A hot steel ball of 5 mm in diameter initially at 100 oC is left to cool down in air at 20 oC.  Assume a constant convective heat transfer coefficient h = 15 W/m2K through the course of the cooling process. Cp, steel = 0.49 kJ / kg K , k,steel = 45.0 W / m K , rho, steel = 7800 kg/m^3 Cp,air = 1.00 kJ/kg K ; k_air = 0.025 W / m K; rho,air = 1.2 kg/m^3  a) Calculate the rate of convective heat transfer when the steel ball is uniformly at 100 oC.   b) Assuming the steel as a lumped system, find the temperature of the steel ball after 0.5 s.

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

Steel balls (diameter = 21 mm, p = 7833 kg/m , k = 54 W/m•°C, Cp = 0.465 kJ/kg.°C, and a = 1.474x10 m /s) are annealed by heating them first to 870°C in a furnace and then allowing them to cool slowly to 85°C in ambient air at 27°C. What is the total rate of heat %3D transfer from the balls to the ambient air, when 2367 balls are to be annealed per hour (kW)? Select one: A. 11.15 B. 9.12 C. 9.85 D. 8.38 E. 10.50

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