Combined free and forced laminar convection in inclined tubes with uniform internal heat generation

Abstract

The effect of uniform internal heat generation on fully developed velocity profiles, temperature profiles, pressure drops and Nusselt numbers is studied for combined free and forced laminar convection with upward flow in inclined tubes subjected to a uniform heating at the tube wall. A numerical solution using a combination of a boundary vorticity method and a line iterative relaxation method is employed. Comparison is made between the numerical analysis and a perturbation analysis available in the literature for a limiting case of horizontal tubes. The perturbation method is known to be valid for rather small values of the parameters representing heat generation and buoyancy effects. In contrast, the numerical solution is shown to be valid up to reasonably high values of the parameters, where in many cases an asymptotic behavior for flow and heat transfer results already appears. At high Rayleigh numbers the tube inclination angle or body-force orientation effects on flow and heat transfer results are found to be particularly significant for any value of the heat-source parameter. The present study is an extension or generalization of earlier work in the literature, dealing with vertical or horizontal tubes.