Chapter 2, Problem 2.3P

The shield of a nuclear reactor is idealized by a large 25-cm-thick flat plate having a thermal conductivity of $\text{3}\text{.5 W/}\left(\text{m K}\right)$. Radiation from the interior of the reactor penetrates the shield and there produces heat generation that decreases exponentially from a value of $\text{187}{\text{.6 kW/m}}^{\text{3}}$ at the inner surface to a value of $\text{18}{\text{.76 kW/m}}^{\text{3}}$ at a distance of 12.5 cm from the interior surface. If the exterior surface is kept at 38°C by forced convection, determine the temperature at the inner surface of the field. Hint: First set up the differential equation for a system in which the heat generation rate varies according to $\stackrel{\dot{}}{q}\left(x\right)=\stackrel{\dot{}}{q}\left(0\right)e^{-Cx}$.