Convective effects in air layers bound by cellular honeycomb arrays

Abstract

Rayleigh-Benard convection in a fluid (air) layer in presence of transparent cellular structure (honeycomb) is reviewed for application to the engineering design of transparent insulation materials devices. The explicit numerical computations of Rayleigh numbers of the characteristic equation at higher wave numbers corresponding to the onset of instability are carried out. Results highlight a new facet of theory that it can indeed be used to estimate the critical Rayleigh number, which corresponds to the layer bound by vertical walls of cellular structure. A relationship between wave number and aspect ratio of honeycomb structure is evolved. Subsequently the stability of inclined fluid layer is considered and base flow existence and the need for its consideration in terms of Nusselt number is discussed. An outline of governing equations of the square celled air temperature, vorticity, stream functions and velocity are presented and it is found that the Nusselt number has a value in the range 1-1.5 for a wide range of Rayleigh numbers in near critical Rayleigh regime. This range may be considered as a trade off region for the engineering design of honeycomb devices. Convection can be suppressed by varying the aspect ratio of honeycomb cell. Honeycomb structure of aspect ratio 10-15 seems suitable for suppression of convection in air layer of depth 5-20 cm for temperature difference (<img src='/image/spc_char/delta.gif'>T)of 20 to 120°.