Chapter 5, Problem 5.33P

As noted in Problem 5.3, microwave ovens operate by rapidly aligning and reversing water molecules within the food. resulting in volumetric energy generation and, in turn. cooking of the food. When the food is initially frozen. however. the water molecules do not readily oscillate in response to the microwaves, and the volumetric generation rates are between one and two orders of magnitude lower than if the water were in liquid form. (Microwave power that is not absorbed in the food is reflected back to the microwave generator, where it must be dissipated in the form of heat to prevent damage to the generator.)

1. Consider a frozen, 1-kg spherical piece of ground beef at an initial temperature of $T_i=-20°\text{C}$ placed in a microwave oven with $T_{\infty }=30°\text{C}$ and $h=15{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ Determine how long it will take the beef to reach a uniform temperature of $T=0°\text{C,}$ with all the water in the form of ice. Assume the properties of the beef are the same as ice. and assume $\text{3\%}$ of the oven power $\left(P=1\text{kW}\text{total}\right)$ is absorbed in the food.
2. After all the ice is converted to liquid. determine how long it will take to heat the beef to $T_f=80°\text{C}$ if $\text{95\%}$ of the oven power is absorbed in the food. Assume the properties of the beef are the same as liquid water.
3. When thawing food in microwave ovens, one may observe that some of the food may still be frozen while other parts of the food are overcooked.

Explain why this occurs. Explain why most microwave ovens have thaw cycles that are associated with very low oven powers.