Chapter 5, Problem 5.16P

A thermal energy storage unit consists of a large rectangular channel. which is well insulated on its outer surface and encloses alternating layers of the storage material and the flow passage.

Each layer of the storage material is an aluminum slab of width $W=0.05\text{m,}$ which is at an initial temperature of $25°\text{C}\text{.}$ Consider conditions for which the storage unit is charged by passing a hot gas through the passages, with the gas temperature and the convection coefficient assumed to have constant values of $T_{\infty }=600°\text{C}$ and $h=100{\text{W/m}}^{\text{2}}\cdot \text{K}$ throughout the channel. How long will it take to achieve $75\%$ of the maximum possible energy storage? What is the temperature of the aluminum at this time?