Question $3($Answer: $3\mathrm{.}98$ BTU$/($h $*f{t}^2$ F$))$

In a meat processing plant, $1-$in thick steaks initially at $75F$ are to be cooled in the racks of a large refrigerator that is maintained at $5F.$ The steaks are placed close to each other, so that heat transfer from the $1-$in$-$thick edges is negligible $($consider $1-$D heat transfer through the thickness of the steaks$).$ The entire steak is to be cooled below $45F,$ but its temperature is not to drop below $35F$ at any point during refrigeration to avoid frostbite. The convective heat transfer coefficient and thus the rate of heat transfer from the steak can be controlled by varying the speed of a circulating fan inside. Determine the heat transfer coefficient $h$ that will enable you to meet both temperature constraints while keeping the refrigeration time to a minimum. The steak can be treated as a homogeneous layer having the properties $=74\mathrm{.}9lb\frac{m}{f}{t}^3,C_P=0\mathrm{.}98BT\frac{U}{lbm*F},k=0\mathrm{.}26BT\frac{U}{h*ft*F}$ and $=0\mathrm{.}0035f\frac{t^2}{h}.$ HINT: Write two equations, one for the location of the maximum temperature and one for the location of the minimum temperature. To optimize the solution, those two temperature must be reach at the same time...