A non-simple heat-conducting fluid

Abstract

The constitutive quantities in thermodynamic theories of fluids are usually assumed to be given by functionals of the histories of density O, velocity v~ and temperature & In simple theories one tends to regard the constitutive quantities at a place x~ and time t as functions of O, v~, ~ and of the derivatives of v~ and at that place and time. Derivatives of O are never considered as variables although there does not seem to be an a priori reason for their omission. After this remark, it becomes an interesting problem to develop a theory where the constitutive quantities depend on the rate of density and on its gradient as well as on the other variables mentioned above. Such a theory is developed in this paper where, to make things simple, I disregard the derivatives of v~ as variables. The simple assumption that the heat flux vanish, if the temperature gradient does, will turn out to be sufficient to remove derivatives of e from all constitutive relations except the one for the pressure. Thus, apart from the expressions involving the pressure, the theory reduces to the theory of simple heat-conducting fluids presented in [1 ], and, in particular, the concept of the coldness is still valid in this more complex theory.