Laminar combined free and forced convection in vertical non-circular ducts under uniform heat flux

Abstract

Fully developed laminar combined free and forced convection through vertical non-circular ducts is studied. Geometries treated are (i) right-angled triangle, (ii) isosceles triangle and (iii) rhombic ducts. Uniform axial heat flux and uniform peripheral wall temperature are assumed. All fluid properties are considered constant except for variation of density in the buoyancy terms. Approximate solutions of the problem have been obtained by (i) variational calculus and (ii) finite-difference procedure. For rhombic duct an exact solution for pure forced convection is also presented. For the right-angled triangle the Nusselt number ( N Nu ) becomes insensitive to the duct angle (α) as the value of the Rayleigh number ( N Ra ) is increased from zero to about two thousand. As the Rayleigh number is further increased to say ten thousand, the duct angle again becomes important. For the right-angled triangle, at N Ra = 0 the maximum value of the Nusselt number is obtained when α = 45°, while when N Ra = 10000 its minimum value is obtained at α = 45°. For the isosceles triangle, the Nusselt number also becomes insensitive to the duct angle as the value of the Rayleigh number is increased from zero to about two thousand. As the Rayleigh number is further increased, to ten thousand, the duct angle again becomes important For the isoceles triangle, at N Ra = 0, maximum value of the Nusselt number is obtained at α = 60° white at N Ra = 10000, its maximum value occurs when α → 90°. For the rhombic duct the effect of the duct angle diminishes as the value of the Rayleigh number is increased from zero.