In a chicken processing plant, whole chickens averaging 5 lbm each and initially at $65^{\circ} \mathrm{F}$ are to be cooled in the racks of a large refrigerator that is maintained at $5^{\circ} \mathrm{F}$. The entire chicken is to be cooled below $45^{\circ} \mathrm{F}$, but the temperature of the chicken is not to drop below $35^{\circ} \mathrm{F}$ at any point during refrigeration. The convection heat transfer coefficient and thus the rate of heat transfer from the chicken can be controlled by varying the speed of a circulating fan inside. Determine the heat transfer-coefficient that will enable us to meet both temperature constraints while keeping the refrigeration time to a minimum. The chicken can be treated as a homogeneous spherical object having the properties $\rho=74.9 \mathrm{lbm} / \mathrm{ft}^3$, $c_p=0.98 \mathrm{Btu} / \mathrm{lbm} \cdot{ }^{\circ} \mathrm{F}, k=0.26 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft} \cdot{ }^{\circ} \mathrm{F}$, and $\alpha=0.0035$ $\mathrm{ft}^2 / \mathrm{h}$.