Natural convective heat transfer from isothermalconic

Abstract

Theoretical considerations on convective heat transfer from isothermal upward conicalsurfaces have been presented. The physical model of this phenomenon consists of an isothermalcone of inclination angle (φ) between the cone generating line ( X) and the radius ( R) of the cone base. The angle is a parameter of conical surface which varied from ( φ = 0−circular horizontal plate) to ( φ = π/2—vertical cylinder) . Onthe basis of Navier–Stokes equations, assuming the parabolic temperature profile in the boundarylayer, the velocity profile tangent to the surface has been calculated. Introduction of the meanvelocity value in the boundary layer into the balance of energy and mass equations andcomparison with the Newton equation leads to the dependence describing the boundary layerthickness. Next the relation of Nusselt and Rayleigh numbers, including a function expressingthe influence of the inclination angle ( φ) on the heat transfer process, has been derived.The obtained solution describes the natural convective heat transfer process for threecharacteristic cases of the conical surface. For the boundary cases φ = π/2 (vertical cylinder) and φ = 0 (circular upward facing horizontal plate), the solution describing convective heat transferintensity is Nu X=H = 0.668 · Ra 1/4 X=H for φ = π/2 and Nu X=R = 0.932 · Ra 1/5 X=R for φ = 0. For the case (0 < φ < π/2) (cones), the solution has the form Nu X = 1.680 · Φ 1/4 · Ra 1/4 X where (Φ) is a function of the inclination angle ( φ) of the generating line of theconical surface to the base of radius ( R) .