Thermo-fluid mechanics of liquid or gas cooled tubular first walls

An analysis for hydrodynamically and thermally, fully developed heat transfer in a circular tube coupled with heat conduction in the tube wall is presented. Anisotropy of turbulent energy transport has been taken into account employing theoretical results for eddy diffusivity in the various directions. Assumptions such as thin-walled structures where radial temperature gradients are negligible and/or constant heat transfer coefficients are relaxed are shown to be special cases of this analysis. The energy equations for the fluid and solid body are solved simultaneously and are subject to continuity in heat flux and temperature at the interface. Circumferential as well as radial temperature gradients are permitted in both energy equations along with internal heat generation in the tube wall and fluid. Solutions of the equations are found by a method of separation-of-variables. We restrict ourselves to cases where the applied surface heat flux may be expressed in terms of a sine-cosine Fourier series. (orig.)