Heat is not classified as either a longitudinal wave or a transverse wave because it does not propagate as a wave in the traditional sense. Heat is actually a form of energy transfer that occurs due to the random motion of particles at the microscopic level.
When heat is transferred, such as through conduction, convection, or radiation, it does not exhibit the characteristic behavior of a wave. Instead, it is the result of the kinetic energy of particles being transferred from regions of higher temperature to regions of lower temperature.
Longitudinal waves involve the oscillation of particles or disturbances in a medium parallel to the direction of wave propagation. Sound waves are an example of longitudinal waves, where the particles in the medium oscillate back and forth along the direction of the sound wave.
Transverse waves involve oscillations that are perpendicular to the direction of wave propagation. Examples of transverse waves include electromagnetic waves (such as light waves) and waves on a string.
Heat transfer, on the other hand, occurs through the transfer of energy and not through the propagation of oscillations in a medium.