On the temperature of water flowing through fractures

Fluids flowing through fractures in impermeable rock exchange heat with the surrounding medium. The fundamental equations governing the transport of heat in such systems are given. Solutions are derived for the case of constant mass flow and the fluid entering the fractures with a temperature that is a sinusoidal function of time. The rock is assumed to be a homogeneous and isotropic conductor. Approximate solutions are derived for the case in which the temperature at the intake is an arbitrary function of time. The case involving weak oscillations in the mass flow is treated on the basis of a perturbation method. Finally, some of the solutions derived are extended to the case of the laminated solid where the fluid flows between the laminas.