A solid object is to be cooled by submerging it in a quiescent fluid, and the associated free convection coefficient is given by h = C∆T1/4, where C is a constant and ∆T = T – Tx.

(a) Invoking the lumped capacitance approximation, obtain an expression for the time required for the object to cool from an initial temperature Ti to a final temperature Tf'

(b) Consider a highly polished, 150-mm square aluminum alloy (2024) plate of 5-mm thickness, initial1y 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, ho. Evaluate h" from an appropriate correlation based on an average surface temperature of T = (Ti + Tf)/2.