Consider the energy equation for the temperature $T(x, t)$ of a fluid in motion.
(a) Review the derivation of the energy equation from section 3 of Chapter 3 when $-\Pi u$ is not negligible and the fluid is Newtonian. Simplify and nondimensionalize the energy equation.
(b) Under various simplifying assumptions, the energy equation can be written
$$
\rho_0 c_p \frac{D}{D t} T(x, t)-\nabla \cdot(k \nabla T(x, t))=0 .
$$
Here $c_p, k$ are the specific heat and thermal conductivity, respectively. Nondimensionalize this simplified energy equation.