Chapter 2, Problem 159P

Consider a spherical reactor of 5-cm diameter operating at steady conditions with a temperature variation that can be expressed in the form of $T(r)=a-b{r}^2,\text{where }a={850}^o\text{C and b = 5 }\times {\text{ 10}}^{\text{5}}{\text{ K/m}}^{\text{2}}$. The reactor is made of material with $\text{c}=200\text{ J/kg}{\text{.}}^{\text{o}}\text{C, k = 40 W/m}{\text{.K, p = 9000 kg/m}}^{\text{3}}$. If the heat generation of the reactor is suddenly set to 9 MW/m³ , determine the time rate of temperature change in the reactor. Is the heat generation of the reactor suddenly increased or decreased to 9 MW/m³ from its steady operating condition?