An analytical solution of the generalized equation of energy transport in one-dimensional semi-infinite domains (Q2566893)

Summary: This paper presents an integral solution of a generalized one-dimensional equation of energy transport with a convective term. The solution of the problem is 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 boundary of domain.