# What about the natural convection heat transfer coefficient (*h*) at low Delta-T?

In a system I am modeling for personal research, I have a sphere (S) submerged in air (A), initially at the same temperature Ts = Ta.

Then the temperature of air is slowly increased (or decreased), by something like 0.5 °C/h. In these conditions the Delta-T = Ts-Ta is necessarily low.

But, would h be so low that the main heat transfer mode is not convection anymore?

UPDATE: It is a sphere of say 20 mm radius, made of steel, and exposed to ambient air - which means the temperature of air will change with the diurnal cycle; 0.5 °C/h is a rough estimate based on the observed diurnal excursion in a certain locality.

In light of the informative comments & answers below, I would then like to ask how is the conductive heat transfer coefficient defined for this case.

• If there is heat transfer from the sphere to the air by natural convection (not forced convection), the surface temperature over the sphere will vary, and so will the temperature of the air around the sphere. So "slowly increasing the air temperature by 0.5C/h" is a very poorly defined concept! Also, whether the main heat transfer mode is convection or conduction (it's unlikely to be radiation, for such a small temperature difference) depends on the thermal properties of the sphere and the air, and also on the size of the sphere. – alephzero Jul 10 '18 at 14:47
• It is a sphere of say 20 mm radius, made of steel, and exposed to ambient air - which means the temperature of air will change with the diurnal cycle; 0.5 °C/h is a rough estimate based on the observed diurnal excursion in a certain locality. If the main heat transfer mode is conduction, how is it practically implemented in this case? – Fabio Capezzuoli Jul 11 '18 at 4:05