Limiting cross-flow velocity below which heat flux is determined by natural convection laws

In estimating heat flux or heat transfer rates in technological or meteorological applications, we propose here that a parameter of considerable interest is the limiting value of the cross-flow velocity upto which the heat flux is given by the free convection laws to a sufficiently good approximation. The question of determining this limiting value is addressed here by analysing available data in three geometries: sphere, flat plate and cylinder. It is found that, in each case, the limiting velocity can be concisely and elegantly expressed in terms of the ‘internal’ Froude number, which is related to a parameter introduced by Klyachko [Trans. ASME J. Heat Transfer 85 (1963) 355] in his work on heat transfer from spheres. We find that departure of the heat flux from the value for natural convection (to within 5%) occurs when the internal Froude number exceeds a limiting value, which is found to be about 0.063 for sphere, about 1.93 for flat plate and about 1.65 for cylinder. The critical cross-flow velocity upto which natural convection provides a good approximation thus appears to be very much larger in 2D than in 3D flows for comparable characteristic length scales.