Abstract
This paper presents an integral solution of the
generalized one-dimensional equation of energy transport
with the convective term.The solution of the problem has been
achieved by the use of a novel technique that involves
generalized derivatives (in particular, derivatives of noninteger
orders). Confluent hypergeometric functions, known as Whittaker's
functions, appear in the course of the solution procedure upon
applying the Laplace transform to the original transport
equation.The analytical solution of the problem is written in
the integral form and provides a relationship between the
local values of the transported property (e.g.,
temperature, mass, momentum, etc.) and its flux.The solution is
valid everywhere within the domain, including the domain boundary.