A generalized relation between the local values of temperature and the corresponding heat flux in a one-dimensional semi-infinite domain with the moving boundary

Abstract

The paper presents generalized relation between the local values of temperature and the corresponding heat flux in a onedimensional

semi-infinite domain with the moving boundary. The generalized relation between the local values of temperature

and the corresponding heat flux has been achieved by the use of a novel technique that involves generalized derivatives (in particular,

derivatives of non-integer orders). Confluent hyper-geometric 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 relation is written in the

integral form and provides a relationship between the local values of the temperature and heat flux.