Auxiliary functions for nonstationary onedimensional diffusion under forced convection  Basic properties and applications
Abstract
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 evennumbered 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 evennumbered 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.
 Publication:

Zeitschrift Angewandte Mathematik und Mechanik
 Pub Date:
 August 1978
 DOI:
 10.1002/zamm.19780580802
 Bibcode:
 1978ZaMM...58..309K
 Keywords:

 Diffusion Theory;
 Forced Convection;
 Functions (Mathematics);
 One Dimensional Flow;
 Unsteady Flow;
 Asymptotic Series;
 Differential Equations;
 Error Functions;
 Laplace Transformation;
 Maclaurin Series;
 Series Expansion;
 Fluid Mechanics and Heat Transfer