CHAPTER V - THERMAL CONDUCTION IN FLUIDS

Abstract

This chapter discusses thermal conduction in fluids. A complete system of equations of fluid dynamics must contain five equations. For fluids in which processes of thermal conduction and internal friction occur, one of these equations is the equation of continuity, and Euler's equations are replaced by the Navier–Stokes equations. If the temperature of the fluids under observation is not constant throughout their volume, there will also be a transfer of heat by what is called thermal conduction. The temperature distribution in a fluid at very high Reynolds numbers exhibits properties similar to those of the velocity distribution. Thereafter, in a system not at thermodynamic equilibrium—such as a fluid with velocity and temperature gradients—the usual definitions of thermodynamic quantities are no longer meaningful and must be modified. The equation of heat transfer for an incompressible fluid at rest is given by Fourier's equation. In problems of thermal conduction in a finite medium, the initial temperature distribution does not suffice to determine a unique solution, and the boundary conditions at the surface of the medium must also be given. The motion of a nonuniformly heated fluid is called convection. In the boundary layer, there occurs both a rapid decrease of the velocity and a rapid change of the fluid temperature to a value equal to the temperature of the solid surface; the boundary layer thus is characterized by the presence of large gradients of both velocity and temperature. Finally, in the turbulent region itself, a very considerable exchange of heat occurs, which is because of the intensive mixing of the fluid characteristic of any turbulent flow. This mechanism of heat transfer may be called turbulent conduction.