In a meat processing plant, 10-cm-thick beef slabs (ρ = 1090 kg/m³, c_p = 3.54 kJ/kg·K, k = 0.47 W/m·K, and α = 0.13 × 10^–6 m²/s) initially at 15°C are to be cooled in the racks of a large freezer that is maintained at -12°C. The meat slabs are placed close to each other so that heat transfer from the 10-cm-thick edges is negligible. The entire slab is to be cooled below 5°C, but the temperature of the steak is not

to drop below -1°C anywhere during refrigeration to avoid “frost bite.” The convection 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 us to meet both temperature constraints while keeping the refrigeration time to a minimum.