A solid ball is dropped into a water container for cooling. The ball has a diameter of D = 4 mm and sinks at a constant terminal velocity of Ut = 0.01 m/s. The thermophysical properties of the solid ball are: density ρ = 8000 kg/m3, thermal conductivity k = 200 W/m · K, and specific heat c = 1000 J/kg · K. The thermophysical properties of the water are: density ρw = 1000 kg/m3, kinematic viscosity νw = 10^(−6) m^(2)/s, thermal conductivity kw = 0.6 W/m · K, and Prandtl number Pr = 7. The vertical distance for the ball to sink from the initial fully submerged depth to the bottom of the container is H = 0.1 m. The initial temperature of the ball is T0 = 800 K, and the water temperature is T∞ = 300 K. Given correlations: For the convection heat transfer caused by flow past a sphere, the averaged Nusselt number is NuD = 2 + 0.6*(Re^(1/2))*(Pr^(1/3)) Questions: (1) Determine the averaged convection heat transfer coefficient h, and check if the Lumped Capacitance Method can be used to solve this problem. (2) Determine the temperature of the ball when it just reaches the bottom, TH.
A solid ball is dropped into a water container for cooling. The ball has a diameter of D = 4 mm and sinks at a constant terminal velocity of Ut = 0.01 m/s. The thermophysical properties of the solid ball are: density ρ = 8000 kg/m3, thermal conductivity k = 200 W/m · K, and specific heat c = 1000 J/kg · K. The thermophysical properties of the water are: density ρw = 1000 kg/m3, kinematic viscosity νw = 10^(−6) m^(2)/s, thermal conductivity kw = 0.6 W/m · K, and Prandtl number Pr = 7. The vertical distance for the ball to sink from the initial fully submerged depth to the bottom of the container is H = 0.1 m. The initial temperature of the ball is T0 = 800 K, and the water temperature is T∞ = 300 K.
Given correlations: For the convection heat transfer caused by flow past a sphere, the averaged Nusselt number is NuD = 2 + 0.6*(Re^(1/2))*(Pr^(1/3))
Questions:
(1) Determine the averaged convection heat transfer coefficient h, and check if the Lumped
Capacitance Method can be used to solve this problem.
(2) Determine the temperature of the ball when it just reaches the bottom, TH.
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