Heat transfer in theory of relativity

Abstract

The traditional Fourier equation just allows us to study the evolution of temperature in an "undeformable" bar. The search for its relativistic variant is a task which is expected to fail because in relativity there are no undeformable bars. Rigid bodies, in the sense of "as rigid as possible", are deformables. In this work we show how to write in relativity the system of equations necessary to study simultaneously deformation and temperature evolution along a rigid deformable bar. The solutions of the two simultaneous equations is discussed assuming convenient constitutive relations for the material. An application is presented.