The onset of convection driven by buoyancy caused by various modes of transient heat conduction: Part II. The sizes of plumes

Abstract

A theory of formation of transient thermals or plumes generated by unsteady-state heat conduction is proposed. Rising or falling mushroom-shaped plumes formed during transient heating or cooling, respectively, originate from the extending thermal boundary layers. The sizes of the hemispherical caps of the plumes can be predicted from the critical wave number and the corresponding Biot number from linear stability analysis, and the critical depth of transient heat conduction at the onset of convection. The rate of generation and size of the hemispherical cap of the thermal are determined by the mode and rate of transient heat conduction, which is characterised by the Biot number. The critical sizes of the plumes are found to be proportional to the square root of the critical times for onset of convection. Equations of critical sizes of plumes for various Biot numbers and a combination of free and solid surfaces are derived. Agreement with observed values for evaporating cooling from the literature is very good, while it is fair for fluids subjected to bottom heating.