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A solid object is to be cooled by submerging it in a quiescent fluid, and the associated free convection coefficient is given by , where C is a constant and ∆T = T - T_{∞}.
(a) Using the results of Section 5.3.3, obtain an expression for the time required for the object to cool from an initial temperature T_{i} to a final temperature T_{f}.
(b) Consider a highly polished, 150-mm square aluminum alloy (2024) plate of 5-mm thickness, initially at 225°C, and suspended in ambient air at 25°C. Using the appropriate approximate correlation from Problem 9.11, determine the time required for the plate to reach 80°C.
(c) Plot the temperature–time history obtained from part (b) and compare with the results from a lumped capacitance analysis using a constant free convection coefficient, _{o}. Evaluate _{o} from an appropriate correlation based on an average surface temperature of
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