The heat transfer by the convection in the annular gap between the rotating inner cylinder and the stationary outer cylinder was measured in the air, spindle oil and mobile oil at varying rotational speeds, cylinder diameters and widths of gap. The results show that characteristics of the flow and heat transfer have two modes. If the rotational speed is low and the width of gap is narrow, namely (vδ/ν)√(δ/γ)<41, the flow is laminar and the heat is transferred by conduction and radiation. But if (vδ/ν)√(δ/γ)<41, the rate of heat transfer increases with rotational speeds under the influence of secondary vortices induced by the centrifugal force, which may be given by Uδ/λ=0.21 ((v²δ²)/(ν²)·δ/γ·P_γ)^1/4 where U denotes the overall coefficient of heat transfer through the gap, δ the width of the gap, λ the thermal conductivity, ν the kinematic viscosity and Pr the Prandtl Number, γ and ν the radius and the peripheral velocity of the rotating cylinder respectively.