Question Statement:
Using Plank's equation for freezing a flat slab of food of thickness $a = 0.04\text{ m}$ ($P = 1/2, R = 1/8$): $t_f = \frac{\rho L}{(T_f - T_a)} \left[\frac{P a}{h} + \frac{R a^2}{k}\right]$. If latent heat per unit volume $\rho L = 2.8 \times 10^8\text{ J/m}^3$, temperature difference $(T_f - T_a) = 20^\circ\text{C}$, heat transfer coefficient $h = 25\text{ W/(m}^2\cdot\text{K)}$, and frozen thermal conductivity $k = 1.6\text{ W/(m}\cdot\text{K)}$, then $\frac{P a}{h} = \frac{0.5 \times 0.04}{25} = 0.0008$, and $\frac{R a^2}{k} = \frac{0.125 \times 0.0016}{1.6} = 0.000125$. The freezing time in hours is: ($t_f = \frac{2.8 \times 10^8}{20} [0.000925] = 14 \times 10^6 \times 0.000925 = 12,950\text{ s}$)