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A metal sphere 25 mm in diameter was heated to 95C, and
Chapter , Problem 7.56(choose chapter or problem)
A metal sphere 25 mm in diameter was heated to \(95^{\circ} \mathrm{C}\), and then suspended in air at \(22^{\circ} \mathrm{C}\). The mass density of the metal is \(7920 \mathrm{~kg} / \mathrm{m}^{3}\), its specific heat at \(30^{\circ} \mathrm{C}\) is \(c_{p}=500 \mathrm{~J} /\left(\mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\), and its thermal conductivity at \(30^{\circ} \mathrm{C}\) is \(400 \mathrm{~W} /\left(\mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right)\). The following sphere temperature data were measured as the sphere cooled.
a. Assume that the sphere’s heat loss rate is due entirely to convection. Estimate the convection coefficient h.
b. Compute the Biot number and discuss the accuracy of the lumped-parameter model used in part (a).
c. Discuss whether some of the heat loss rate could be due to radiation. Give a numerical reason for your answer.
Questions & Answers
QUESTION:
A metal sphere 25 mm in diameter was heated to \(95^{\circ} \mathrm{C}\), and then suspended in air at \(22^{\circ} \mathrm{C}\). The mass density of the metal is \(7920 \mathrm{~kg} / \mathrm{m}^{3}\), its specific heat at \(30^{\circ} \mathrm{C}\) is \(c_{p}=500 \mathrm{~J} /\left(\mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\), and its thermal conductivity at \(30^{\circ} \mathrm{C}\) is \(400 \mathrm{~W} /\left(\mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right)\). The following sphere temperature data were measured as the sphere cooled.
a. Assume that the sphere’s heat loss rate is due entirely to convection. Estimate the convection coefficient h.
b. Compute the Biot number and discuss the accuracy of the lumped-parameter model used in part (a).
c. Discuss whether some of the heat loss rate could be due to radiation. Give a numerical reason for your answer.
ANSWER:Step 1 of 8
(a)
The Biot number, defined as
Here 
For a metal sphere of radius 
Substitute 
