The Heat and Diffusion equations are fundamentally the same mathematical construct, classified as parabolic partial differential equations (PDEs). The distinction arises in their applications and the sign of the coefficient k in the second derivative of u with respect to x. When k > 0, the equation describes heat flow, while k < 0 indicates diffusion processes. Understanding these nuances is crucial for applying the correct model in physical scenarios.
PREREQUISITESMathematicians, physicists, and engineers involved in modeling heat transfer and diffusion processes will benefit from this discussion.
HallsofIvy said:There is no difference. They are just different names, referring to different applications, for the same type of equation: more formally, a parabolic PDE.