Heat Transfer from a Rotating Sphere

This thesis is mainly concerned with the heat transfer from a rotating sphere to an air stream flowing at right angles to the plane of rotation of the sphere. A theoretical analysis of the laminar boundary layer on the forward portion of the sphere was made using an integral momentum method, and introducing a velocity distribution round a sphere meridian based on known experimental results for a stationary sphere in an air stream. The experimental method used was a transient cooling technique. Tests were carried out to measure the surface temperature distribution and to validate the method of calculation of the heat transfer coefficient. A conduction correction for the heat transferred through the supporting shaft was carefully calculated and results taken for natural convection and for flow across a stationary sphere were compared with previous experimental work as a check on this correction.
A subsidiary investigation was undertaken to determine the turbulence level produced downstream of a square mesh wire grid, and how this is affected by the free stream turbulence upstream of the grid. The effect of free stream turbulence on the heat transfer from a stationary sphere to an air stream was investigated and the results compared with those of other investigators. Experiments were performed with the sphere rotating in still air, and with various air flow velocities at right angles to the plane of rotation. The experimental results for the heat transfer from a rotating sphere in an air stream were compared with the theoretical results for the forward portion of the sphere, an attempt being made to assess the proportions of heat transferred from the front and rear halves of the sphere.

The following deductions can be made:
a) free stream turbulence increases the heat transfer from a sphere, even at flow Reynolds numbers below that which would lead to transition to turbulence in the boundary layer.
b) for a sphere rotating in still air, Nu = 0.353 Re0.5R for Gr/Re2R < 0.02 (properties at mean film temperature.)
c) for a rotating sphere in an air stream the rotation does not influence the total heat transfer from the sphere until the circumferential velocity of the sphere equator is greater than half the free stream velocity of the impinging air; the results may be correlated by, Nu = 0.228 RE0.598 + 0.0381 Re0.598 (ReR/Re - 0.54) for ReR/Re >> 0.54, T = 0.0085, 4600< Re<21 000, 2700<ReR< 12 300 - (properties at mean film temperature.)
d) the theoretical analysis shows that at values of ReR/Re less than 0.5 the heat transfer from the front half of the sphere is virtually unaffected by the rotation, and that the increase in heat transfer is only 2% due to rotation when ReR/Re is 1.2; this leads to the conclusion that the increase in heat transfer due to rotation is mainly due to the alteration of the flow pattern on the rear half of the sphere.