A 2-cm diameter copper sphere with a thermocouple at its center is suddenly imme

Question

A 2-cm diameter copper sphere with a thermocouple at its center is suddenly immersed in liquid nitrogen contained in a Dewar flask. The temperature response is determined using a digital data acquisition system that records the temperature every 0.05 s. The maximum rate of temperature change dT/dt is found to occur when T = 92.5 K, with a value of 19.8 K/s. The saturation temperature of nitrogen at 1 atm pressure is 77.4 K. Take ? = 8930 kg/m3, c = 235 J/(kg K), and k = 450 W/(m K) for copper at 92.5 K. 1) Using the lumped thermal capacity model, determine the corresponding heat transfer coefficient. Check the Biot number to ensure that the model is valid.

Explanation / Answer

Volume of sphere = 4.188*10^-6 surface area = 1.2566*10^-3 from lumped parameter analysis, h*A*difference in temp. = density*volume *thermal capacity*rate of rise in temp. h * 1.2566*10^-3* (92.5-77.4) = 8930*235*4.188*10^-6 * 19.8 h = 9171 W/m^2 K

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