Abstract
Mixed convection in laminar boundary layer flow along slender vertical cylinders is analyzed for the situation in which the surface temperature T w( x) varies arbitrarily with the axial coordinate ϵ. It covers the entire mixed convection regime from pure free convection ( ϵ = 0) to pure forced convection ( ϵ = l), where ϵ = [1 + (Gr x/Re x 2) 1 4 ] −1 is the mixed convection parameter. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a non-similar transformation and the resulting system of equations is then solved by a weighted finite-difference method of solution in conjunction with cubic spline interpolation. Sample calculations are performed for the case of power law variation in surface temperature, T w ( x)− T ∞ = ax n , for fluids with Prandtl numbers of 0.1, 0.7, 7, and 100 over a wide range of surface curvature parameters 0 ⩽ Λ⩽ 50 (or 0 ⩽ ξ⩽ 5). Local and average Nusselt numbers are presented. It is found that the local Nusselt number in the form Nu x (Re x 1 2 + Gr x 1 4 ) increases with increasing surface curvature, Prandtl number, and the exponent n, but for low values of Λ, it initially decreases and then increases as ϵ goes from 0 to 1. As curvature increases a linear relationship is found to exist between the Nusselt number and the mixed convection parameter. Correlation equations for the local and average Nusselt numbers are also presented.
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