The non-mechanical principle of transport of a liquid crystal (LC) encapsulated in a narrow cavity between two coaxially arranged cylinders is introduced based on the interaction of the temperature and director field gradients. The temperature gradient is created due to a heat flow from the inner cylinder surface, whereas the temperature on the outer cylinder surface is maintained constant. The director field gradient is caused by the deformation of the planar-oriented LC cavity upon exposure to a double electrostatic layer, which naturally appears at the LC phase-solid interface. The size of the gap between the bounding surfaces, cylinder curvatures, and thermal conditions are determined, which allow initiation of the LC phase flow in the horizontal direction.