Natural Convection: A Case of Simple Harmonics

Natural convection has been an area of intense research since it was discovered over 100 years ago. However, a phenomenological explanation for the onset of natural convection is still not available. The role of surface roughness in various thermal hydraulic phenomena is widely accepted; however, the scale of roughness is missing from Rayleigh number (Ra) which is commonly used to predict the onset of natural convection. Using the mass-spring analogy, an analytical derivation is presented to accurately characterize the thermal system and the interplay of gravity, viscosity and scale of roughness responsible for the onset of natural convection. The necessary conditions for the onset of natural convection are given in terms of a new dimensionless number which captures the effect of surface roughness. Using the mass-springs analogy, the natural frequency of the convection system is shown to depend on thermal and kinematic property of the fluid and the scale of roughness. These results are applicable to many natural system and engineering designs.