time required for the cooling process.

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- A 40 x 40 cm copper slab # mm thick at a uniform temperature of 250 °C suddenly has its surface temperature lowered 30 °C. Find the time at which the slab temperature becomes 90°C ; p=9000 ke/m’, c=0.38 KJ/kgK, k=370 W/mK and h=00 W/m’K. 2

5.52 Steel is sequentially heated and cooled (annealed) to relieve stresses and to make it less brittle. Consider a 100-mm-thick plate (k = 45 W/m.K, p = 7800 kg/m³, Cp c, = 500 J/kg .K) that is initially at a uniform tempera- ture of 300°C and is heated (on both sides) in a gas-fired furnace for which T = 700°C and h = 500 W/m² K. How long will it take for a minimum temperature of 550°C to be reached in the plate?

Suppose that the 10 cm thick concrete wall of a commercial building measures 30 mby 4 m. The energy impinging on the surface is 700 Wm-2. Under these conditionsthe external air temperature is 25ºC, and the internal and external surfacetemperatures of the concrete wall are 17ºC and 40ºC, respectively.(a) State and briefly describe the three heat transfer mechanisms.[30%](b) Calculate the net amount of thermal energy radiated by the wall.[40%](c) State your assumptions and briefly discuss their effect on the relativesizes of the heat transfer mechanisms.[30%]Data for Question A3.Heat transfer coefficient of air at 25ºC = 5 Wm-2K-1Thermal conductivity of concrete = 1.2 Wm-1K-1Emissivity of concrete = 0.85Stefan’s constant = 5.7 x 10-8 Wm-2K-4

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3.4 Estimate the rate of heat loss due to radiation from a covered pot of water at 95 ° C. How does this compare with the 60 W that is lost due only to convection and conduction losses? What amount of energy input would be needed to maintain the water at its boiling point for 30 minutes? The polished stainless steel pot is cylindrical, 20 cm in diameter and 14 cm high, with a tight-fitting flat cover. The air temperature in the kitchen is about 25 ° C. State any assumptions you make in deriving your estimates

2-1. Temperature Response in Cooling a Wire. 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/m K. The physical properties can be assumed constant and are k =374 W/m K, c, = 0.389 kJ/kg K, and p = 8890 kg/m2. (a) Determine the time in seconds for the average temperature of the wire to drop to 338.8 K (one-half the initial temperature difference). (b) Do the same but for h 11.36 W/m2 K (c) For part (b), calculate the total amount of heat removed for a wire 1.0 m р u (A long. (a) t 5.66 s Ans. the Smou hire is lons asbume Nhere rraolius , here radlius yinder hitu x Chapter 14 Principles of Unsteady-State Heat Transfer

Example: . A steel ball [c-0.46 kJ/kg C, k-35 W/m. C] 5.0 cm in diameter and initially at a uniform temperature of 450°C is suddenly placed in a controlled environment in which the temperature is maintained at 100°C. The convection heat-transfer coefficient is 10 W/m². C. Calculate the time required for the ball to attain a temperature of 150°C. Solution: We anticipate that the lumped-capacity method will apply because of the low value of h and high value of k.We can check by using Equation (3.9): hLc B₁ = k 3 Lc = T 0.025 =-= = 0.00833 A₂ 4mr² 3 3 hle 10-0.00833 B₁ = = = 0.0023 < 0.1 k 35 The lumped system capacitance method is valid and can used. Therefore, may can use equation 3.4: t= pvc In 0₁ hAs 0 92 HEAT TRANSFER t = pvc In pvc Ti-Too hAs T-Too T = 150 °C, p = 7800 kg/m³. Too-100 °C, h=10 w/m².C. T₁-450 °C, c-460 J/kg. "C. pvc In Ti-Too t = hAs T-Too t= Pr³c In Ti-Too h4r² T-T t= 1 In Ti-To pre 3h T-T V -= = 7800+0.025-460 In 3.10 450-100 150-100 = 5818.3 s= 1.62 h 6

Steel balls 12 mm in diameter are annealed by heating to 1100 K and then slowly cooling to 360 K in an air environment for which T. = 325 Kand h = 20 W/m2-K. Assuming the properties of the steel to be k = 40 W/m-K,p = 7800 kg/m, and c = 600 J/kg-K, estimate the time required for the cooling process. The time required for the cooling process isi h.