Thermal fluid physics associated with natural convection is investigated by using Rayleigh-Bénard convection experiments and numerical simulations. An analogy is proposed between the phenomenon of natural convection and an integrator circuit. This analogy is a logical extension of the resistor circuit analogy for conduction. Both experimental data and thermo-fluid simulations support the proposed model. It is observed that the characteristic time constant of the phenomenon of convection is a function of Prandtl number and acceleration due to gravity. The effect of reduced gravity and increased fluid viscosity is discussed. These results can significantly assist in thermal fluid analysis of future space reactors.