Write the heat equation for each of the following cases:
a. A wall, steady state, stationary, one-dimensional, incompressible and no energy generation.
b. A wall, transient, stationary, one-dimensional, incompressible, constant k with energy generation.
c. A cylinder, steady state, stationary, two-dimensional (radial and axial), constant k, incompressible, with no energy generation.
d. A wire moving through a furnace with constant velocity, steady state, one-dimensional (axial), incompressible, constant k and no energy generation.
e. A sphere, transient, stationary, one-dimensional (radial), incompressible, constant k with energy generation.