The potential habitability in icy giant moons such as Ganymede, Callisto (moons of Jupiter), and Titan (moon of Saturn) has been recently studied, where some basic conditions of life may be abundant. Namely, the conditions include the presence of liquid water, a stable source of energy and supply of nutrients. A systematic understanding of the physical processes taking place on these giant moons may be a key to addressing the fundamental question of habitability of these moons. A common feature of such giant moons relates to the presence of a liquid water layer sandwiched in between two layers of ice: a surface layer and a deep layer with a different polymorphism triggered by the high pressure conditions. The study of the exchange processes that occur in the deep layers of giant icy moons and water-rich worlds is a highly non-trivial one. The origin of the natural phenomena cannot be easily reproduced in laboratory experiments particularly because the high pressures acting on the inner ice layers of the moons are virtually impossible to reproduce in table top laboratory experiments. However, based on the fundamental rule of thermodynamic phases stated by Gibbs, we attempt herein to replace in the table top experiments the pressure differences existing on the moons by another pair of (thermodynamically) conjugated variables: an external shear and a stress. To support this, we present preliminary scaling arguments and design a table-top experimental setup able to capture the main physics taking place within the giant moons. The similarity is mainly based on the similaritybetween the convective and thermo-diffusive time scales. Additionally, we pay attention that the flows at laboratory scale remain laminar at all times which is the case of the convective flows existing on the moons. As an appropriate phase change material that models the ice we chose a paraffin wax. The thermophysical and rheological properties of the paraffin wax have been investigated which allows us to estimate the suitable dimensions of the table top experimental setup that may capture most physics taking place on the giant moons.