Shape effect on natural convection heat transfer over a constant surface area vertical hollow frustum

Abstract

Numerical simulations have been conducted to analyse the shape effect of a vertical hollow frustum, either hanging in air or sitting on the ground, on heat transfer by natural convection in the laminar regime (104 ≤ Ra ≤ 108) while all the shapes are having same surface area.The study involves a comparison of heat loss from both the inner and the outer surfaces of frustums with the respective equal area cylinders. It is realized that both straight and inverted frustums always lose less heat from their outer surfaces than that of the cylinders for all Ra. A similar behaviour from the inner surface of a frustum is noticed for both the frustums when in air and only for the inverted frustum on ground. The Nu of inner and outer surfaces for both inverted and the straight frustum changes with the orientation, θ, of the surface. For both the frustums in air, the Nu of outer surface is smaller for an inverted frustum than for a straight one at all Ra and the reverse holds true for the inner surface. If both the frustums are sitting on ground, the outer surface of an inverted frustum has greater Nu value than the straight one and reverse is true for the inner surface.