Effect of tube inclination on laminar convection in uniformly heated tubes for flat-plate solar collectors

A numerical study using a combination of boundary vorticity method and line iterative relaxation method is carried out to determine the free convection effects on fully developed upward laminar forced flow in uniformly heated inclined tubes. The combined free and forced laminar convection for water with the inclined tube configuration in the low Reynolds number flow regime has practical application in flat-plate solar collectors for water heating. The tube inclination or gravitational force orientation effects on flow and heat transfer characteristics are clarified and show that in high Rayleigh number regime the tube orientation effect has considerable influence on the results, particularly in the neighborhood of horizontal direction. The numerical results show that the perturbation analysis in terms of power series of Rayleigh number is invalid for the present problem and reveal further that a maximum value for Nusselt number does not exist for any tube inclination angle with given values of the dimensionless parameters which is clearly contrary to the result from perturbation solution.