Thermal convection in a horizontal fluid layer with internal heat sources

Abstract

This paper is concerned with thermal convection in a horizontal fluid layer bounded below and above by two rigid planes of constant and equal temperature. The convection is generated by uniformly distributed internal heat (cool) sources. Stable hexagons are found for Rayleigh numbers up to 3.6 times the critical value~ down-hexagons when the fluid is internally heated, and up-hexagons when the fluid is internally cooled. Moreover, a subcritical region,where the hexagons may exist, is also found.

Effects of heat source distribution on natural convection induced by internal heating

“…For example, Tritton and Zarraga [7] and Schwiderski and Schwab [8] carried out experimental investigations and found various interesting features; of particular interest was the dilatation of convection cells with increasing rate of internal heat generation. Theoretical studies by Roberts [9], Tveitereid and Palm [10] and Tveitereid [11], however, could not clarify this phenomenon. They attributed the cell dilatation to non-uniform heat generation due to imperfections in the experiments; that is, a deviation from uniform heating due to a spatially varying electrical conductivity (an improved and more precise experimental investigation is under progress by us [12]).…”

Effect of rotational speed modulation on heat transport in a fluid layer with temperature dependent viscosity and internal heat source

“…Therefore, the role of internal heat generation becomes very important in several applications including storage of radioactive materials, combustion and fire studies, geophysics, reactor safety analysis and metal waste form development for spent nuclear fuel. However, there are only few studies available in which the effect of internal heating on convective flow in a fluid layer has been investigated [34][35][36][37][38][39][40][41][42][43][44].…”

Effect of internal-heating on weakly non-linear stability analysis of Rayleigh–Bénard convection under g-jitter

“…However, there are relatively very few studies available in which the effect of internal heating on convective flow has been investigated. Some of these studies are Roberts [14], Tveitereid and Palm [15], Tveitereid [16], Yu and Shih [17], Bhattacharya and Jena [18], Takashima [19], Tasaka and Takeda [20], and Joshi et al [21].…”