Auxiliary functions for non-stationary one-dimensional diffusion under forced convection - Basic properties and applications

An investigation is conducted of a class of functions, called 'Omega functions'. The Omega functions can be used as terms in the series solution of a diffusion equation for which the source function is given as a delta distribution and a MacLaurin expansion. A diffusion equation with a radiation term can be solved immediately in terms of Omega functions. Applications of the considered approaches are also discussed. Attention is given to the definition of Omega functions, the representation of Omega functions as a series of even-numbered repeated integrals of the (complementary) error function, a recurrence relation, the differential equation obtained with the aid of the recurrence relation, a generating function, asymptotic behavior for large t, the Laplace transform of an Omega function, a generating function for even-numbered repeated integrals of the (complementary) error function, diffusion under forced convection, diffusion under force convection with a removal process, and diffusion without a removal processes and without convection.