Influence of Tube Orientation on Combined Free and Forced Laminar Convection Heat Transfer

Combined free and forced convection inside inclined circular tubes is studied theoretically. The case considered is that of fully developed laminar flow with constant-pressure gradient and constant-heat flux. Fluid properties are considered constant except for the variation of density in the buoyancy terms. Upward flow only is considered. Velocity and temperature fields are calculated by perturbation analysis in terms of power series of Rayleigh numbers. A detailed analysis of the final equations is made to determine the range of values of nondimensional parameter such as Rayleigh and Reynolds numbers over which the mathematical results are valid. Nusselt numbers are calculated based on bulk temperature difference and in final form are also expressed in terms of power series of Rayleigh numbers. Rayleigh number appears to be the dominant parameter in equations of velocity and temperature fields and Nusselt number. However Rayleigh and Reynolds number product and Prandtl number also influence the equations independently. As the tube inclination varies from horizontal, the Nusselt number increases up to a maximum which may occur before the vertical position is reached. The angle at which this maximum occurs appears to be a function of Rayleigh, Reynolds, and Prandtl number, and in most instances lies between 20 and 60 deg of tube inclination.