ABSTRACT
This chapter considers a general class of equations known as parabolic equations, and their solutions. It deals with two physical examples: heat conduction and diffusion. Heat may be defined as the flow of energy through a body due to a difference in temperature. This is a kinetic process at the molecular level and it involves energy transfer due to molecular collisions. Diffusion is a mixing process which occurs when one substance is introduced into a second substance. The introduced quantity, by means of molecular or atomic transport, spreads from locations where its concentration is higher to locations where the concentration is lower. As a Reading Exercise, choose values of parameters in real physical units and estimate how much time it takes to reach equilibrium for different materials and for samples of different size. The chapter focuses on the heat conduction equation because the associated terminology is more concrete and intuitively fruitful than that for diffusion.
