Mixed Convection Along Vertical Cylinders and Needles With Uniform Surface Heat Flux

Mixed convection along vertical cylinders and needles with uniform surface heat flux is investigated for the entire mixed convection regime. A single modified buoyancy parameter χ and a single curvature parameter Λ are employed in the analysis such that a smooth transition from pure forced convection (χ = 1) to pure free convection (χ = 0) can be accomplished. For large values of the curvature parameter and/or Prandtl number, the governing transformed equations become stiff. Thus, a numerically stable finite-difference method is employed in the numerical solution in conjunction with the cubic spline interpolation scheme to overcome the difficulties that arise from the stiffness of the equations. Local Nusselt numbers are presented for 0.1 ≤ Pr ≤ 100 that cover 0 ≤ χ ≤ 1 (∞ ≥ Ω_χ ≥ 0) and 0 ≤ Λ ≤ 50. For needles (Λ ≥ 5), the local Nusselt numbers Nu_χ/(Re_χ^1/2 + Gr_χ^*1/5) are found to be nearly independent of the buoyancy parameter χ. Correlation equations for the local Nusselt numbers are also presented.