Preservation of Food

A food slab of thickness $a = 0.05\text{ m}$ is frozen from both faces in a plate freezer operating at $-30^\circ\text{C}$. Initial freezing temperature is $-1.5^\circ\text{C}$ (temperature difference $\Delta T = 28.5^\circ\text{C}$). The food material has density $\rho = 1050\text{ kg/m}^3$, latent heat $\lambda = 250\text{ kJ/kg}$, thermal conductivity $k = 1.50\text{ W/(m}\cdot\text{K)}$, and convective coefficient $h = 50\text{ W/(m}^2\cdot\text{K)}$. Using Planck's equation with shape factors $P = 1/2$ and $R = 1/8$ ($t_f = \frac{\rho \lambda}{\Delta T} \left[\frac{P a}{h} + \frac{R a^2}{k}\right]$), the freezing time in hours is ________ (round off to 2 decimal places).