On half-space solutions of a modified heat equation
where e is the internal energy (per unit volume), q the heat flux vector, r the heat supply (per unit volume), v the entropy (per unit volume), <p the conductive temperature, and 6 the thermodynamic temperature. They [8] also proved that in general the two temperatures <p and 6 are equal. Subsequently, Chen and Gurtin [2] formulated a theory of materials in which the two temperatures were unequal. They showed that for an isotropic material the linearized version of the energy equation takes the form c<p = kA<p -fctA<p r (1)