Some unsteady diffusion and absorption problems

Specific problems of the diffusion type, focusing on the absorption of heat (or matter) at one or more boundary surfaces after its release within the adjacent medium at a localized source, are considered, and the measures of absorption or outflow during arbitrary intervals of time are directly expressed in terms of auxiliary temperature/matter distributions with given sources on the pertinent surfaces. Detailed applications of these reciprocal relations are presented, as is a brief analysis that includes some nonlinear or convective aspects in the basic diffusion equations.