Thermal feedback during viscous flow in cylindrical conduits in media with finite thermal properties

Abstract

An explicit finite-difference scheme to compute solutions of the heat equation with a generation term is presented. The heat is produced by viscous dissipation in a fluid where the viscosity is an exponential function of the temperature. Cylindrical conduits of infinite extent and walls of non-zero. finite thermal characteristics are considered. In earlier work. where only the internal impedance of the fluid was considered. thermal instabilities occurred for some combinations of the physical and geometrical parameters of the system. II) this paper we show that the thermal properties of the boundary walls are of great importance to determine the time of occurrence of the instability and that instability can occur even in cases where the isothermal boundary case predicts stability. A mechanism of this type may account for the occurrence of magma intrusions and the periodicity of eruptions in polygenetic volcanism.