Steel balls 10 mm in diameter are annealed by heating to 1,150 K and then slowly cooling to 450 K in an air environment for which T∞ = 325 K + at, where a = 0.1875 K/s and h = 25 W/m2 · K. Assuming the properties of the steel to be k = 40 W/m · K, ρ = 7,800 kg/m3, and c = 600 J/kg · K, estimate the time required for the cooling process.
Steel balls 10 mm in diameter are annealed by heating to 1,150 K and then slowly cooling to 450 K in an air environment for which T∞ = 325 K + at, where a = 0.1875 K/s and h = 25 W/m2 · K. Assuming the properties of the steel to be k = 40 W/m · K, ρ = 7,800 kg/m3, and c = 600 J/kg · K, estimate the time required for the cooling process.
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.36P
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Steel balls 10 mm in diameter are annealed by heating to 1,150 K and then slowly cooling to 450 K in an air environment for which T∞ = 325 K + at, where a = 0.1875 K/s and h = 25 W/m2 · K. Assuming the properties of the steel to be k = 40 W/m · K, ρ = 7,800 kg/m3, and c = 600 J/kg · K, estimate the time required for the cooling process.
Find an expression for the ball temperature as a function of time T(t), and plot the ball temperature for 0 ≤ t ≤ 1 h and ambient temperature.
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